Method for constructing a map while performing work

[0001] This application is a Continuation in Part of U.S. Non-Provisional application Ser. No. 16/597,945, filed Oct. 10, 2019, which is Continuation of U.S. Non-Provisional application Ser. No. 16/163,562, filed Oct. 17, 2018, which claims the benefit of U.S. Provisional Patent Application Nos. 62/573,591, filed Oct. 17, 2017; 62/637,185, filed Mar. 1, 2018; 62/613,005, filed Jan. 2, 2018; 62/599,216, filed Dec. 15, 2017; 62/573,579, filed Oct. 17, 2017; 62/637,156, filed Mar. 1, 2018; 62/740,558, filed Oct. 3, 2018; 62/573,598, filed Oct. 17, 2017; 62/591,217, filed Nov. 28, 2017; 62/616,928, filed Jan. 12, 2018; 62/614,449, filed Jan. 7, 2018; 62/590,205, filed Nov. 22, 2017; 62/666,266, filed May 3, 2018; 62/661,802, filed Apr. 24, 2018; 62/631,050, filed Feb. 15, 2018; 62/746,688, filed Oct. 17, 2018; 62/740,573, filed Oct. 3, 2018; and 62/740,580, filed Oct. 3, 2018; 62/640,444, filed Mar. 8, 2018; 62/648,026, filed Mar. 26, 2018; 62/655,494, filed Apr. 10, 2018; 62/665,095, filed May 1, 2018; 62/674,173, filed May 21, 2018; 62/688,497, filed Jun. 22, 2018, each of which is hereby incorporated herein by reference. This application claims the benefit of U.S. Provisional Patent Application Nos. 62/914,190, filed Oct. 11, 2019; 62/933,882, filed Nov. 11, 2019; 62/942,237, filed Dec. 2, 2019; 62/952,376, filed Dec. 22, 2019; and 62/952,384, filed Dec. 22, 2019, each of which is hereby incorporated by reference.

[0002] In this patent, certain U.S. patents, U.S. patent applications, or other materials (e.g., articles) have been incorporated by reference. Specifically, U.S. patent application Ser. Nos. 15/272,752, 15/949,708, 16/277,991, 16/048,179, 16/048,185, 16/163,541, 16/163,562, 16/163,508, 16/185,000, 16/051,328, 15/449,660, 16/041,286, 16/422,234, 15/406,890, 14/673,633, 15/676,888, 16/163,530, 16/297,508, 16/418,988, 15/614,284, 15/955,480, 15/425,130, 15/955,344, 15/243,783, 15/954,335, 15/954,410, 15/257,798, 15/674,310, 15/224,442, 15/683,255, 15/048,827, 14/817,952, 15/619,449, 16/198,393, 15/981,643, 15/986,670, 15/447,623, 15/951,096, 16/270,489, 16/130,880, 14/948,620, 16/239,410, 16/230,805, 15/447,122, 16/393,921, 16/389,797, 16/509,099, 16/389,797, 16/427,317, 62/208,791, and 16/109,617 are hereby incorporated by reference. The text of such U.S. patents, U.S. patent applications, and other materials is, however, only incorporated by reference to the extent that no conflict exists between such material and the statements and drawings set forth herein. In the event of such conflict, the text of the present document governs, and terms in this document should not be given a narrower reading in virtue of the way in which those terms are used in other materials incorporated by reference.

[0003] The disclosure relates to autonomous robots.

[0004] Autonomous or semi-autonomous robotic devices are increasingly used within consumer homes and commercial establishments. Such devices may include a robotic vacuum cleaner, lawn mower, mop, or other similar devices. To operate autonomously or to operate with minimal (or less than fully manual) input and/or external control within a working environment, mapping, localization, and path planning methods may be such that robotic devices may autonomously create a map of the working environment, subsequently use the map for navigation, and devise intelligent path plans and task plans for efficient navigation and task completion.

[0005] The following presents a simplified summary of some embodiments of the techniques described herein in order to provide a basic understanding of the invention. This summary is not an extensive overview of the invention. It is not intended to identify key/critical elements of the invention or to delineate the scope of the invention. Its sole purpose is to present some embodiments of the invention in a simplified form as a prelude to the more detailed description that is presented below.

[0006] Some aspects include a method for mapping and covering a workspace, including: capturing, with at least one sensor of a robot, first data indicative of the position of the robot in relation to objects within the workspace and second data indicative of movement of the robot; recognizing, with a processor of the robot, a first area of the workspace based on observing at least one of: a first part of the first data and a first part of the second data; generating, with the processor of the robot, at least part of a map of the workspace based on at least one of: the first part of the first data and the first part of the second data; generating, with the processor of the robot, a first movement path covering at least part of the first recognized area of the workspace; actuating, with the processor of the robot, the robot to move along the first movement path; recognizing, with the processor of the robot, a second area of the workspace based on observing at least one of: a second part of the first data and a second part of the second data; updating, with the processor of the robot, the at least the part of the map of the workspace based on at least one of: the second part of the first data and the second part of the second data; generating, with the processor of the robot, a second movement path covering at least part of the second recognized area of the workspace; and actuating, with the processor of the robot, the robot to move along the second movement path, wherein actuating the robot to move along at least one of the first movement path and the second movement path comprises at least a repetitive iteration of: actuating, with the processor of the robot, the robot to traverse a first linear segment; actuating, with the processor of the robot, the robot to rotate 180 degrees in a first rotation comprising traversing a distance of less than a coverage width of the robot in a direction perpendicular to the first linear segment after starting the first rotation and before finishing the first rotation; actuating, with the processor of the robot, the robot to traverse a second linear segment; and actuating, with the processor of the robot, the robot to rotate 180 degrees in a second rotation comprising traversing a distance of less than the coverage width of the robot in a direction perpendicular to the second linear segment after starting the second rotation and before finishing the second rotation.

[0007] Some aspects include a robot configured to execute the above-described process.

[0135] The present inventions will now be described in detail with reference to a few embodiments thereof as illustrated in the accompanying drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present inventions. It will be apparent, however, to one skilled in the art, that the present inventions, or subsets thereof, may be practiced without some or all of these specific details. In other instances, well known process steps and/or structures have not been described in detail in order to not unnecessarily obscure the present inventions. Further, it should be emphasized that several inventive techniques are described, and embodiments are not limited to systems implanting all of those techniques, as various cost and engineering trade-offs may warrant systems that only afford a subset of the benefits described herein or that will be apparent to one of ordinary skill in the art.

[0136] In some embodiments, a robot may include one or more autonomous or semi-autonomous robotic devices having communication, mobility, actuation and/or processing elements. In some embodiments, a robot includes a vehicle, such as a car or truck, with an electric motor. For example, the robot may include an electric car with an electric motor. In some embodiments, a vehicle, such as a car or truck, with an electric motor includes a robot. For example, an electric car with an electric motor may include a robot powered by an electric motor. In some embodiments, a robot may include, but is not limited to include, one or more of a casing, a chassis including a set of wheels, a motor to drive the wheels, a receiver that acquires signals transmitted from, for example, a transmitting beacon, a transmitter for transmitting signals, a processor, a memory, a controller, tactile sensors, obstacle sensors, network or wireless communications, radio frequency communications, power management such as a rechargeable battery or solar panels or fuel, one or more clock or synchronizing devices, temperature sensors, imaging sensors, and at least one cleaning tool (e.g., impeller, brush, mop, scrubber, steam mop, polishing pad, UV sterilizer, etc.). The processor may, for example, receive and process data from internal or external sensors, execute commands based on data received, control motors such as wheel motors, map the environment, localize the robot, determine division of the environment into zones, and determine movement paths. In some embodiments, at least a portion of the sensors of the robot are provided in a sensor array, wherein the at least a portion of sensors are coupled to a flexible, semi-flexible, or rigid frame. In some embodiments, the frame is fixed to a chassis or casing of the robot. In some embodiments, the sensors are positioned along the frame such that the field of view of the robot is maximized while the cross-talk or interference between sensors is minimized. In some cases, a component may be placed between adjacent sensors to minimize cross-talk or interference. In some embodiments, the robot may include sensors to detect or sense acceleration, angular and linear movement, temperature, humidity, water, pollution, particles in the air, supplied power, proximity, external motion, device motion, sound signals, ultrasound signals, light signals, fire, smoke, carbon monoxide, global-positioning-satellite (GPS) signals, radio-frequency (RF) signals, other electromagnetic signals or fields, visual features, textures, optical character recognition (OCR) signals, spectrum meters, and the like. In some embodiments, a microprocessor or a microcontroller of the robot may poll a variety of sensors at intervals.

[0137] In some embodiments, the robot may include a camera sensor that may be communicatively coupled with a microprocessor or microcontroller. In some embodiments, images captured by the camera may be processed to identify objects or faces, as further described below. For example, the microprocessor may identify a face in an image and perform an image search in a database on the cloud to identify an owner of the robot. In some embodiments, the camera may include an integrated processor. For example, object detection and face recognition may be executed on an integrated processor of a camera. In some embodiments, the camera may capture still images and record videos and may be a depth camera. For example, a camera may be used to capture images or videos in a first time interval and may be used as a depth camera emitting structured light in a second time interval. Given high frame rates of cameras some frame captures may be time multiplexed into two or more types of sensing. In some embodiments, the camera may be used to capture still images and video by a user of the robot. For example, a user may use the camera of the robot to perform a video chat, wherein the robot may optimally position itself to face the user. In embodiments, various configurations (e.g., types of camera, number of cameras, internal or external cameras, etc.) that allow for desired types of sensing (e.g., distance, obstacle, presence) and desired functions (e.g., sensing and capturing still images and videos) may be used to provide a better user experience. In some embodiments, the camera of the robot may have different fields of view (FOV). For example, a camera may have a horizontal FOV up to or greater than 90 degrees and a vertical FOV up to or greater than 20 degrees. In another example, the camera may have a horizontal FOV between 60-120 degrees and a vertical FOV between 10-80 degrees. In some embodiments, the camera may include lenses and optical arrangements of lenses to increase the FOV vertically or horizontally. For example, the camera may include fish eye lenses to achieve a greater field of view. In some embodiments, the robot may include more than one camera and each camera may be used for a different function. For example, one camera may be used in establishing a perimeter of the environment, a second camera may be used for obstacle sensing, and a third camera may be used for presence sensing. In another example, a depth camera may be used in addition to a main camera. The depth camera may be of various forms. In some embodiments, the camera output may be provided to an image processor for use by a user and to a microcontroller of the camera for depth sensing, obstacle detection, presence detection, etc. In some embodiments, the camera output may be processed locally on the robot by a processor that combine standard image processing functions and user presence detection functions. Alternatively, in some embodiments, the video/image output from the camera may be streamed to a host for processing further or visual usage. In some embodiments, there may be different options for communication and data processing between a dedicated image processor and an obstacle detecting co-processor. For example, a presence of an obstacle in the FOV of a camera may be detected, then a distance to the obstacle may be determined, then the type of obstacle may be determined (e.g., human, pet, table, wire, or another object), then, in the case where the obstacle type is a human, facial recognition may be performed to identify the human. All the information may be processed in multiple layers of abstraction. In embodiments, information may be processed by local microcontrollers, microprocessors, GPUs, on the cloud, or on a central home control unit.

[0138] In some embodiments, additional sensors of the robot, such as a proximity sensor may be used to provide additional data points to further enhance accuracy of estimations or predictions. In some embodiments, the additional sensors of the robot may be connected to the microprocessor or microcontroller. In some embodiments, the additional sensors may be complementary to other sensing methods of the robot. For example, in some sensor types, the active emitted lights may be in the form of square waves or other waveforms. The light may be mixed with a sine wave and a cosine wave that may be synchronized with the LED modulation. Then, a first and a second object present in the FOV of the sensor, each of which is positioned at a different distance, may produce a different phase shift that may be associated with their respective distance.

[0139] In some embodiments, the robot may include a controller, a multiplexer, and an array of light emitting diodes (LEDs) that may operate in a time division multiplex to create a structured light which the camera may capture at a desired time slot. In some embodiments, a suitable software filter may be used at each time interval to instruct the LED lights to alternate in a particular order or combination and the camera to capture images at a desirable time slot. In some embodiments, a micro electrical-mechanical device may be used to multiplex one or more of the LEDs such that fields of view of one or more cameras may be covered. In some embodiments, the LEDs may operate in any suitable range of wavelengths and frequencies, such as a near-infrared region of the electromagnetic spectrum. In some embodiments, pulses of light may be emitted at a desired frequency and the phase shift of the reflected light signal may be measured.

[0140] In some embodiments, the robot may include a tiered sensing system, wherein data of a first sensor may be used to initially infer a result and data of a second sensor, complementary to the first sensor, may be used to confirm the inferred result. In some embodiments, the robot may include a conditional sensing system, wherein data of a first sensor may be used to initially infer a result and a second sensor may be operated based on the result being successful or unsuccessful. Additionally, in some embodiments, data collected with the first sensor may be used to determine if data collected with the second sensor is needed or preferred. In some embodiments, the robot may include a state machine sensing system, wherein data from a first sensor may be used to initially infer a result and if a condition is met, a second sensor may be operated. In some embodiments, the robot may include a poll based sensing system wherein data from a first sensor may be used to initially infer a result, and if a condition is met, a second sensor may be operated. In some embodiments, the robot may include a silent synapse activator sensing system, wherein data from a first a sensor may be used to make an observation but the observation does not cause an actuation. In some embodiments, an actuation occurs when a second similar sensing occurs within a predefined time period. In some embodiments, there may be variations wherein a microcontroller may ignore a first sensor reading and may allow processing of a second (or third) sensor reading. For example, a missed light reflection from the floor may not be interpreted to be a cliff unless a second light reflection from the floor is missed. In some embodiments, a Hebbian based sensing method may be used to create correlations between different types of sensing. For example, in Hebb's theory, any two cells repeatedly active at the same time may become associated such that activity in one neuron facilitates activity in the other. When one cell repeatedly assists in firing another cell, an axon of the first cell may develop (or enlarge) synaptic knobs in contact with the soma of the second cell. In some embodiments, Hebb's principle may be used to determine how to alter the weights between artificial neurons (i.e., nodes) of an artificial neural network. In some embodiments, the weight between two neurons increases when two neurons activate simultaneously and decreases when they activate at different times. For example, two nodes that are both positive or negative may have strong positive weights while nodes with opposite sign may have strong negative weights. In some embodiments, the weight ω_ij=x_ix_j may be determined, wherein ω_ij is the weight of the connection from neuron j to neuron i and x_i the input for neuron i. For binary neurons, connections may be set to one when connected neurons have the same activation for a pattern. In some embodiments, the weight ω_ij may be determined using

[0141] $\frac{1}{p}\sum _{k=1}^p{x}_i^k{x}_j^k,$
wherein p is the number of training patterns, and x_i^k is input k for neuron i. In some embodiments, Hebb's rule Δω_i=ηx_iy may be used, wherein Δω_i is the change in synaptic weight i, η is a learning rate, and y a postsynaptic response. In some embodiments, the postsynaptic response may be determined using y=Σ_yω_jx_j. In some embodiments, other methods such as BCM theory, Oja's rule, or generalized Hebbian algorithm may be used.

[0142] In some embodiments, the arrangement of LEDs, proximity sensors, and cameras of the robot may be directed towards a particular FOV. In some embodiments, at least some adjacent sensors of the robot may have overlapping FOVs. In some embodiments, at least some sensors may have a FOV that does not overlap with a FOV of another sensor. In some embodiments, sensors may be coupled to a curved structure to form a sensor array wherein sensors have diverging FOVs. Given the geometry of the robot is known, implementation and arrangement of sensors may be chosen based on the purpose of the sensors and the application.

[0143] FIG. 1A illustrates an example of a robot including sensor windows 100 behind which sensors are positioned, sensors 101 (e.g., camera, laser emitter, TOF sensor, IR sensors, range finders, LIDAR, depth cameras, etc.), user interface 102, and bumper 103. FIG. 1B illustrates internal components of the robot including sensors 101 of sensor array 104, PCB 105, wheel modules each including suspension 106, battery 107, floor sensor 108, and wheel 109. In some embodiments, a processor of the robot may use data collected by various sensors to devise, through various phases of processing, a polymorphic path plan. FIG. 2 illustrates another example of a robot, specifically an underside of a robotic cleaner including rotating screw compressor type dual brushes 200, drive wheels 201, castor wheel 202, peripheral brush 203, sensors on an underside of the robot 204, USB port 205, power port 206, power button 207, speaker 208, and a microphone 209. Indentations 210 may be indentations for fingers of a user for lifting the robot. In some embodiments, the indentations may be coated with a material different than the underside of the robot such that a user may easily distinguish the indentations. In this example, there are three sensors, one in the front and two on the side. The sensors may be used to sense presence and a type of driving surface. In some embodiments, some sensors are positioned on the front, sides, and underneath the robot. In some embodiments, the robot may include one or more castor wheels. In some embodiments, the wheels of the robot include a wheel suspension system. In some embodiments, the wheel suspension includes a trailing arm suspension coupled to each wheel and positioned between the wheel and perimeter of the robot chassis. An example of a dual wheel suspension system is described in U.S. patent application Ser. Nos. 15/951,096 and 16/270,489, the entire contents of which are hereby incorporated by reference. Other examples of wheel suspension systems that may be used are described in U.S. patent application Ser. No. 16/389,797, the entire contents of which is hereby incorporated by reference. In some embodiments, the different wheel suspension systems may be used independently or in combination. In some embodiments, one or more wheels of the robot may be driven by one or more electric motors. In some embodiments, the wheels of the robot are mecanum wheels.

[0144] FIG. 3A illustrates another example of a robot with vacuuming and mopping capabilities. The robot includes a module 300 that is removable from the robot, as illustrated in FIG. 3B. FIG. 3C illustrates the module 300 with a dustbin lid 301 that interfaces with an intake path of debris, module connector 302 for connecting the module 300 to the robot, water intake tab 303 that may be opened to insert water into a water container, and a mopping pad (or cloth) 304. FIG. 3D illustrates internal components of the module 300 including a gasket 305 of the dustbin lid 301 to prevent the contents of dustbin 306 from escaping, opening 307 of the dustbin lid 301 that allows debris collected by the robot to enter the dustbin 306, and a water pump 308 positioned outside of the water tank 309 that pumps water from the water tank 309 to water dispensers 310. Mopping pad 304 receives water from water dispensers 310 which moistens the mopping pad 304 for cleaning a floor. FIG. 3E illustrates debris path 311 from the robot into the dustbin 306 and water 312 within water tank 309. Both the dustbin 306 and the water tank 309 may be washed as the impeller is not positioned within the dustbin 306 and the water pump 308 is not positioned within the water tank 309. FIG. 3F illustrates a bottom of module 300 including water dispensers 310 and Velcro strips 311 that may be used to secure mopping pad 304 to the bottom of module 300. FIG. 3G illustrates an alternative embodiment for dustbin lid 301, wherein dustbin lid 301 opens from the top of module 300. FIGS. 4A and 4B illustrates alternative embodiment of the robot in FIGS. 3A-3E. In FIG. 4A the water pump 400 is positioned within the dustbin of module 401 and in FIG. 4B the water pump 400 is positioned outside the module 401 and is connected to the module via connecting tube 402 with gasket 403 to seal fluid and prevent it from escaping at the connection point. FIG. 4C illustrates a module 403 for converting water into hydrogen peroxide and water pump 400 positioned within module 401. In some cases, module 403 may suction water (or may be provided water using a pump) from the water tank of the module 401, convert the water into hydrogen peroxide, and dispense the hydrogen peroxide into an additional container for storing the hydrogen peroxide. The container storing hydrogen peroxide may use similar methods as described for dispensing the fluid onto the mopping pad. In some embodiments, the process of water electrolysis may be used to generate the hydrogen peroxide. In some embodiments, the process of converting water to hydrogen peroxide may include water oxidation over an electrocatalyst in an electrolyte, that results in hydrogen peroxide dissolved in the electrolyte which may be directly applied to the surface or may be further processed before applying it to the surface.

[0145] In some embodiments, the robot may be built into an area of an environment (e.g., kitchen, living room, laundry room, mud room, etc.). In some embodiments, the bin of the surface cleaner may directly connect to and may be directly emptied into the central vacuum system of the environment. In some embodiments, the robot may be docked at a charging station while simultaneously connected to the central vacuum system. In some embodiments, the contents of a dustbin of a robot may be emptied at a charging station of the robot. For example, FIG. 5A illustrates robot 500 docked at charging station 501. Robot 500 charges by a connection between charging nodes (not shown) of robot 500 with charging pads 502 of charging station 501. When docked, a soft hose 503 may connect to a port of robot 500 with a vacuum motor 504 connected to a disposable trash bag (or detachable reusable container) 505. Vacuum motor 504 may suction debris 506 from a dustbin of robot 500 into disposable trash bag 505, as illustrated in FIG. 5B. Robot 500 may align itself during docking based on signals received from signal transmitters 507 positioned on the charging station 501. FIG. 5C illustrates components of rear-docking robot 500 including charging nodes 508, port 509 to which soft hose 503 may connect, and presence sensors 510 used during docking to achieve proper alignment. FIG. 5D illustrates magnets 511 that may be coupled to soft hose 503 and port 509. Magnets 511 may be used in aligning and securing a connection between soft hose 503 and port 509 of robot 500. FIG. 5E illustrates an alternative embodiment wherein the vacuum motor 504 is connected to an outdoor bin 512 via a soft plastic hose 513. FIG. 5F illustrates another embodiment, wherein the vacuum motor 504 and soft plastic hose 513 are placed on top of charging station 501. In some cases, the vacuum motor may be connected to a central vacuum system of a home or a garbage disposal system of a home. In embodiments, the vacuum motor may be placed on either side of the charging station.

[0146] FIG. 6A illustrates another example of a charging station of a robot. The charging station includes charging pads 600, area 601 behind which signal transmitters are positioned, plug 602, and button 603 for retracting plug 602. Plug 602 may be pulled from hole 604 to a desired length and button 603 may be pushed to retract plug 602 back within hole 604. FIG. 6B illustrates plug 602 extended from hole 604. FIG. 6C illustrates a robot with charging nodes 605 that may interface with charging pads 600 to charge the robot. The robot includes sensor windows 606 behind which sensors (e.g., camera, time of flight sensor, LIDAR, etc.) are positioned, bumper 607, brush 608, wheels 609, and tactile sensors 610. Each tactile sensor may be triggered when pressed and may notify the robot of contact with an object. FIG. 6D illustrates panel 611, printed buttons 612 and indicators 613, and the actual buttons 614 and LED indicators 615 positioned within the robot that are aligned with the printed buttons 612 and indicators 613 on the panel 611. FIG. 6E illustrates the robot positioned on the charging station and a connection between charging nodes 605 of the robot and charging pads 600 of the charging station. The charging pads 600 may be spring loaded such that the robot does not mistake them as an obstacle. FIG. 6F illustrates an alternative embodiment of the charging station wherein the charging pads 616 are circular and positioned in a different location. FIG. 6G illustrates an alternative embodiment of the robot wherein sensors window 617 is continuous. FIG. 6H illustrates an example of an underside of the robot including UV lamp 618. FIG. 6I illustrates a close up of the UV lamp an internal reflective surface 619 to maximize lamp coverage and a bumpy glass cover 620 to scatter UV rays.

[0147] In some embodiments, peripheral brushes of a robotic cleaner, such as peripheral brush 203 of the robotic cleaner in FIG. 2, may implement strategic methods for bristle attachment to reduce the loss of bristles during operation. For example, FIGS. 7A and 7B illustrate one method for bristle attachment wherein each bristle bundle 700 may be wrapped around a cylinder 701 coupled to a main body 702 of the peripheral brush. Each bristle bundle 700 may be wrapped around the cylinder 701 at least once and then knotted with itself to secure its attachment to the main body 702 of the peripheral brush. FIG. 7C illustrates another method for bristle attachment wherein each bristle bundle 703 may be threaded in and out of main body 702 to create two adjacent bristle bundles which may reduce the loss of bristles during operation. In some cases, the portion of each bristle bundle within the main body 702 may attached to the inside of main body 702 using glue, stitching, or another means. FIGS. 7D, 7E, and 7F illustrate another method for bristle attachments wherein bristle bundles 704 positioned opposite to one another are hooked together, as illustrated in FIG. 7F. In all embodiments, the number of bristles in each bristle bundle may vary.

[0148] In embodiments, floor sensors may be positioned in different locations on an underside of the robotic cleaner and may also have different orientations and sizes. FIGS. 8A-8D illustrate examples of alternative positions (e.g., displaced at some distance from the wheel or immediately adjacent to the wheel) and orientations (e.g., vertical or horizontal) for floor sensors 800. The specific arrangement of sensors may depend on the geometry of the robot.

[0149] In some embodiments, floor sensors may be infrared (IR) sensors, ultrasonic sensors, laser sensors, time-of-flight (TOF) sensors, distance sensors, 3D or 2D range finders, 3D or 2D depth cameras, etc. For example, the floor sensor positioned on the front of the robot in FIG. 2 may be an IR sensor while the floor sensors positioned on the sides of the robot may be TOF sensors. In another example, FIGS. 9A and 9B illustrate examples of alternative positions (e.g., displaced at some distance from the wheel so there is time for the robot to react, wherein the reaction time depends on the speed of the robot and the sensor position) of IR floor sensors 900 positioned on the sides of the underside of the robot. In these examples, the floor sensors are positioned in front of the wheel (relative to a forward moving direction of the wheel) to detect a cliff as the robot moves forward within the environment. Floor sensors positioned in front of the wheel may detect cliffs faster than floor sensors positioned adjacent to or further away from the wheel.

[0150] In embodiments, the number of floor sensors coupled to the underside of the robotic cleaner may vary depending on the functionality. For example, some robots may rarely drive backwards while others may drive backwards more often. Some robots may only turn clockwise while some may turn counterclockwise while some may do both. Some robots may execute a coastal drive or navigation from one side of the room. For example, FIG. 10 illustrates an example of an underside of a robotic cleaner with four floor sensors 1000. FIG. 11 illustrates an example of an underside of a robotic cleaner with five floor sensors 1100. FIG. 12 illustrates an example of an underside of a robotic cleaner with six floor sensors 1200.

[0151] In some embodiments, the robot is a robotic cleaner. In some embodiments, the robot includes a removable brush compartment with roller brushes designed to avoid collection of hair and debris at a connecting point of the roller brushes and a motor rotating the roller brushes. In some embodiments, the component powering rotation of the roller brushes may be masked from a user, the brush compartment, and the roller brushes by separating the power transmission from the brush compartment. In some embodiments, the roller brushes may be cleaned without complete removal of the roller brushes thereby avoiding tedious removal and realignment and replacement of the brushes after cleaning.

[0152] FIG. 13A illustrates an example of a brush compartment of a robotic cleaner including frame 1300, gear box 1301, and brushes 1302. The robotic cleaner includes a motor 1303 and gearbox 1304 that interfaces with gear box 1301 of the brush compartment when it is fully inserted into the underside of the robotic cleaner, as illustrated in FIG. 13B. In some embodiments, the motor is positioned above the brush compartment such that elements like hair and debris cannot become entangled at the point of connection between the power transmission and brushes. In some embodiments, the motor and gearbox of the robot is positioned adjacent to the brush compartment or in another position. In some embodiments, the power generating motion in the motor is normal to the axis of rotation the brushes. In some embodiments, the motor and gearbox of the robot and the gearbox of the brush compartment may be positioned on either end of the brush compartment. In some embodiments, more than one motor and gearbox interface with the brush compartment. In some embodiments, more than one motor and gearbox of the robot may each interface with a corresponding gearbox of the brush compartment. FIG. 13C illustrates brush 1302 comprised of two portions, one portion of which is rotatably coupled to frame 1300 on an end opposite the gear box 1301 of the brush compartment such that the rotatable portion of the brush may rotate about an axis parallel to the width of the frame. In some embodiments, the two portions of brush 1302 may be separated when the brushes are non-operable. In some embodiments, the two portions of brush 1302 are separated such that brush blade 1305 may be removed from brush 1302 by sliding brush blade 1305 in direction 1306. In some embodiments, brush blades may be replaced when worn out or may be removed for cleaning. In some instances, this eliminates the tedious task of realigning brushes when they are completely removed from the robot. In some embodiments, a brush may be a single piece that may be rotatably coupled to the frame on one end such that the brush may rotate about an axis parallel to the width of the frame. In some embodiments, the brush may be fixed to the module such there is no need for removal of the brush during cleaning and may be put back together by simply clicking the brush into place. In some embodiments, separation of the brush from the module may not be a necessity for fully cleaning the brush but separation may be possible. In some embodiments, either end of a brush may be rotatably coupled to either end of the frame of the brush compartment. In some embodiments, the brushes may be directly attached to the chassis of the robotic cleaner, without the use of the frame. In some embodiments, brushes of the brush compartment may be configured differently from one another. For example, one brush may only rotate about an axis of the brush during operation while the other may additionally rotate about an axis parallel to the width of the frame when the brush is non-operable for removal of brush blades. FIG. 13E illustrates brush blade 1305 completely removed from brush 1302. FIG. 13F illustrates motor 1303 and gearbox 1304 of the robotic cleaner that interfaces with gearbox 1301 of the brush compartment through insert 1307. FIG. 13G illustrates brushes 1302 of the brush compartment, each brush including two portions. To remove brush blades 1305 from brushes 1302, the portions of brushes 1302 opposite gearbox 1301 rotate about an axis perpendicular to rotation axes of brushes 1302 and brush blades 1305 may be slid off of the two portions of brushes 1302 as illustrated in FIGS. 13D and 13E. FIG. 13H illustrates an example of a locking mechanism that may be used to lock the two portions of each brush 1302 together including locking core 1308 coupled to one portion of each brush and lock cavity 1309 coupled to a second portion of each brush. Locking core 1308 and lock 1309 interface with another to lock the two portions of each brush 1302 together.

[0153] FIG. 14A illustrates another example of a brush compartment of a robotic cleaner with similar components as described above including motor 2400 and gearbox 1401 of the robotic cleaner interfacing with gearbox 1402 of the brush compartment. Component 1403 of gearbox 1401 of the robotic cleaner interfacing with gearbox 1402 of the brush compartment differs from that shown in FIG. 13A. FIG. 14B illustrates that component 1403 of gearbox 1401 of the robotic cleaner is accessible by the brush compartment when inserted into the underside of the robotic cleaner, while motor 1400 and gearbox 1401 of the robotic cleaner are hidden within a chassis of the robotic cleaner.

[0154] In some instances, the robotic cleaner may include a mopping module including at least a reservoir and a water pump driven by a motor for delivering water from the reservoir indirectly or directly to the driving surface. In some embodiments, the water pump may autonomously activate when the robotic cleaner is moving and deactivate when the robotic cleaner is stationary. In some embodiments, the water pump may include a tube through which fluid flows from the reservoir. In some embodiments, the tube may be connected to a drainage mechanism into which the pumped fluid from the reservoir flows. In some embodiments, the bottom of the drainage mechanism may include drainage apertures. In some embodiments, a mopping pad may be attached to a bottom surface of the drainage mechanism. In some embodiments, fluid may be pumped from the reservoir, into the drainage mechanism and fluid may flow through one or more drainage apertures of the drainage mechanism onto the mopping pad. In some embodiments, flow reduction valves may be positioned on the drainage apertures. In some embodiments, the tube may be connected to a branched component that delivers the fluid from the tube in various directions such that the fluid may be distributed in various areas of a mopping pad. In some embodiments, the release of fluid may be controlled by flow reduction valves positioned along one or more paths of the fluid prior to reaching the mopping pad. FIG. 15A illustrates an example of a charging station 1500 including signal transmitters 1501 that transmit signals that the robot 1502 may use to align itself with the charging station 1500 during docking, vacuum motor 1503 for emptying debris from the dustbin of the robot 1502 into disposable trash bag (or reusable trash container) 1504 via tube and water pump 1505 for refilling a water tank of robot 1502 via tube 1506 using water from the house supply coming through piping 1507 into water pump 1505. In some cases, the trash bag 1504 of charging station 1500 may be removed by pressing a button on the charging station 1500. FIG. 15B illustrates debris collection path 1508 and charging pads 1509 and FIG. 15C illustrates water flow path 1510 and charging pads 1509 (robot not shown for visualization of the debris path and water flow path). Charging pads of the robot interface with charging pads 1509 during charging. Charging station 1500 may be used for a robot with combined vacuuming and mopping capabilities. In some instances, the dustbin is emptied or the water tank is refilled when the dustbin or the water tank reaches a particular volume, after a certain amount of surface coverage by the robot, after a certain number of operational hours, after a predetermined amount of time, after a predetermined number of working sessions, or based on another metric. In some instances, the processor of the robot may communicate with the charging station to notify the charging station that the dustbin needs to be emptied or the water tank needs to be refilled. In some cases, a user may use an application paired with the robot to instruct the robot to empty its dustbin or refill its water tank. The application may communicate the instruction to the robot and/or the charging station. In some cases, the charging station may be separate from the dustbin emptying station or the water refill station.

[0155] Some embodiments may provide a mopping extension unit for the robotic cleaner to enable simultaneous vacuuming and mopping of a driving surface and reduce (or eliminate) the need for a dedicated robotic mopping to run after a dedicated robotic vacuum. In some embodiments, a mopping extension may be installed in a dedicated compartment of or built into the chassis of the robotic cleaner. In some embodiments, the mopping extension may be detachable by, for example, activating a button or latch. In some embodiments, a cloth positioned on the mopping extension may contact the driving surface as the robotic cleaner drives through an area. In some embodiments, nozzles may direct fluid from a fluid reservoir to a mopping cloth. In some embodiments, the nozzles may continuously deliver a constant amount of cleaning fluid to the mopping cloth. In some embodiments, the nozzles may periodically deliver predetermined quantities of cleaning fluid to the cloth. In some embodiments, a water pump may deliver fluid from a reservoir to a mopping cloth, as described above. In some embodiments, the mopping extension may include a set of ultrasonic oscillators that vaporize fluid from the reservoir before it is delivered through the nozzles to the mopping cloth. In some embodiments, the ultrasonic oscillators may vaporize fluid continuously at a low rate to continuously deliver vapor to the mopping cloth. In some embodiments, the ultrasonic oscillators may turn on at predetermined intervals to deliver vapor periodically to the mopping cloth. In some embodiments, a heating system may alternatively be used to vaporize fluid. For example, an electric heating coil in direct contact with the fluid may be used to vaporize the fluid. The electric heating coil may indirectly heat the fluid through another medium. In other examples, radiant heat may be used to vaporize the fluid. In some embodiments, water may be heated to a predetermined temperature then mixed with a cleaning agent, wherein the heated water is used as the heating source for vaporization of the mixture. In some embodiments, water may be placed within the reservoir and the water may be reacted to produce hydrogen peroxide for cleaning and disinfecting the floor. In such embodiments, the process of water electrolysis may be used to generate hydrogen peroxide. In some embodiments, the process may include water oxidation over an electrocatalyst in an electrolyte, that results in hydrogen peroxide dissolved in the electrolyte which may be directly applied to the driving surface or mopping pad or may be further processed before applying it to the driving surface. In some embodiments, the robotic cleaner may include a means for moving the mopping cloth (and a component to which the mopping cloth may be attached) back and forth (e.g., forward and backwards or left and right) in a horizontal plane parallel to the driving surface during operation (e.g., providing a scrubbing action) such that the mopping cloth may pass over an area more than once as the robot drives. In some embodiments, the robot may pause for a predetermined amount of time while the mopping cloth moves back and forth in a horizontal plane, after which, in some embodiments, the robot may move a predetermined distance before pausing again while the mopping cloth moves back and forth in the horizontal plane again. In some embodiments, the mopping cloth may move back and forth continuously as the robot navigates within the environment. In some embodiments, the mopping cloth may be positioned on a front portion of the robotic cleaner. In some embodiments, a dry cloth may be positioned on a rear portion of the robotic cleaner. In some embodiments, as the robot navigates, the dry cloth may contact the driving surface and because of its position on the robot relative to the mopping cloth, dries the driving surface after the driving surface is mopped with the mopping cloth. For example, FIG. 16A illustrates a robot including sensor windows 1600 behind which sensors are positioned, sensors 1601 (e.g., camera, laser emitter, TOF sensor, etc.), user interface 1602, a battery 1603, a wet mop movement mechanism 1604, a PCB and processing unit 1605, a wheel motor and gearbox 1606, wheels 1607, a wet mop tank 1608, a wet mop cloth 1609, and a dry mop cloth 1610. FIG. 16B illustrates the robot driving in a direction 1611. While driving, or while pausing, wet mop cloth 1609 moves back and forth in a forward direction 1612 and backward direction 1613, respectively. As the robot drives forward, dry cloth 1610 dries the driving surface that has been cleaned by wet mop cloth 1609. In some embodiments, the mopping extension may include a means to vibrate the mopping extension during operation (e.g., eccentric rotating mass vibration motors). In some embodiments, the mopping extension may include a means to engage and disengage the mopping extension during operation by moving the mopping extension up and down in a vertical plane perpendicular to the work surface. In some embodiments, engagement and disengagement may be manually controlled by a user. In some embodiments, engagement and disengagement may be controlled automatically by the processor based on sensory input. For example, the processor may actuate the mopping extension to move in an upwards direction away from the driving surface upon detecting carpet using sensor data.

[0156] In some embodiments, the processor of the robot may generate a global and local map of the environment using data collected by sensors of the robot. In some embodiments, the sensors may include at least one imaging sensor. In one embodiment, an imaging sensor may measure vectors from the imaging sensor to objects in the environment and the processor may calculate the L2 norm of the vectors using ∥x∥_P=(Σ_i|x_i|^P)^1/P with P=2 to estimate depths to objects. In some embodiments, the processor may adjust previous data to account for a measured movement of the robot as it moves from observing one field of view to the next (e.g., differing from one another due to a difference in sensor pose). In some embodiments, a movement measuring device such as an odometer, optical tracking sensor (OTS), gyroscope, inertial measurement unit (IMU), optical flow sensor, etc. may measure movement of the robot and hence the sensor (assuming the two move as a single unit). In some instances, the processor matches a new set of data with data previously captured. In some embodiments, the processor compares the new data to the previous data and identifies a match when a number of consecutive readings from the new data and the previous data are similar. In some embodiments, identifying matching patterns in the value of readings in the new data and the previous data may also be used in identifying a match. In some embodiments, thresholding may be used in identifying a match between the new and previous data wherein areas or objects of interest within an image may be identified using thresholding as different areas or objects have different ranges of pixel intensity. In some embodiments, the processor may determine a cost function and may minimize the cost function to find a match between the new and previous data. In some embodiments, the processor may create a transform and may merge the new data with the previous data and may determine if there is a convergence. In some embodiments, the processor may determine a match between the new data and the previous data based on translation and rotation of the sensor between consecutive frames measured by an IMU. For example, overlap of data may be deduced based on interoceptive sensor measurements. In some embodiments, the translation and rotation of the sensor between frames may be measured by two separate movement measurement devices (e.g., optical encoder and gyroscope) and the movement of the robot may be the average of the measurements from the two separate devices. In some embodiments, the data from one movement measurement device is the movement data used and the data from the second movement measurement device is used to confirm the data of the first movement measurement device. In some embodiments, the processor may use movement of the sensor between consecutive frames to validate the match identified between the new and previous data. Or, in some embodiments, comparison between the values of the new data and previous data may be used to validate the match determined based on measured movement of the sensor between consecutive frames. For example, the processor may use data from an exteroceptive sensor (e.g., image sensor) to determine an overlap in data from an IMU, encoder, or OTS. In some embodiments, the processor may stitch the new data with the previous data at overlapping points to generate or update the map. In some embodiments, the processor may infer the angular disposition of the robot based on a size of overlap of the matching data and may use the angular disposition to adjust odometer information to overcome inherent noise of an odometer.

[0157] In some embodiments, the map may be a state space with possible values for x, y, z. In some embodiments, a value of x and y may be a point on a Cartesian plane on which the robot drives and the value of z may be a height of obstacles or depth of cliffs. In some embodiments, the map may include additional dimensions (e.g., debris accumulation, floor type, obstacles, cliffs, stalls, etc.). For example, FIG. 17 illustrates an example of a map that represents a driving surface with vertical undulations (e.g., indicated by measurements in x-, y-, and z-directions). In some embodiments, a map filler may assign values to each cell in a map (e.g., Cartesian). In some embodiments, the value associated with each cell may be used to determine a location of the cell in a planar surface along with a height from a ground zero plane. In some embodiments, a plane of reference (e.g., x-y plane) may be positioned such that it includes a lowest point in the map. In this way, all vertical measurements (e.g., z values measured in a z-direction normal to the plane of reference) are always positive. In some embodiments, the processor of the robot may adjust the plane of reference each time a new lower point is discovered and all vertical measurements accordingly. In some embodiments, the plane of reference may be positioned at a height of the work surface at a location where the robot begins to perform work and data may be assigned a positive value when an area with an increased height relative to the plane of reference is discovered (e.g., an inclination or bump) and assigned a negative value when an area with a decreased height relative to the plane of reference is observed. In some embodiments, a map may include any number of dimensions. For example, a map may include dimensions that provide information indicating areas that were previously observed to have a high level of debris accumulation or areas that were previously difficult to traverse or areas that were previously identified by a user (e.g., using an application of a communication device), such as areas previously marked by a user as requiring a high frequency of cleaning. In some embodiments, the processor may identify a frontier (e.g., corner) and may include the frontier in the map.

[0158] In some embodiments, the processor may generate or update the map based at least on the L2 norm of vectors measured by sensors to objects within the environment. In some embodiments, each L2 norm of a vector may be replaced with an average of the L2 norms corresponding with neighboring vectors. In some embodiments, the processor may use more sophisticated methods to filter sudden spikes in the sensor readings. In some embodiments, sudden spikes may be deemed as outliers. In some embodiments, sudden spikes or drops in the sensor readings may be the result of a momentary environmental impact on the sensor. In some embodiments, the processor may generate or update a map using captured images of the environment. In some embodiments, a captured image may be processed prior to using the image in generating or updating the map. In some embodiments, processing may include replacing readings corresponding to each pixel with averages of the readings corresponding to neighboring pixels. FIG. 18 illustrates an example of replacing a reading 1800 corresponding with a pixel with an average of the readings 1801 of corresponding neighboring pixels 1802. In some embodiments, pixel values of an image may be read into an array or any data structure or container capable of indexing elements of the pixel values. In some embodiments, the data structure may provide additional capabilities such as insertion or deletion in the middle, start, or end by swapping pointers in memory. In some embodiments, indices such as i, j, and k may be used to access each element of the pixel values. In some embodiments, negative indices count from the last element backwards. In some embodiments, the processor of the robot may transform the pixel values into grayscale. In some embodiments, the grayscale may range from black to white and may be divided into a number of possibilities. For example, numbers ranging from 0 to 256 may be used to describe 256 buckets of color intensities. Each element of the array may have a value that corresponds with one of buckets of color intensities. In some embodiments, the processor may create a chart showing the popularity of each color bucket within the image. For example, the processor may iterate through the array and may increase a popularity vote of the 0 color intensity bucket for each element of the array having a value of 0. This may be repeated for each of the 256 buckets of color intensities. In some embodiments, characteristics of the environment at the time the image is captured may affect the popularity of the 256 buckets of color intensities. For example, an image captured on a bright day may have increased popularity for color buckets corresponding with less intense colors. In some embodiments, principal component analysis may be used to reduce the dimensionality of an image as the number of pixels increases with resolution. For example, dimensions of a megapixel image are in the millions. In some embodiments, singular value decomposition may be used to find principal components.

[0159] In some embodiments, the processor of the robot stores a portion of the L2 norms, such as L2 norms to critical points within the environment. In some embodiments, critical points may be second or third derivatives of a function connecting the L2 norms. In some embodiments, critical points may be second or third derivatives of raw pixel values. In some embodiments, the simplification may be lossy. In some embodiments, the lost information may be retrieved and pruned in each tick of the processor as the robot collects more information. In some embodiments, the accuracy of information may increase as the robot moves within the environment. For example, a critical point may be discovered to include two or more critical points over time. In some embodiments, loss of information may not occur or may be negligible when critical points are extracted with high accuracy.

[0160] In some embodiments, depths may be measured to all objects within the environment. In some embodiments, depths may be measured to particular landmarks (e.g., some identified objects) or a portion of the objects within the environment (e.g., a subset of walls). In some embodiments, the processor may generate a map based on depths to a portion of objects within the environment. FIG. 19A illustrates an example of a robot 1900 with a sensor collecting data that is indicative of depth to a subset of points 1901 along the walls 1902 of the environment. FIG. 19B illustrates an example of a spatial model 1903 generated based on the depths to the subset of points 1901 of the environment shown in FIG. 119A, assuming the points are connected by lines. As robot 1900 moves from a first position at time t₀ to a second position at time t₁₀ within the environment and collects more data, the spatial model 1903 may be updated to more accurately represent the environment, as illustrated in FIG. 19C.

[0161] In some embodiments, the sensor of the robot 1900 continues to collect data to the subset of points 1901 along the walls 1902 as the robot 1900 moves within the environment. For example, FIG. 20A illustrates the sensor of the robot 1900 collecting data to the same subset of points 1901 at three different times 2000, 2001, and 2002 as the robot moves within the environment. In some cases, depending on the position of the robot, two particularities may appear as a single feature (or characteristic). For example, FIG. 20B illustrates the robot 1900 at a position s₁ collecting data indicative of depths to points A and B. From position s₁ points A and B appear to be the same feature. As the robot 1900 travels to a position s₂ and observes the edge on which points A and B lie from a different angle, the processor of the robot 1900 may differentiate points A and B as separate features. In some embodiments, the processor of the robot gains clarity on features as it navigates within the environment and observes the features from different positions and may be able to determine if a single feature is actually two features combined.

[0162] In some embodiments, the path of the robot may overlap while mapping. For example, FIG. 21 illustrates a robot 2100, a path of the robot 2101, an environment 2102, and an initial area mapped 2103 while performing work. In some embodiments, the path of the robot may overlap resulting in duplicate coverage of areas of the environment. For instance, the path 2101 illustrated in FIG. 21 includes overlapping segment 2104. In some cases, the processor of the robot may discard some overlapping data from the map. In some embodiments, the processor of the robot may determine overlap in the path based on images captured with a camera of the robot as the robot moves within the environment.

[0163] In some embodiments, the processor may extract lines that may be used to construct the environment of the robot. In some cases, there may be uncertainty associated with each reading of a noisy sensor measurement and there may be no single line that passes through the measurement. In such cases, the processor may select the best possible match, given some optimization criterion. In some cases, sensor measurements may be provided in polar coordinates, wherein x_i=(ρ_i, θ_i). The processor may model uncertainty associated with each measurement with two random variables, X_i=(P_i, Q_i). To satisfy the Markovian requirement, the uncertainty with respect to the actual value of P and Q must be independent, wherein E[P_i·p_i]=E[P_i]E[P_j], E [Q_i·Q_j]=E[Q_i]E[Q_j], and E [P_i·Q_i]=E[P_i]E[Q_i], ∀i,j=1, . . . , n. In some embodiments, each random variable may be subject to a Gaussian probability, wherein P_i˜N(ρ_i, (σ²)_ρi) and Q_i˜N(θ_i, (σ²)_θi). In some embodiments, the processor may determine corresponding Euclidean coordinates x=ρ cos θ and y=ρ sin θ of a polar coordinate. In some embodiments, the processor may determine a line on which all measurements lie, i.e., ρ cos θ cos α+ρ sin θ sin α−r=ρ cos(θ−α)−r=0. However, obtaining a value of zero represents an ideal situation wherein there is no error. In actuality, this is a measure of the error between a measurement point (ρ, θ) and the line, specifically in terms of the minimum orthogonal distance between the point and the line. In some embodiments, the processor may minimize the error. In some embodiments, the processor may minimize the sum of square of all the errors using S=Σ_id_i²=Σ_i(ρ_i cos(θ−α)−r)², wherein

[0164] $\frac{\partial S}{\partial \alpha }=0$
and

[0165] $\frac{\partial S}{\partial r}=0.$
In some instances, measurements may not have the same errors. In some embodiments, a measurement point of the spatial representation of the environment may represent a mean of the measurement and a circle around the point may indicate the variance of the measurement. The size of circle may be different for different measurements and may be indicative of the amount of influence that each point may have in determining where the perimeter line fits. For example, in FIG. 22A, three measurements A, B, and C are shown, each with a circle 2200 indicating variance of the respective measurement. The perimeter line 2201 is closer to measurement B as it has a higher confidence and less variance. In some instances, the perimeter line may not be a straight line depending on the measurements and their variance. While this method of determining a position of a perimeter line may result in a perimeter line 2201 shown in FIG. 22B, the perimeter line of the environment may actually look like the perimeter line 2202 or 2203 illustrated in FIG. 22C or FIG. 22D. In some embodiments, the processor may search for particular patterns in the measurement points. For example, it may be desirable to find patterns that depict any of the combinations in FIG. 23.

[0166] In some embodiments, the processor (or a SLAM algorithm executed by the processor) may obtain scan data collected by sensors of the robot during rotation of the robot. In some embodiments, a subset of the data may be chosen for building the map. For example, 49 scans of data may be obtained for map building and four of those may be identified as scans of data that are suitable for matching and building the map. In some embodiments, the processor may determine a matching pose of data and apply a correction accordingly. For example, a matching pose may be determined to be (−0.994693, −0.105234, −2.75821) and may be corrected to (−1.01251, −0.0702046, −2.73414) which represents a heading error of 1.3792 degrees and a total correction of (−0.0178176, 0.0350292, 0.0240715) having traveled (0.0110555, 0.0113022, 6.52475). In some embodiments, a multi map scan matcher may be used to match data. In some embodiments, the multi map scan matcher may fail if a matching threshold is not met. In some embodiments, a Chi-squared test may be used.

[0167] Some embodiments may afford the processor of the robot constructing a map of the environment using data from one or more cameras while the robot performs work within recognized areas of the environment. The working environment may include, but is not limited to (a phrase which is not here or anywhere else in this document to be read as implying other lists are limiting), furniture, obstacles, static objects, moving objects, walls, ceilings, fixtures, perimeters, items, components of any of the above, and/or other articles. The environment may be closed on all sides or have one or more openings, open sides, and/or open sections and may be of any shape. In some embodiments, the robot may include an on-board camera, such as one with zero-degrees of freedom of actuated movement relative to the robot (which may itself have three degrees of freedom relative to an environment), or some embodiments may have more or fewer degrees of freedom; e.g., in some cases, the camera may scan back and forth relative to the robot.

[0168] A camera as described herein may include, but is not limited to, various optical and non-optical imaging devices, like a depth camera, stereovision camera, time-of-flight camera, or any other type of camera that outputs data from which depth to objects can be inferred over a field of view, or any other type of camera capable of generating a pixmap, or any device whose output data may be used in perceiving the environment. A camera may also be combined with an infrared (IR) illuminator (such as a structured light projector), and depth to objects may be inferred from images captured of objects onto which IR light is projected (e.g., based on distortions in a pattern of structured light). Examples of methods for estimating depths to objects using at least one IR laser, at least one image sensor, and an image processor are detailed in U.S. patent applications Ser. Nos. 15/243,783, 62/208,791, 15/224,442, and 15/674,310, the entire contents of each of which are hereby incorporated by reference. Other imaging devices capable of observing depth to objects may also be used, such as ultrasonic sensors, sonar, LIDAR, and LADAR devices. Thus, various combinations of one or more cameras and sensors may be used.

[0169] In some embodiments, a camera, installed on the robot, for example, measures the depth from the camera to objects within a first field of view. In some embodiments, a processor of the robot constructs a first segment of the map from the depth measurements taken within the first field of view. The processor may establish a first recognized area within the working environment, bound by the first segment of the map and the outer limits of the first field of view. In some embodiments, the robot begins to perform work within the first recognized area. As the robot with attached camera rotates and translates within the first recognized area, the camera continuously takes depth measurements to objects within the field of view of the camera. Assuming the frame rate of the camera is fast enough to capture more than one frame of data in the time it takes the robot to rotate the width of the frame, a portion of data captured within each field of view overlaps with a portion of data captured within the preceding field of view. As the robot moves to observe a new field of view, in some embodiments, the processor adjusts measurements from previous fields of view to account for movement of the robot. The processor, in some embodiments, uses data from devices such as an odometer, gyroscope and/or optical encoder to determine movement of the robot with attached camera.

[0170] In some embodiments, the processor compares depth measurements taken within the second field of view to those taken within the first field of view in order to find the overlapping measurements between the two fields of view. The processor may use different methods to compare measurements from overlapping fields of view. An area of overlap between the two fields of view is identified (e.g., determined) when (e.g., during evaluation a plurality of candidate overlaps) a number of consecutive (e.g., adjacent in pixel space) depths from the first and second fields of view are equal or close in value. Although the value of overlapping depth measurements from the first and second fields of view may not be exactly the same, depths with similar values, to within a tolerance range of one another, can be identified (e.g., determined to correspond based on similarity of the values). Furthermore, identifying matching patterns in the value of depth measurements within the first and second fields of view can also be used in identifying the area of overlap. For example, a sudden increase then decrease in the depth values observed in both sets of measurements may be used to identify the area of overlap. Examples include applying an edge detection algorithm (like Haar or Canny) to the fields of view and aligning edges in the resulting transformed outputs. Other patterns, such as increasing values followed by constant values or constant values followed by decreasing values or any other pattern in the values of the perceived depths, can also be used to estimate the area of overlap. A Jacobian and Hessian matrix can be used to identify such similarities.

[0171] In some embodiments, thresholding may be used in identifying overlap wherein areas or objects of interest within an image may be identified using thresholding as different areas or objects have different ranges of pixel intensity. For example, an object captured in an image, the object having high range of intensity, can be separated from a background having low range of intensity by thresholding wherein all pixel intensities below a certain threshold are discarded or segmented, leaving only the pixels of interest. In some embodiments, a metric such as the Szymkiewicz-Simpson coefficient can be used to indicate how good of an overlap there is between the two sets of depth measurements. In some embodiments, the angular speed and time between consecutive fields of view may be used to estimate the area of overlap. Or some embodiments may determine an overlap with a convolution. Some embodiments may implement a kernel function that determines an aggregate measure of differences (e.g., a root mean square value) between some or all of a collection of adjacent depth readings in one image relative to a portion of the other image to which the kernel function is applied. Some embodiments may then determine the convolution of this kernel function over the other image, e.g., in some cases with a stride of greater than one pixel value. Some embodiments may then select a minimum value of the convolution as an area of identified overlap that aligns the portion of the image from which the kernel function was formed with the image to which the convolution was applied.

[0172] In some embodiments, the processor may identify overlap using raw pixel intensity values. FIGS. 24A and 24B illustrate an example of identifying an area of overlap using raw pixel intensity data and the combination of data at overlapping points. In FIG. 24A, the overlapping area between overlapping image 2400 captured in a first field of view and image 2401 captured in a second field of view may be determined by comparing pixel intensity values of each captured image (or transformation thereof, such as the output of a pipeline that includes normalizing pixel intensities, applying Gaussian blur to reduce the effect of noise, detecting edges in the blurred output (such as Canny or Haar edge detection), and thresholding the output of edge detection algorithms to produce a bitmap like that shown) and identifying matching patterns in the pixel intensity values of the two images, for instance by executing operations by which some embodiments determine an overlap with a convolution. Lines 2402 represent pixels with high pixel intensity value (such as those above a certain threshold) in each image. Area 2403 of image 2400 and area 2404 of image 2401 capture the same area of the environment and, as such, the same pattern for pixel intensity values is sensed in area 2403 of image 2400 and area 2404 of image 2401. After identifying matching patterns in pixel intensity values in image 2400 and 2401, a matching overlapping area between both images may be determined. In FIG. 24B, the images are combined at overlapping area 2405 to form a larger image 2406 of the environment. In some cases, data corresponding to the images may be combined. For instance, depth values may be aligned based on alignment determined with the image.

[0173] FIGS. 25A-25C illustrate another example of identifying an area of overlap using raw pixel intensity data and the combination of data at overlapping points. FIG. 25A illustrates a top (plan) view of an object, such as a wall, with uneven surfaces wherein, for example, surface 2500 is further away from an observer than surface 2501 or surface 2502 is further away from an observer than surface 2503. In some embodiments, at least one infrared line laser positioned at a downward angle relative to a horizontal plane coupled with at least one camera may be used to determine the depth of multiple points across the uneven surfaces from captured images of the line laser projected onto the uneven surfaces of the object. Since the line laser is positioned at a downward angle, the position of the line laser in the captured image will appear higher for closer surfaces and will appear lower for further surfaces. Similar approaches may be applied with lasers offset from a camera in the horizontal plane. The position of the laser line (or feature of a structured light pattern) in the image may be detected by finding pixels with intensity above a threshold. The position of the line laser in the captured image may be related to a distance from the surface upon which the line laser is projected. In FIG. 25B, captured images 2504 and 2505 of the laser line projected onto the object surface for two different fields of view are shown. Projected laser lines with lower position, such as laser lines 2506 and 2507 in images 2504 and 2505 respectively, correspond to object surfaces 2500 and 2502, respectively, further away from the infrared illuminator and camera. Projected laser lines with higher position, such as laser lines 2508 and 2509 in images 2504 and 2505 respectively, correspond to object surfaces 2501 and 2503, respectively, closer to the infrared illuminator and camera. Captured images 2504 and 2505 from two different fields of view may be combined into a larger image of the environment by finding an overlapping area between the two images and stitching them together at overlapping points. The overlapping area may be found by identifying similar arrangement of pixel intensities in both images, wherein pixels with high intensity may be the laser line. For example, areas of images 2504 and 2505 bound within dashed lines 2510 have similar arrangement of pixel intensities as both images captured a same portion of the object within their field of view. Therefore, images 2504 and 2505 may be combined at overlapping points to construct larger image 2511 of the environment shown in FIG. 25C. The position of the laser lines in image 2511, indicated by pixels with intensity value above a threshold intensity, may also be used to infer depth of surfaces of objects from the infrared illuminator and camera (see, U.S. patent application Ser. No. 15/674,310, the entire contents of which is hereby incorporated by reference).

[0174] In some embodiments, the processor uses measured movement of the robot with attached camera to find the overlap between depth measurements taken within the first field of view and the second field of view. In other embodiments, the measured movement is used to verify the identified overlap between depth measurements taken within overlapping fields of view. In some embodiments, the area of overlap identified is verified if the identified overlap is within a threshold angular distance of the overlap identified using at least one of the method described above. In some embodiments, the processor uses the measured movement to choose a starting point for the comparison between measurements from the first field of view and measurements from the second field of view. For example, the processor uses the measured movement to choose a starting point for the comparison between measurements from the first field of view and measurements from the second field of view. The processor iterates using a method such as that described above to determine the area of overlap. The processor verifies the area of overlap if it is within a threshold angular distance of the overlap estimated using measured movement.

[0175] Some embodiments may implement DB-SCAN on depths and related values like pixel intensity, e.g., in a vector space that includes both depths and pixel intensities corresponding to those depths, to determine a plurality of clusters, each corresponding to depth measurements of the same feature of an object. Some embodiments may execute a density-based clustering algorithm, like DBSCAN, to establish groups corresponding to the resulting clusters and exclude outliers. To cluster according to depth vectors and related values like intensity, some embodiments may iterate through each of the depth vectors and designate a depth vectors as a core depth vector if at least a threshold number of the other depth vectors are within a threshold distance in the vector space (which may be higher than three dimensional in cases where pixel intensity is included). Some embodiments may then iterate through each of the core depth vectors and create a graph of reachable depth vectors, where nodes on the graph are identified in response to non-core corresponding depth vectors being within a threshold distance of a core depth vector in the graph, and in response to core depth vectors in the graph being reachable by other core depth vectors in the graph, where to depth vectors are reachable from one another if there is a path from one depth vector to the other depth vector where every link and the path is a core depth vector and is it within a threshold distance of one another. The set of nodes in each resulting graph, in some embodiments, may be designated as a cluster, and points excluded from the graphs may be designated as outliers that do not correspond to clusters.

[0176] Some embodiments may then determine the centroid of each cluster in the spatial dimensions of an output depth vector for constructing floor plan maps. In some cases, all neighbors have equal weight and in other cases the weight of each neighbor depends on its distance from the depth considered or (i.e., and/or) similarity of pixel intensity values. In some embodiments, the k-nearest neighbors algorithm is only applied to overlapping depths with discrepancies. In some embodiments, a first set of readings is fixed and used as a reference while the second set of readings, overlapping with the first set of readings, is transformed to match the fixed reference. In some embodiments, the transformed set of readings is combined with the fixed reference and used as the new fixed reference. In another embodiment, only the previous set of readings is used as the fixed reference. Initial estimation of a transformation function to align the newly read data to the fixed reference is iteratively revised in order to produce minimized distances from the newly read data to the fixed reference. The transformation function may be the sum of squared differences between matched pairs from the newly read data and prior readings from the fixed reference. For example, in some embodiments, for each value in the newly read data, the closest value among the readings in the fixed reference is found. In a next step, a point to point distance metric minimization technique is used such that it will best align each value in the new readings to its match found in the prior readings of the fixed reference. One point to point distance metric minimization technique that may be used estimates the combination of rotation and translation using a root mean square. The process is iterated to transform the newly read values using the obtained information. These methods may be used independently or may be combined to improve accuracy. In some embodiments, the adjustment applied to overlapping depths within the area of overlap is applied to other depths beyond the identified area of overlap, where the new depths within the overlapping area are considered ground truth when making the adjustment.

[0177] In some embodiments, due to measurement noise, discrepancies between the value of overlapping depth measurements from a first field of view and a second field of view may exist and the values of the overlapping depths may not be the exact same. In such cases, new depths may be calculated, or some of the depths may be selected as more accurate than others. For example, the overlapping depths from the first field of view and the second field of view (or more fields of view where more images overlap, like more than three, more than five, or more than 10) may be combined using a moving average (or some other measure of central tendency may be applied, like a median or mode) and adopted as the new depths for the area of overlap. The minimum sum of errors may also be used to adjust and calculate new depths for the overlapping area to compensate for the lack of precision between overlapping depths perceived within the first and second fields of view. By way of further example, the minimum mean squared error may be used to provide a more precise estimate of depths within the overlapping area. Other mathematical methods may also be used to further process the depths within the area of overlap, such as split and merge algorithm, incremental algorithm, Hough Transform, line regression, Random Sample Consensus, Expectation-Maximization algorithm, or curve fitting, for example, to estimate more realistic depths given the overlapping depths perceived within the first and second fields of view. The calculated depths are used as the new depth values for the overlapping depths identified. In another embodiment, the k-nearest neighbors algorithm can be used where each new depth is calculated as the average of the values of its k-nearest neighbors. These mathematical methods are not an exhaustive list of methods which may be used to process depth measurements, but provide an example of types of methods which may be used. Furthermore, mathematical methods may be combined.

[0178] In some cases, a confidence score is calculated for overlap determinations, e.g., based on an amount of overlap and aggregate amount of disagreement between depth vectors in the area of overlap in the different fields of view, and the above Bayesian techniques down-weight updates to priors based on decreases in the amount of confidence. In some embodiments, the size of the area of overlap is used to determine the angular movement and is used to adjust odometer information to overcome inherent noise of the odometer (e.g., by calculating an average movement vector for the robot based on both a vector from the odometer and a movement vector inferred from the fields of view). The angular movement of the robot from one field of view to the next may, for example, be determined based on the angular increment between vector measurements taken within a field of view, parallax changes between fields of view of matching objects or features thereof in areas of overlap, and the number of corresponding depths overlapping between the two fields of view.

[0179] In some embodiments, the processor expands the number of overlapping depth measurements to include a predetermined (or dynamically determined) number of depth measurements recorded immediately before and after (or spatially adjacent) the identified overlapping depth measurements. Once an area of overlap is identified (e.g., as a bounding box of pixel positions or threshold angle of a vertical plane at which overlap starts in each field of view), the processor constructs a larger field of view by combining the two fields of view using the overlapping depth measurements as attachment points. Combining may include transforming vectors with different origins into a shared coordinate system with a shared origin, e.g., based on an amount of translation or rotation of a depth sensing device between frames, for instance, by adding a translation or rotation vector to depth vectors. The transformation may be performed before, during, or after combining. The method of using the camera to perceive depths within consecutively overlapping fields of view and the processor to identify and combine overlapping depth measurements is repeated, e.g., until all areas of the environment are discovered and a map is constructed.

[0180] In some embodiments, the processor assigns a weight to each depth measurement. The value of the weight is determined based on various factors, such as the degree of similarity between depth measurements recorded from separate fields of view, the quality of the measurements, the weight of neighboring depth measurements, or the number of neighboring depth measurements with high weight. In some embodiments, the processor ignores depth measurements with weight less than as amount (such as a predetermined or dynamically determined threshold amount) as depth measurements with higher weight are considered to be more accurate. In some embodiments, increased weight is given to overlapping depths belonging to a larger number of overlapping depths between two sets of data, and less weight is given to overlapping depths belonging to a smaller number of overlapping depths between two sets of data. In some embodiments, the weight assigned to readings is proportional to the number of overlapping depth measurements.

[0181] In some embodiments, more than two consecutive fields of view overlap, resulting in more than two sets of depths falling within an area of overlap. This may happen when the amount of angular movement between consecutive fields of view is small, especially if the frame rate of the camera is fast such that several frames within which vector measurements are taken are captured while the robot makes small movements, or when the field of view of the camera is large or when the robot has slow angular speed and the frame rate of the camera is fast. Higher weight may be given to depths overlapping with more depths measured within other fields of view, as increased number of overlapping sets of depths provide a more accurate ground truth. In some embodiments, the amount of weight assigned to measured depths is proportional to the number of depths from other sets of data overlapping with it. Some embodiments may merge overlapping depths and establish a new set of depths for the overlapping depths with a more accurate ground truth. The mathematical method used can be a moving average or a more complex method.

[0182] In some embodiments, more than one camera may be used to improve accuracy of the map. For example, a plurality of depth measuring cameras (e.g., carried by the robot) may be used simultaneously (or concurrently) where depth measurements from each camera are used to more accurately map the environment. The use of a plurality of depth measuring cameras is expected to allow for the collection of depth measurements from different perspectives and angles, for example. Where more than one depth measuring camera is used, triangulation or others suitable methods may be used for further data refinement and accuracy. In some embodiments, a 360-degree LIDAR is used to create a map of the environment. It should be emphasized, though, that embodiments are not limited to techniques that construct a map in this way, as the present techniques may also be used for plane finding in augmented reality, barrier detection in virtual reality applications, outdoor mapping with autonomous drones, and other similar applications, which is not to suggest that any other description is limiting.

[0183] In some embodiments, images may be preprocessed before determining overlap. For instance, some embodiments may infer an amount of displacement of the robot between images, e.g., by integrating readings from an inertial measurement unit or odometer (in some cases after applying a Kalman filter), and then transform the origin for vectors in one image to match an origin for vectors in the other image based on the measured displacement, e.g., by subtracting a displacement vector from each vector in the subsequent image. Further, some embodiments may down-res images to afford faster matching, e.g., by selecting every other, every fifth, or more or fewer vectors, or by averaging adjacent vectors to form two lower-resolution versions of the images to be aligned. The resulting alignment may then be applied to align the two higher resolution images.

[0184] In some embodiments, a modified RANSAC approach is used where any two points, one from each data set, are connected by a line. A boundary is defined with respect to either side of the line. Any points from either data set beyond the boundary are considered outliers and are excluded. The process is repeated using another two points. The process is intended to remove outliers to achieve a higher probability of being the true distance to the perceived wall. Consider an extreme case where a moving object is captured in two frames overlapping with several frames captured without the moving object. The approach described or RANSAC method may be used to reject data points corresponding to the moving object. This method or a RANSAC method may be used independently or combined with other processing methods described above.

[0185] In some embodiments, computations may be expedited based on a type of movement of the robot between images. For instance, some embodiments may determine if the robot's displacement vector between images has less than a threshold amount of vertical displacement (e.g., is zero). In response, some embodiments may apply the above described convolution in with a horizontal stride and less or zero vertical stride, e.g., in the same row of the second image from which vectors are taken in the first image to form the kernel function.

[0186] In some embodiments, the processor (or set thereof) on the robot, a remote computing system in a data center, or both in coordination, may translate depth measurements from on-board sensors of the robot from the robot's (or the sensor's, if different) frame of reference, which may move relative to a room, to the room's frame of reference, which may be static. In some embodiments, vectors may be translated between the frames of reference with a Lorentz transformation or a Galilean transformation. In some cases, the translation may be expedited by engaging a basic linear algebra subsystem (BLAS) of a processor of the robot. In some instances where linear algebra is used, Basic Linear Algebra Subprograms (BLAS) are implemented to carry out operations such as vector addition, vector norms, scalar multiplication, matrix multiplication, matric transpose, matrix-vector multiplication, linear combinations, dot products, cross products, and the like.

[0187] In some embodiments, the robot's frame of reference may move with one, two, three, or more degrees of freedom relative to that of the room, e.g., some frames of reference for some types of sensors may both translate horizontally in two orthogonal directions as the robot moves across a floor and rotate about an axis normal to the floor as the robot turns. The “room's frame of reference” may be static with respect to the room, or as designation and similar designations are used herein, may be moving, as long as the room's frame of reference serves as a shared destination frame of reference to which depth vectors from the robot's frame of reference are translated from various locations and orientations (collectively, positions) of the robot. Depth vectors may be expressed in various formats for each frame of reference, such as with the various coordinate systems described above. (A data structure need not be labeled as a vector in program code to constitute a vector, as long as the data structure encodes the information that constitutes a vector.) In some cases, scalars of vectors may be quantized, e.g., in a grid, in some representations. Some embodiments may translate vectors from non-quantized or relatively granularly quantized representations into quantized or coarser quantizations, e.g., from a sensor's depth measurement to 16 significant digits to a cell in a bitmap that corresponds to 8 significant digits in a unit of distance. In some embodiments, a collection of depth vectors may correspond to a single location or pose of the robot in the room, e.g., a depth image, or in some cases, each depth vector may potentially correspond to a different pose of the robot relative to the room.

[0188] In embodiments, the constructed map may be encoded in various forms. For instance, some embodiments may construct a point cloud of two dimensional or three dimensional points by transforming each of the vectors into a vector space with a shared origin, e.g., based on the above-described displacement vectors, in some cases with displacement vectors refined based on measured depths. Or some embodiments may represent maps with a set of polygons that model detected surfaces, e.g., by calculating a convex hull over measured vectors within a threshold area, like a tiling polygon. Polygons are expected to afford faster interrogation of maps during navigation and consume less memory than point clouds at the expense of greater computational load when mapping. Vectors need not be labeled as “vectors” in program code to constitute vectors, which is not to suggest that other mathematical constructs are so limited. In some embodiments, vectors may be encoded as tuples of scalars, as entries in a relational database, as attributes of an object, etc. Similarly, it should be emphasized that images need not be displayed or explicitly labeled as such to constitute images. Moreover, sensors may undergo some movement while capturing a given image, and the pose of a sensor corresponding to a depth image may, in some cases, be a range of poses over which the depth image is captured.

[0189] In some embodiments, maps may be three dimensional maps, e.g., indicating the position of walls, furniture, doors, and the like in a room being mapped. In some embodiments, maps may be two dimensional maps, e.g., point clouds or polygons or finite ordered list indicating obstructions at a given height (or range of height, for instance from zero to 5 or 10 centimeters or less) above the floor. Two dimensional maps may be generated from two dimensional data or from three dimensional data where data at a given height above the floor is used and data pertaining to higher features are discarded. Maps may be encoded in vector graphic formats, bitmap formats, or other formats.

[0190] The robot may, for example, use the map to autonomously navigate the environment during operation, e.g., accessing the map to determine that a candidate route is blocked by an obstacle denoted in the map, to select a route with a route-finding algorithm from a current point to a target point, or the like. In some embodiments, the map is stored in memory for future use. Storage of the map may be in temporary memory such that a stored map is only available during an operational session or in more permanent forms of memory such that the map is available at the next session or startup. In some embodiments, the map is further processed to identify rooms and other segments. In some embodiments, a new map is constructed at each use, or an extant map is updated based on newly acquired data.

[0191] Some embodiments may reference previous maps during subsequent mapping operations. For example, embodiments may apply Bayesian techniques to simultaneous localization and mapping and update priors in existing maps based on mapping measurements taken in subsequent sessions. Some embodiments may reference previous maps and classifying objects in a field of view as being moveable objects upon detecting a difference of greater than a threshold size.

[0192] In some embodiments, gaps in the plotted boundary of the enclosure may be identified by one or more processors of the robot and further explored by one or more processors of the robot directing the camera until a complete (or more complete) closed loop boundary of the enclosure is plotted. In some embodiments, beacons are not required and the methods and apparatuses work with minimal or reduced processing power in comparison to traditional methods, which is not to suggest that any other described feature is required.

[0193] FIG. 26A illustrates camera 2600 mounted on robot 2601 measuring depths 2602 at predetermined increments within a first field of view 2603 of working environment 2604. Depth measurements 2602 taken by camera 2600 measure the depth from camera 2600 to object 2605, which in this case is a wall. Referring to FIG. 26B, a processor of the robot constructs 2D map segment 2606 from depth measurements 2602 taken within first field of view 2603. Dashed lines 2607 demonstrate that resulting 2D map segment 2606 corresponds to depth measurements 2602 taken within field of view 2603. The processor establishes first recognized area 2608 of working environment 2604 bounded by map segment 2606 and outer limits 2609 of first field of view 2603. Robot 2601 begins to perform work within first recognized area 2608 while camera 2600 continuously takes depth measurements.

[0194] FIG. 27A illustrates robot 2601 translating forward in direction 2700 to move within recognized area 2608 of working environment 2604 while camera 2600 continuously takes depth measurements within the field of view of camera 2600. Since robot 2601 translates forward without rotating, no new areas of working environment 2604 are captured by camera 2600, however, the processor combines depth measurements 2701 taken within field of view 2702 with overlapping depth measurements previously taken within area 2608 to further improve accuracy of the map. As robot 2601 begins to perform work within recognized area 2608 it positions to move in vertical direction 2703 by first rotating in direction 2704.

[0195] FIG. 27B illustrates robot 2601 rotating in direction 2704 while camera 2600 takes depth measurements 2701, 2705 and 2706 within fields of view 2707, 2708, and 2709, respectively. The processor combines depth measurements taken within these fields of view with one another and with previously taken depth measurements 2602 (FIG. 26A), using overlapping depth measurements as attachment points. The increment between fields of view 2707, 2708, and 2709 is trivial and for illustrative purposes.

[0196] In FIG. 27C the processor constructs larger map segment 2710 from depth measurements 2602, 2701, 2705 and 2706 taken within fields of view 2603, 2707, 2708 and 209, respectively, combining them by using overlapping depth measurements as attachment points. Dashed lines 2711 demonstrate that resulting 2D map segment 2710 corresponds to combined depth measurements 2602, 2701, 2705, and 2706. Map segment 2710 has expanded from first map segment 2606 (FIG. 26B) as plotted depth measurements from multiple fields of view have been combined to construct larger map segment 2710. The processor also establishes larger recognized area 2712 of working environment 2604 (compared to first recognized area 2608 (FIG. 26B)) bound by map segment 2710 and outer limits of fields of view 2603 and 2710 represented by dashed line 2713.

[0197] FIG. 28A illustrates robot 2601 continuing to rotate in direction 2704 before beginning to move vertically in direction 2703 within expanded recognized area 2712 of working environment 2604. Camera 2600 measures depths 2800 from camera 2600 to object 2605 within field of view 2801 overlapping with preceding depth measurements 2706 taken within field of view 2709 (FIG. 27B). Since the processor of robot 2601 is capable of tracking its position (using devices such as an odometer or gyroscope) the processor can estimate the approximate overlap with previously taken depth measurements 2706 within field of view 2709. Depth measurements 2802 represent the overlap between previously taken depth measurements 2706 and depth measurements 2800. FIG. 28B illustrates 2D map segment 2710 resulting from previously combined depth measurements 2602, 2701, 2705 and 2706 and map segment 2803 resulting from depth measurements 2800. Dashed lines 2711 and 2804 demonstrate that resulting 2D map segments 2710 and 2803 correspond to previously combined depth measurements 2602, 2701, 2705, 2706 and to depth measurements 2800, respectively. The processor constructs 2D map segment 2805 from the combination of 2D map segments 2710 and 2803 bounded by the outermost dashed lines of 2711 and 2804. The camera takes depth measurements 2800 within overlapping field of view 2801. The processor compares depth measurements 2800 to previously taken depth measurements 2706 to identify overlapping depth measurements bounded by the innermost dashed lines of 2711 and 2804. The processor uses one or more of the methods for comparing depth measurements and identifying an area of overlap described above. The processor estimates new depth measurements for the overlapping depth measurements using one or more of the combination methods described above. To construct larger map segment 2805, the processor combines previously constructed 2D map segment 2710 and 2D map segment 2803 by using overlapping depth measurements, bound by innermost dashed lines of 2711 and 2804, as attachment points. The processor also expands recognized area 2712 within which robot 2601 operates to recognized area 2808 of working environment 2604 bounded by map segment 2805 and dashed line 2809.

[0198] FIG. 29A illustrates robot 2601 rotating in direction 2900 as it continues to perform work within working environment 2604. The processor expanded recognized area 308 to area 2901 bound by wall 2605 and dashed line 2902. Camera 2600 takes depth measurements 2903 from camera 2600 to object 2605 within field of view 2904 overlapping with preceding depth measurements 2905 taken within field of view 2906. Depth measurements 2907 represent overlap between previously taken depth measurements 2905 and depth measurements 2903. FIG. 29B illustrates expanded map segment 2908 and expanded recognized area 2909 resulting from the processor combining depth measurements 2903 and 2905 at overlapping depth measurements 2907. This method is repeated as camera 2600 takes depth measurements within consecutively overlapping fields of view as robot 2601 moves within the environment and the processor combines the depth measurements at overlapping points until a 2D map of the environment is constructed.

[0199] FIG. 30 illustrates an example of a complete 2D map 3000 with bound area 3001. The processor of robot 2601 constructs map 3000 by combining depth measurements taken within consecutively overlapping fields of view of camera 2600. 2D map 3000 can, for example, be used by robot 2601 with mounted depth camera 2600 to autonomously navigate throughout the working environment during operation. In some embodiments, the robot is in a position where observation of the environment by sensors is limited. This may occur when, for example, the robot is positioned at one end of an environment and the environment is very large. In such a case, the processor of the robot constructs a temporary partial map of its surroundings as it moves towards the center of the environment where its sensors are capable of observing the environment. This is illustrated in FIG. 31A, where robot 2601 is positioned at a corner of large room 3100, approximately 20 centimeters from each wall. Observation of the environment by sensors is limited due to the size of room 3100 wherein field of view 3101 of the sensor does not capture any features of environment 3100. A large room, such as room 3100, may be 8 meters long and 6 meters wide for example. The processor of robot 2601 creates a temporary partial map using sensor data as it moves towards center 3102 of room 3100 in direction 3103. In FIG. 31B robot 2601 is shown at the center of room 3100 where sensors are able to observe features of environment 3100.

[0200] Feature and location maps as described herein are understood to be the same. For example, in some embodiments a feature-based map includes multiple location maps, each location map corresponding with a feature and having a rigid coordinate system with origin at the feature. Two vectors X and X′, correspond to rigid coordinate systems S and S′ respectively, each describe a different feature in a map. The correspondences of each feature may be denoted by C and C′, respectively. Correspondences may include, angle and distance, among other characteristics. If vector X is stationary or uniformly moving relative to vector X′, the processor of the robot may assume that a linear function U(X′) exists that may transform vector X′ to vector X and vice versa, such that a linear function relating vectors measured in any two rigid coordinate systems exists.

[0201] In some embodiments, the processor determines transformation between the two vectors measured. In some embodiments, the processor uses Galilean Group Transformation to determine the transformations between the two vectors, each measured relative to a different coordinate system. Galilean transformation may be used to transform between coordinates of two coordinate systems that only differ by constant relative motion. These transformations combined with spatial rotations and translations in space and time form the inhomogeneous Galilean Group, for which the equations are only valid at speeds much less than the speed of light. In some embodiments, the processor uses the Galilean Group for transformation between two vectors X and X′, measured relative to coordinate systems S and S′, respectively, the coordinate systems with spatial origins coinciding at t=t′=0 and in uniform relative motion in their common directions.

[0202] In some embodiments, the processor determines the transformation X′=RX+a+vt between vector X′ measured relative to coordinate system 5′ and vector X measured relative to coordinate system S to transform between coordinate systems, wherein R is a rotation matrix acting on vector X, X is a vector measured relative to coordinate system S, X′ is a vector measured relative to coordinate system 5′, a is a vector describing displacement of coordinate system 5′ relative to coordinate system S, ν is a vector describing uniform velocity of coordinate system 5′ and t is the time. After displacement, the time becomes t′=t+s where s is the time over which the displacement occurred.

[0203] If T₁=T₁ (R₁; a₁; ν₁; s₁) and T₂=T₂ (R₁; a₁; ν₁; s₁) denote a first and second transformation, the processor of the robot may apply the first transformation to vector X at time t resulting in T₁{X, t}={X′,t′} and apply the second transformation to resulting vector X′ at time t′ giving T₂{X′, t′}={X″, t″}. Assuming T₃=T₂T₁, wherein the transformations are applied in reverse order, is the only other transformation that yields the same result of {X″, t″}, then the processor may denote the transformations as T₃ {X, t}={X″, t″}. The transformation may be determined using X″=R₂ (R₁X+a₁+ν₁t)+a₂+ν₂ (t+s₁) and t″=t+s₁+s₂, wherein (R₁X+a₁+ν₁t) represents the first transformation T₁{X, t}={X′, t′}. Further, R₃=R₂R₁, a₃=a₂+R₂+12₂s₁, ν₃=ν₂+R₂ν₁, and s₃=s₂+s₁ hold true.

[0204] In some embodiments, the Galilean Group transformation is three dimensional, there are ten parameters used in relating vectors X and X′. There are three rotation angles, three space displacements, three velocity components and one time component, with the three rotation matrices

[0205] $R_1\left(\theta \right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \theta & -\sin \theta \\ 0& \sin \theta & \cos \theta \end{array}\right],R_2\left(\theta \right)=\left[\begin{array}{ccc}\cos \theta & 0& \sin \theta \\ 0& 1& 0\\ -\sin \theta & 0& \cos \theta \end{array}\right],$
and

[0206] $R_3\left(\theta \right)=\left[\begin{array}{c}\begin{array}{c}\cos \theta \\ \sin \theta \end{array}\\ 0\end{array}\begin{array}{c}\begin{array}{c}-\mathrm{sin\theta }\\ \cos \theta \end{array}\\ 0\end{array}\begin{array}{c}\begin{array}{c}0\\ 0\end{array}\\ 1\end{array}\right].$
The vector X and X′ may for example be position vectors with components (x, y, z) and (x′, y′, z′) or (x, y, θ) and (x′, y′, θ′), respectively. The method of transformation described herein allows the processor to transform vectors measured relative to different coordinate systems and describing the environment to be transformed into a single coordinate system.

[0207] In some embodiments, the processor of the robot uses sensor data to estimate its location within the environment prior to beginning and during the mapping process. In some embodiments, sensors of the robot capture data and the processor initially estimates the location of the robot based on the data and measured movement (e.g., using devices such as a gyroscope, optical encoder, etc.) of the robot. As more data is collected, the processor increases the confidence in the estimated location of the robot, and when movement occurs the processor decreases the confidence due to noise in measured movement.

[0208] In some embodiments, IMU measurements in a multi-channel stream indicative of acceleration along three or six axes may be integrated over time to infer a change in pose of the robot, e.g., with a Kalman filter. In some cases, the change in pose may be expressed as a movement vector in the frame of reference of the room through which the robot moves. Some embodiments may localize the robot or map the room based on this movement vector (and contact sensors in some cases) even if the image sensor is inoperative or degraded. In some cases, IMU measurements may be combined with image-based (or other exteroceptive) mapping data in a map or localization determination, e.g., with techniques like those described in Chen et. al “Real-time 3D mapping using a 2D laser scanner and IMU-aided visual SLAM,” 2017 IEEE International Conference on Real-time Computing and Robotics (RCAR), DOI: 10.1109/RCAR.2017.8311877, or in Ye et. al, LiDAR and Inertial Fusion for Pose Estimation by Non-linear Optimization, arXiv:1710.07104 [cs.RO], the contents of each of which are hereby incorporated by reference. Or in some cases, data from one active sensor may be used at a time for localization or mapping, and the other sensor may remain passive, e.g., sensing data, but that data may not be used for localization or mapping while the other sensor is active. Some embodiments may maintain a buffer of sensor data from the passive sensor (e.g., including measurements over a preceding duration, like one second or ten seconds), and upon failover from the active sensor to the passive sensor, which may then become active, some embodiments may access the buffer to infer a current position or map features based on both currently sensed data and buffered data. In some embodiments, the buffered data may be calibrated to the location or mapped features from the formerly active sensor, e.g., with the above-described sensor fusion techniques.

[0209] In embodiments, the constructed map of the robot may only be valid with accurate localization of the robot. For example, in FIG. 32, accurate localization of robot 3200 at location 3201 with position x₁, y₁ may result in map 3202 while inaccurate localization of robot 3200 at location 3203 with position x₂, y₂ may result in inaccurate map 3204 wherein perimeters of the map incorrectly appearing closer to robot 3200 as robot 3200 is localized to incorrect location 3203. To eliminate or reduce such occurrences, in some embodiments, the processor constructs a map for each or a portion of possible locations of robot 3200 and evaluates the alternative scenarios of possible locations of robot 3200 and corresponding constructed maps of such locations. The processor determines the number of alternative scenarios to evaluate in real-time or it is predetermined. In some embodiments, each new scenario considered adds a new dimension to the environment of robot 3200. Over time, the processor discards less likely scenarios. For example, if the processor considers a scenario placing robot 3200 at the center of a room and yet robot 3200 is observed to make contact with a perimeter, the processor determines that the considered scenario is an incorrect interpretation of the environment and the corresponding map is discarded. In some embodiments, the processor substitutes discarded scenarios with more likely scenarios or any other possible scenarios. In some embodiments, the processor uses a Fitness Proportionate Selection technique wherein a fitness function is used to assign a fitness to possible alternative scenarios and the fittest locations and corresponding maps survive while those with low fitness are discarded. In some embodiments, the processor uses the fitness level of alternative scenarios to associate a probability of selection with each alternative scenario that may be determined using the fitness function

[0210] $p_i=\frac{f_i}{\sum _{j=1}^N{f}_j},$
wherein ƒ₁ is the fitness of alternative scenario i of N possible scenarios and p_i is the probability of selection of alternative scenario i. In some embodiments, the processor is less likely to eliminate alternative scenarios with higher fitness level from the alternative scenarios currently considered. In some embodiments, the processor interprets the environment using a combination of a collection of alternative scenarios with high fitness level.

[0211] In some embodiments, the movement pattern of the robot during the mapping process is a boustrophedon movement pattern. This can be advantageous for mapping the environment. For example, if the robot begins in close proximity to a wall of which it is facing and attempts to map the environment by rotating 360 degrees in its initial position, areas close to the robot and those far away may not be observed by the sensors as the areas surrounding the robot are too close and those far away are too far. Minimum and maximum detection distances may be, for example, 30 and 400 centimeters, respectively. Instead, in some embodiments, the robot moves backwards (i.e., opposite the forward direction as defined below) away from the wall by some distance and the sensors observe areas of the environment that were previously too close to the sensors to be observed. The distance of backwards movement is, in some embodiments, not particularly large, it may be 40, 50, or 60 centimeters for example. In some cases, the distance backward is larger than the minimal detection distance. In some embodiments, the distance backward is more than or equal to the minimal detection distance plus some percentage of a difference between the minimal and maximal detection distances of the robot's sensor, e.g., 5%, 10%, 50%, or 80%.

[0212] The robot, in some embodiments, (or sensor thereon if the sensor is configured to rotate independently of the robot) then rotates 180 degrees to face towards the open space of the environment. In doing so, the sensors observe areas in front of the robot and within the detection range. In some embodiments, the robot does not translate between the backward movement and completion of the 180 degree turn, or in some embodiments, the turn is executed while the robot translates backward. In some embodiments, the robot completes the 180 degree turn without pausing, or in some cases, the robot may rotate partially, e.g., degrees, move less than a threshold distance (like less than 10 cm), and then complete the other 90 degrees of the turn.

[0213] References to angles should be read as encompassing angles between plus or minus 20 degrees of the listed angle, unless another tolerance is specified, e.g., some embodiments may hold such tolerances within plus or minus 15 degrees, 10 degrees, 5 degrees, or 1 degree of rotation. References to rotation may refer to rotation about a vertical axis normal to a floor or other surface on which the robot is performing a task, like cleaning, mapping, or cleaning and mapping. In some embodiments, the robot's sensor by which a workspace is mapped, at least in part, and from which the forward direction is defined, may have a field of view that is less than 360 degrees in the horizontal plane normal to the axis about which the robot rotates, e.g., less than 270 degrees, less than 180 degrees, less than 90 degrees, or less than 45 degrees. In some embodiments, mapping may be performed in a session in which more than 10%, more than 50%, or all of a room is mapped, and the session may start from a starting position, is where the presently described routines start, and may correspond to a location of a base station or may be a location to which the robot travels before starting the routine.

[0214] The robot, in some embodiments, then moves in a forward direction (defined as the direction in which the sensor points, e.g., the centerline of the field of view of the sensor) by some first distance allowing the sensors to observe surroundings areas within the detection range as the robot moves. The processor, in some embodiments, determines the first forward distance of the robot by detection of an obstacle by a sensor, such as a wall or furniture, e.g., by making contact with a contact sensor or by bringing the obstacle closer than the maximum detection distance of the robot's sensor for mapping. In some embodiments, the first forward distance is predetermined or in some embodiments the first forward distance is dynamically determined, e.g., based on data from the sensor indicating an object is within the detection distance.

[0215] The robot, in some embodiments, then rotates another 180 degrees and moves by some second distance in a forward direction (from the perspective of the robot), returning back towards its initial area, and in some cases, retracing its path. In some embodiments, the processor may determine the second forward travel distance by detection of an obstacle by a sensor, such moving until a wall or furniture is within range of the sensor. In some embodiments, the second forward travel distance is predetermined or dynamically determined in the manner described above. In doing so, the sensors observe any remaining undiscovered areas from the first forward distance travelled across the environment as the robot returns back in the opposite direction. In some embodiments, this back and forth movement described is repeated (e.g., with some amount of orthogonal offset translation between iterations, like an amount corresponding to a width of coverage of a cleaning tool of the robot, for instance less than 100% of that width, 95% of that width, 90% of that width, 50% of that width, etc.) wherein the robot makes two 180 degree turns separated by some distance, such that movement of the robot is a boustrophedon pattern, travelling back and forth across the environment. In some embodiments, the robot may not be initially facing a wall of which it is in close proximity with. The robot may begin executing the boustrophedon movement pattern from any area within the environment. In some embodiments, the robot performs other movement patterns besides boustrophedon alone or in combination.

[0216] In other embodiments, the boustrophedon movement pattern (or other coverage path pattern) of the robot during the mapping process differs. For example, in some embodiments, the robot is at one end of the environment, facing towards the open space. From here, the robot moves in a first forward direction (from the perspective of the robot as defined above) by some distance then rotates 90 degrees in a clockwise direction. The processor determines the first forward distance by which the robot travels forward by detection of an obstacle by a sensor, such as a wall or furniture. In some embodiments, the first forward distance is predetermined (e.g., and measured by another sensor, like an odometer or by integrating signals from an inertial measurement unit). The robot then moves by some distance in a second forward direction (from the perspective of the room, and which may be the same forward direction from the perspective of the robot, e.g., the direction in which its sensor points after rotating); and rotates another 90 degrees in a clockwise direction. The distance travelled after the first 90-degree rotation may not be particularly large and may be dependent on the amount of desired overlap when cleaning the surface. For example, if the distance is small (e.g., less than the width of the main brush of a robotic vacuum), as the robot returns back towards the area it began from, the surface being cleaned overlaps with the surface that was already cleaned. In some cases, this may be desirable. If the distance is too large (e.g., greater than the width of the main brush) some areas of the surface may not be cleaned. For example, for small robots, like a robotic vacuum, the brush size typically ranges from 15-30 cm. If 50% overlap in coverage is desired using a brush with 15 cm width, the travel distance is 7.5 cm. If no overlap in coverage and no coverage of areas is missed, the travel distance is 15 cm and anything greater than 15 cm would result in coverage of area being missed. For larger commercial robots brush size can be between 50-60 cm. The robot then moves by some third distance in forward direction back towards the area of its initial starting position, the processor determining the third forward distance by detection of an obstacle by a sensor, such as wall or furniture. In some embodiments, the third forward distance is predetermined. In some embodiments, this back and forth movement described is repeated wherein the robot repeatedly makes two 90-degree turns separated by some distance before travelling in the opposite direction, such that movement of the robot is a boustrophedon pattern, travelling back and forth across the environment. In other embodiments, the directions of rotations are opposite to what is described in this exemplary embodiment. In some embodiments, the robot may not be initially facing a wall of which it is in close proximity. The robot may begin executing the boustrophedon movement pattern from any area within the environment. In some embodiments, the robot performs other movement patterns besides boustrophedon alone or in combination.

[0217] FIGS. 33A-33D illustrate an example of a boustrophedon movement pattern of the robot. In FIG. 33A robot 3300 begins near wall 3301, docked at its charging or base station 3302. Robot 3300 rotates 360 degrees in its initial position to attempt to map environment 3303, however, areas 3304 are not observed by the sensors of robot 3300 as the areas surrounding robot 3300 are too close, and the areas at the far end of environment 3303 are too far to be observed. Minimum and maximum detection distances may be, for example, 30 and 400 centimeters, respectively. Instead, in FIG. 33B, robot 3300 initially moves backwards in direction 3305 away from charging or base station 3302 by some distance 3306 where areas 3307 are observed. Distance 3306 is not particularly large, it may be 40 centimeters, for example. In FIG. 33C, robot 3300 then rotates 180 degrees in direction 3308 resulting in observed areas 3307 expanding. Areas immediately to either side of robot 3300 are too close to be observed by the sensors while one side is also unseen, the unseen side depending on the direction of rotation. In FIG. 33D, robot 3300 then moves in forward direction 3309 by some distance 3310, observed areas 3307 expanding further as robot 3300 explores undiscovered areas. The processor of robot 3300 determines distance 3310 by which robot 3300 travels forward by detection of an obstacle, such as wall 3311 or furniture or distance 3310 is predetermined. In FIG. 33E, robot 3300 then rotates another 180 degrees in direction 3308. In FIG. 33F, robot 3300 moves by some distance 3312 in forward direction 3313 observing remaining undiscovered areas. The processor determines distance 3312 by which the robot 3300 travels forward by detection of an obstacle, such as wall 3301 or furniture or distance 3312 is predetermined. The back and forth movement described is repeated wherein robot 3300 makes two 180 degree turns separated by some distance, such that movement of robot 3300 is a boustrophedon pattern, travelling back and forth across the environment while mapping. In other embodiments, the direction of rotations may be opposite to what is illustrated in this exemplary embodiment.

[0218] FIGS. 34A-34D illustrate another embodiment of a boustrophedon movement pattern of the robot during the mapping process. FIG. 34A illustrates robot 3300 beginning the mapping process facing wall 3400, when for example, it is docked at charging or base station 3401. In such a case, robot 3300 initially moves in backwards direction 3402 away from charging station 3401 by some distance 3403. Distance 3403 is not particularly large, it may be 40 centimeters for example. In FIG. 34B, robot 3300 rotates 180 degrees in direction 3404 such that robot 3300 is facing into the open space of environment 3405. In FIG. 34C, robot 3300 moves in forward direction 3406 by some distance 3407 then rotates 90 degrees in direction 3404. The processor determines distance 3407 by which robot 3300 travels forward by detection of an obstacle, such as wall 3408 or furniture or distance 3407 is predetermined. In FIG. 34D, robot 3300 then moves by some distance 3409 in forward direction 3410 and rotates another 90 degrees in direction 3404. Distance 3409 is not particularly large and depends on the amount of desired overlap when cleaning the surface. For example, if distance 3409 is small (e.g., less than the width of the main brush of a robotic vacuum), as robot 3300 returns in direction 3412, the surface being cleaned may overlap with the surface that was already cleaned when robot 3300 travelled in direction 3406. In some cases, this may be desirable. If distance 3409 is too large (e.g., greater than the width of the main brush) some areas of the surface may not be cleaned. For example, for small robots, like a robotic vacuum, the brush size typically ranges from 15-30 cm. If 50% overlap in coverage is desired using a brush with 15 cm width, the travel distance is 7.5 cm. If no overlap in coverage and no coverage of areas is missed, the travel distance is 15 cm and anything greater than 15 cm would result in coverage of area being missed. For larger commercial robots brush size can be between 50-60 cm. Finally, robot 3300 moves by some distance 3411 in forward direction 3412 towards charging station 3401. The processor determines distance 3411 by which robot 3300 travels forward may be determined by detection of an obstacle, such as wall 3400 or furniture or distance 3411 is predetermined. This back and forth movement described is repeated wherein robot 3300 repeatedly makes two 90-degree turns separated by some distance before travelling in the opposite direction, such that movement of robot 3300 is a boustrophedon pattern, travelling back and forth across the environment while mapping. Repeated movement 3413 is shown in FIG. 34D by dashed lines. In other embodiments, the direction of rotations may be opposite to what is illustrated in this exemplary embodiment.

[0219] FIG. 35 illustrates a flowchart describing embodiments of a path planning method of a robot 3500, 3501, 3502 and 3503 corresponding with steps performed in some embodiments.

[0220] In some embodiments, the map of the area, including but not limited to doorways, sub areas, perimeter openings, and information such as coverage pattern, room tags, order of rooms, etc. is available to the user through a graphical user interface (GUI) such as a smartphone, computer, tablet, dedicated remote control, or any device that may display output data from the robot and receive inputs from a user. Through the GUI, a user may review, accept, decline, or make changes to, for example, the map of the environment and settings, functions and operations of the robot within the environment, which may include, but are not limited to, type of coverage algorithm of the entire area or each subarea, correcting or adjusting map boundaries and the location of doorways, creating or adjusting subareas, order of cleaning subareas, scheduled cleaning of the entire area or each subarea, and activating or deactivating tools such as UV light, suction and mopping. User inputs are sent from the GUI to the robot for implementation. Data may be sent between the robot and the user interface through one or more network communication connections. Any type of wireless network signals may be used, including, but not limited to, Wi-Fi signals, or Bluetooth signals. These techniques are further described in U.S. patent application Ser. Nos. 15/949,708 and 15/272,752, the entirety of each of which is incorporated herein by reference.

[0221] In some embodiments, the processor may manipulate the map by cleaning up the map for navigation purposes or aesthetics purposes (e.g., displaying the map to a user). For example, FIG. 36A illustrates a perimeter 3600 of an environment that may not be aesthetically pleasing to a user. FIG. 36B illustrates an alternative version of the map illustrated in FIG. 36A wherein the perimeter 3601 may be more aesthetically pleasing to the user. In some embodiments, the processor may use a series of techniques, a variation of each technique, and/or a variation in order of applying the techniques to reach the desired outcome in each case. For example, FIG. 37A illustrates a series of measurements 3700 to perimeter 3701 of an environment. In some cases, it may be desirable that the perimeter 3701 of the environment is depicted. In embodiments, different methods may be used in processing the data to generate a perimeter line. In some embodiments, the processor may generate a line from all the data points using least square estimation, such as in FIG. 37A. In some embodiments, the processor may determine the distances from each point to the line and may select local maximum and minimum L2 norm values. FIG. 37B illustrates the series of measurements 3700 to line 3701 generated based on least square estimation of all data points and selected local maximum and minimum L2 norm values 3702. In some embodiments, the processor may connect local maximum and minimum L2 norm values. For example, FIG. 37C illustrates local maximum and minimum L2 norm values 3702 connected to each other. In some embodiments, the connected local maximum and minimum L2 norm values may represent the perimeter of the environment. FIG. 37D illustrates a possible depiction of the perimeter 3703 of the environment.

[0222] In another method, the processor may initially examine a subset of the data. For example, FIG. 38A illustrates data points 3800. Initially, the processor may examine data points falling within columns one to three or area 3801. In some embodiments, the processor may fit a line to the subset of data using, for example, least square method. FIG. 38B illustrates a line 3802 fit to data points falling within columns one to three. In some embodiments, the processor may examine data points adjacent to the subset of data and may determine whether the data points belong with the same line fitted to the subset of data. For example, in FIG. 38C, the processor may consider data points falling within column four 3803 and may determine if the data points belong with the line 3802 fitted to the data points falling with columns one to three. In some embodiments, the processor may repeat the process of examining data adjacent to the last set of data points examined. For example, after examining data points falling with column four in FIG. 38C, the processor may examine data points falling with column five. In some embodiments, other variations of this technique may be used. For example, the processor may initially examine data falling within the first three columns, then may examine the next three columns. The processor may compare a line fitted to the first three columns to a line fitted to the next three columns. This variation of the technique may result in a perimeter line such as that illustrated in FIG. 39. In another variation, the processor examines data points falling within the first three columns, then examines data points falling within another three columns, some of which overlap with the first three columns. For example, the first three columns may be columns one to three and the other three columns may be columns three to five or two to four. The processor may compare a line fitted to the first three columns to a line fitted to the other three columns. In other embodiments, other variations may be used.

[0223] In another method, the processor may choose a first data point A and a second data point B from a set of data points. In some embodiments, data point A and data point B may be next to each other or close to one another. In some embodiments, the processor may choose a third data point C from the set of data points that is spatially positioned in between data point A and data point B. In some embodiments, the processor may connect data point A and data point B by a line. In some embodiments, the processor may determine if data point C fits the criteria of the line connecting data points A and B. In some embodiments, the processor determines that data points A and B within the set of data points are not along a same line. For example, FIG. 40 illustrates a set of data points 4000, chosen data points A, B, and C, and line 4001 connecting data point A and B. Since data point C does not fit criteria of lines 4001, it may be determined that data points A and B within the set of data point 4000 do not fall along a same line. In another variation, the processor may choose a first data point A and a second data point B from a set of data points and may connect data points A and B by a line. In some embodiments, the processor may determine a distance between each data point of the set of data points to the line connecting data points A and B. In some embodiments, the processor may determine the number of outliers and inliers. In some embodiments, the processor may determine if data points A and B fall along the same line based on the number of outliers and inliers. In some embodiments, the processor may choose another two data points C and D if the number of outliers or the ratio of outliers to inliers is greater than a predetermined threshold and may repeat the processor with data points C and D. FIG. 41A illustrates a set of data points 4100, data points A and B and line 4101 connecting data points A and B. The processor determines distances 4102 from each of the data points of the set of data points 4100 to line 4101. The processor determines the number of data points with distances falling within region 4103 as the number of inlier data points and the number of data points with distances falling outside of region 4103 as the number of outlier points. In this example, there are too many outliers. Therefore, FIG. 41B illustrates another two selected data points C and D. The process is repeated and less outliers are found in this case as there are less data points with distances 4104 falling outside of region 4105. In some embodiments, the processor may continue to choose another two data points and repeat the process until a minimum number of outliers is found or the number of outliers or the ratio of outliers to inliers is below a predetermined threshold. In some embodiments, there may be too may data points within the set of data points to select data points in sets of two. In some embodiments, the processor may probabilistically determine the number of data points to select and check based on the accuracy or minimum probability required. For example, the processor may iterate the method 20 times to achieve a 99% probability of success. Any of the methods and techniques described may be used independently or sequentially, one after another, or may be combined with other methods and may be applied in different orders.

[0224] In some embodiments, the processor may use image derivative techniques. Image derivative techniques may be used with data provided in various forms and are not restricted to being used with images. For example, image derivative techniques may be used with an array of distance readings (e.g., a map) or other types of readings just as well work well with a combination of these methods. In some embodiments, the processor may use a discrete derivative as an approximation of a derivative of an image I. In some embodiments, the processor determines a derivative in an x-direction for a pixel x₁ as the difference between the value of pixel x₁ and the values of the pixels to the left and right of the pixel x₁. In some embodiments, the processor determines a derivative in a y-direction for a pixel y₁ as the difference between the value of pixel y₁ and the values of the pixels above and below the pixel y_i. In some embodiments, the processor determines an intensity change I_x and I_y for a grey scale image as the pixel derivatives in the x- and y-directions, respectively. In some embodiments, the techniques described may be applied to color images. Each RGB of a color image may add an independent pixel value. In some embodiments, the processor may determine derivatives for each of the RGB or color channels of the color image. More colors and channels may be used for better quality. In some embodiments, the processor determines an image gradient ∇I, a 2D vector, as the derivative in the x- and y-direction. In some embodiments, the processor may determine a gradient magnitude, |∇I|=√{square root over ((I_x²+I_y²))}, which may indicate the strength of intensity change. In some embodiments, the processor may determine a gradient angle, α=arctan 2(I_x, I_y), which may indicate the angle at which the image intensity change is more dominant. Since the derivatives of an image are discrete values, there is no mathematical derivative, therefore the processor may employ approximations for the derivatives of an image using discrete differentiation operators. For example, the processor may use the Prewitt operator which convolves the image with a small, separable, and integer valued filter in horizontal and vertical directions. The Prewitt operator may use two 3 x3 kernels,

[0225] $\left[\begin{array}{c}\begin{array}{c}-1\\ -1\end{array}\\ -1\end{array}\begin{array}{c}0\\ \begin{array}{c}0\\ 0\end{array}\end{array}\begin{array}{c}1\\ \begin{array}{c}1\\ 1\end{array}\end{array}\right]\mathrm{and}\left[\begin{array}{c}\begin{array}{c}-1\\ 0\end{array}\\ 1\end{array}\begin{array}{c}\begin{array}{c}-1\\ 0\end{array}\\ 1\end{array}\begin{array}{c}-1\\ \begin{array}{c}0\\ 1\end{array}\end{array}\right],$
that may be convolved with the original image I to determine approximations of the derivatives in an x- and y-direction, i.e.,

[0226] $I_x=I*\left[\begin{array}{c}\begin{array}{c}-1\\ -1\end{array}\\ -1\end{array}\begin{array}{c}0\\ \begin{array}{c}0\\ 0\end{array}\end{array}\begin{array}{c}1\\ \begin{array}{c}1\\ 1\end{array}\end{array}\right]$
and

[0227] $I_y=I*\left[\begin{array}{c}\begin{array}{c}-1\\ 0\end{array}\\ 1\end{array}\begin{array}{c}\begin{array}{c}-1\\ 0\end{array}\\ 1\end{array}\begin{array}{c}-1\\ \begin{array}{c}0\\ 1\end{array}\end{array}\right].$
In another example, the processor may use the Sobel-Feldman operator, an isotropic 3×3 image gradient operator which at each point in the image returns either the corresponding gradient vector or the norm of the gradient vector, which convolves the image with a small, separable, and integer valued filter in horizontal and vertical directions. The Sobel-Feldman operator may use two 3 x3 kernels,

[0228] $\left[\begin{array}{c}\begin{array}{c}-1\\ -2\end{array}\\ -1\end{array}\begin{array}{c}0\\ \begin{array}{c}0\\ 0\end{array}\end{array}\begin{array}{c}1\\ \begin{array}{c}2\\ 1\end{array}\end{array}\right]$
and

[0229] $\left[\begin{array}{c}\begin{array}{c}-1\\ 0\end{array}\\ 1\end{array}\begin{array}{c}\begin{array}{c}-2\\ 0\end{array}\\ 2\end{array}\begin{array}{c}-1\\ \begin{array}{c}0\\ 1\end{array}\end{array}\right],$
that may be convolved with the original image I to determine approximations of the derivatives in an x- and y-direction, i.e., I_x=I*

[0230] $\left[\begin{array}{c}\begin{array}{c}-1\\ -2\end{array}\\ -1\end{array}\begin{array}{c}0\\ \begin{array}{c}0\\ 0\end{array}\end{array}\begin{array}{c}1\\ \begin{array}{c}2\\ 1\end{array}\end{array}\right]$
and

[0231] $I_y=I*\left[\begin{array}{c}\begin{array}{c}-1\\ 0\end{array}\\ 1\end{array}\begin{array}{c}\begin{array}{c}-2\\ 0\end{array}\\ 2\end{array}\begin{array}{c}-1\\ \begin{array}{c}0\\ 1\end{array}\end{array}\right].$
The processor may use other operators, such as Kayyali operator, Laplacian operator, and Robert Cross operator.

[0232] In some embodiments, the processor may use image denoising methods image in one or more processing steps to remove noise from an image while maintaining the integrity, detail, and structure of the. In some embodiments, the processor may determine the total variation of an image as the sum of the gradient norm, J(I)=∫|∇I|dxdy or J(I)=Σ_xy|∇I|, wherein the integral is taken over all pixels of the image. In some embodiments, the processor may use Gaussian filters to determine derivatives of an image, I_x=I*G_σx and I_y=I*G_σy, wherein G_σx and G_σy are the x and y derivatives of a Gaussian function G_σ with standard deviation a. In some embodiments, the processor may use total variation denoising or total variation regularization to remove noise while preserving edges. In some embodiments, the processor may determine a total variation norm of 2D signals y (e.g., images) using V(y)=Σ_i,j√{square root over (|y_i+1,j−y_i,j|²+|y_i,j+1−y_i,j|²)}, which is isotropic and not differentiable. In some embodiments, the processor may use an alternative anisotropic version, V(y)=Σ_i,j√{square root over (|y_i+1,j−y_i,j|²)}+√{square root over (|y_i,j+1−y_i,j|²)}=Σ_i,j|y_i+1,j−y_i,j|+|y_i,j+1−y_i,j|. In some embodiments, the processor may solve the standard total variation denoising problem

[0233] $\underset{y}{\min }\left[E\left(x,y\right)+\lambda V\left(y\right)\right],$
wherein E is the 2D L2 norm. In some embodiments, different algorithms may be used to solve the problem, such as prime dual method or split-Bergman method. In some embodiments, the processor may employ Rudin-Osher-Fatemi (ROF) denoising technique to a noisy image ƒ to determine a denoised image u over a 2D space. In some embodiments, the processor may solve the ROF minimization problem

[0234] $\underset{u\in \mathrm{BV}\left(\Omega \right)}{\min }{u}_{\mathrm{TV}\left(\Omega \right)}+\frac{\lambda }{2}{\int }_{\Omega }{\left(f-u\right)}^2\mathrm{dx},$
wherein BV(Ω) is the bounded variation over the domain Ω, TV (Ω) is the total variation over the doman, and λ is a penalty term. In some embodiments, u may be smooth and the processor may determine the total variation using ∥u∥_TV(Ω)=∫_Ω∥∇u∥dx and the minimization problem becomes

[0235] $\underset{u\in \mathrm{BV}\left(\Omega \right)}{\min }{\int }_{\Omega }{\left[\nabla u+\frac{\lambda }{2}\left(f-u\right)\right]}^2\mathrm{dx}.$
Assuming no time dependence, the Euler-Lagrange equation for minimization may provide the nonlinear elliptic partial differential equation

[0236] $\{\begin{array}{c}\nabla ·\left(\frac{\nabla u}{\nabla u}\right)+\lambda \left(f-u\right)=0,u\in \Omega \\ \frac{\partial u}{\partial n}=0,u\in \partial \Omega \end{array}.$
In some embodiments, the processor may instead solve the time-dependent version of the ROF problem,

[0237] $\frac{\partial u}{\partial n}=\nabla ·\left(\frac{\nabla u}{\nabla u}\right)+\lambda \left(f-u\right).$
In some embodiments, the processor may use other denoising techniques, such as chroma noise reduction, luminance noise reduction, anisotropic diffusion, Rudin-Osher-Fatemi, and Chambolle. Different noise processing techniques may provide different advantages and may be used in combination and in any order.

[0238] In some embodiments, the processor may determine correlation in x- and y-directions, C_(I1I2)xy=Σ_xyƒ(I₁(xy),I₂(xy)) between two neighborhoods, wherein points in a first image I₁ correspond with points in a second image I₂ and ƒ is a cross location function. In some embodiments, the processor takes the summation over all pixels in neighboring windows in x- and y-directions. In some embodiments, the size of neighboring windows may be a one-pixel radius, a two-pixel radius, or an n-pixels radius. In some embodiments, the window geometry may be a triangle, square, rectangle, or another geometrical shape. In some embodiments, the processor may use a transform to associate an image with another image by identifying points of similarities. Various transformation methods may be used (e.g., linear or more complex). For example, an affine map ƒ: A→B between two affine spaces A and B may be a map on the points that acts linearly on the vectors, wherein ƒ determines a linear transformation φ such that for any pair of points P, Q∈A, {right arrow over (ƒ(P)ƒ(Q))}=φ{right arrow over ((PQ))} or ƒ(Q)−ƒ(P)=φ(Q−P). Other interpretations may be used. For example, for an origin O∈A and when B denotes its image ƒ(O)∈B, then for any vector {right arrow over (x)}, ƒ: (O+{right arrow over (x)})→(B+φ({right arrow over (x)})). And a chosen origin O′∈B may be decomposed as an affine transformation g: A→B that sends O→O′, i.e., g: (O+{right arrow over (x)})→(O′+φ({right arrow over (x)})) followed by the translation by a vector {right arrow over (b)}={right arrow over (O′B)}. In this example, ƒ includes a translation and a linear map.

[0239] In some embodiments, the processor may employ unsupervised learning or clustering to organize unlabeled data into groups based on their similarities. Clustering may involve assigning data points to clusters wherein data points in the same cluster are as similar as possible. In some embodiments, clusters may be identified using similarity measures, such as distance. In some embodiments, the processor may divide a set of data points into clusters. For example, FIG. 42 illustrates a set of data points 4200 divided into four clusters 4201. In some embodiments, the processor may split or merge clusters. In some embodiments, the processor may use proximity or similarity measures. A similarity measure may be a real-valued function that may quantify similarity between two objects. In some embodiments, the similarity measure may be the inverse of distance metrics, wherein they are large in magnitude when the objects are similar and small in magnitude (or negative) when the objects are dissimilar. For example, the processor may use a similarity measure s(x_i, x_j) which may be large in magnitude if x_i, x_j are similar, or a dissimilarity (or distance) measure d(x_i, x_j) which may be small in magnitude if x_i, x_j are similar. This is visualized in FIG. 43. Examples of a dissimilarity measure include Euclidean distance,

[0240] $d\left(x_i,x_j\right)=\sqrt{\sum _{k=1}^d{\left(x_i^{\left(k\right)}-x_j^{\left(k\right)}\right)}^2},$
which is translation invariant, Manhattan distance,

[0241] $d\left(x_i,x_j\right)=\sum _{k=1}^d\left(x_i^{\left(k\right)}-x_j^{\left(k\right)}\right),$
which is an approximation to the Euclidean distance, Minkowski distance,

[0242] $d_p\left(x_i,x_j\right)=\sum _{k=1}^m{\left({\left(x_{ik}-x_{jk}\right)}^p\right)}^{\frac{1}{p}},$
wherein p is a positive integer. An example of a similarity measure includes Tanimoto similarity,

[0243] $T_s=\frac{\sum _{j=1}^k\left(a_j\times b_j\right)}{\sum _{j=1}^k{a}_j^2+\sum _{j=1}^k{b}_j^2-\sum _{j=1}^k{a}_j\times b_j},$
between two points a_j, b_j, with k dimensions. The Tanimoto similarity may only be applicable for a binary variable and ranges from zero to one, wherein one indicates a highest similarity. In some cases, Tanimoto similarity may be applied over a bit vector (where the value of each dimension is either zero or one) wherein the processor may use

[0244] $f\left(A,B\right)=\frac{A·B}{{A}^2+{B}^2-A·B}$
to determine similarity. This representation relies on A·B=Σ_iA_iB_i=Σ_iA_i∧B_i and |A|²=Σ_i=Σ_iA_i. Note that the properties of T_s do not necessarily apply to ƒ. In some cases, other variations of the Tanimoto similarity may be used. For example, a similarity ratio,

[0245] $T_s=\sum _i\frac{X_i\bigwedge Y_i}{\sum _i\left(X_i\bigvee Y_i\right)},$
wherein X and Y are bitmaps and X_i is bit i of X. A distance coefficient, T_d(X,Y)=log₂(T_s(X, Y)), based on the similarity ratio may also be used for bitmaps with non-zero similarity. Other similarity or dissimilarity measures may be used, such as RBF kernel in machine learning. In some embodiments, the processor may use a criterion for evaluating clustering, wherein a good clustering may be distinguished from a bad clustering. For example, FIG. 44 illustrates a bad clustering. In some embodiments, the processor may use a similarity measure that provides an n×n sized similarity matrix for a set of n data points, wherein the entry i,j may be the negative of the Euclidean distance between i and j or may me a more complex measure such as the Gaussian e

[0246] $\frac{{s_1-s_2}^2}{2{\sigma }^2}.$

[0247] In some embodiments, the processor may employ fuzzy clustering wherein each data point may belong to more than one cluster. In some embodiments, the processor may employ fuzzy c-means (FCM) clustering wherein a number of clusters are chosen, coefficients are randomly assigned to each data point for being in the clusters, and the process is repeated until the algorithm converges, wherein the change in the coefficients between two iterations is less than a sensitivity threshold. The process may further include determining a centroid for each cluster and determining the coefficient of each data point for being in the clusters. In some embodiments, the processor determines the centroid of a cluster using

[0248] $\begin{array}{cc}{c}_k=\frac{\sum _x{{\omega }_k\left(x\right)}^{m}x}{\sum _k{{\omega }_k\left(x\right)}^m},& \end{array}$
wherein a point x has a set of coefficients ω_k (x) giving the degree of being in the cluster k, wherein m is the hyperparameter that controls how fuzzy the cluster will be. In some embodiments, the processor may use an FCM algorithm that partitions a finite collection of n elements X={x₁, . . . , x_n} into a collection of c fuzzy clusters with respect to a given criterion. In some embodiments, given a finite set of data, the FCM algorithm may return a list of c cluster centers C={c₁, . . . , c₂} and a partition matrix W=ω_i,j∈[0, 1] for i=1, . . . , n and j=1, . . . , c, wherein each element ω_ij indicates the degree to which each element x_i belongs to cluster c_j. In some embodiments, the FCM algorithm minimizes the objective functions

[0249] $\underset{C}{\arg \min }\sum _{i=1}^n\sum _{j=1}^c{\omega }_{\mathrm{ij}}^m{x_i-c_j}^2,$
wherein

[0250] ${\omega }_{\mathrm{ij}}=\frac{1}{\sum _{k=1}^c{\left(\frac{x_i-c_j}{x_i-c_k}\right)}^{\frac{2}{m-1}}}.$
In some embodiments, the processor may use k-means clustering, which also minimizes the same objective function. The difference with c-means clustering is the additions of ω_ij and m∈R, for m≥1. A large m results in smaller ω_ij values as clusters are fuzzier, and when m=1, ω_ij converges to zero or one, implying crisp partitioning. For example, FIG. 45A illustrates one dimensional data points 4500 along an x-axis. The data may be grouped into two clusters. In FIG. 45B, a threshold 4501 along the x-axis may be chosen to group data points 4500 into clusters A and B. Each data point may have membership coefficient ω with a value of zero or one that may be represented along the y-axis. In fuzzy clustering, each data point may have may a membership to multiple clusters and the membership coefficient may be any value between zero and one. FIG. 45C illustrates fuzzy clustering of data points X00, wherein a new threshold 4502 and membership coefficients ω for each data point may be chosen based on the centroids of the clusters and a distance from each cluster centroid. The data point intersecting with the threshold 4502 belongs to both clusters A and B and has a membership coefficient of 0.4 for clusters A and B.

[0251] In some embodiments, the processor may use spectral clustering techniques. In some embodiments, the processor may use a spectrum (or eigenvalues) of a similarity matrix of data to reduce the dimensionality before clustering in fewer dimensions. In some embodiments, the similarity matrix may indicate the relative similarity of each pair of points in a set of data. For example, the similarity matrix for a set of data points may be a symmetric matrix A, wherein A_ij≥0 indicates a measure of similarity between data points with indices i and j. In some embodiments, the processor may use a general clustering method, such a k-means, on relevant eigenvectors of a Laplacian matrix of A. In some embodiments, the relevant eigenvectors are those corresponding to smallest several eigenvalues of the Laplacian except for the eigenvalue with a value of zero. In some embodiments, the processor determines the relevant eigenvectors as the eigenvectors corresponding to the largest several eigenvalues of a function of the Laplacian. In some embodiments, spectral clustering may be compared to partitioning a mass-spring system, wherein each mass may be associated with a data point and each spring stiffness may correspond to a weight of an edge describing a similarity of two related data points. In some embodiments, the eigenvalue problem of transversal vibration modes of a mass spring system may be the same as the eigenvalue problem of the graph Laplacian matric, L:=D−A, wherein D is the diagonal matrix D_ii=Σ_jA_ij. The masses tightly connected by springs move together from the equilibrium position in low frequency vibration modes, such that components of the eigenvectors corresponding to the smallest eigenvalues of the graph Laplacian may be used for clustering of the masses. In some embodiments, the processor may use normalized cuts algorithm for spectral clustering, wherein points may be partitioned into two sets (B₁, B₂) based on an eigenvector ν corresponding to the second smallest eigenvalue of the symmetric normalized Laplacian,

[0252] $L_{norm}:=I-D^{-\frac{1}{2}}A{D}^{-\frac{1}{2}}.$
Alternatively, the processor may determine the eigenvector corresponding to the largest eigenvalue of the random walk normalized adjacency matrix, P=D⁻¹A. In some embodiments, the processor may partition the data by determining a median m of the components of the smallest eigenvector ν and placing all data points whose component in ν is greater than m in B₁ and the rest in B₂. In some embodiments, the processor may use such an algorithm for hierarchical clustering by repeatedly partitioning subsets of data using the partitioning method described.

[0253] In some embodiments, the clustering techniques described may be used to obtain insight into data (which may be fine-tuned using other methods) with relatively low computational cost. However, in some cases, generic classification may be challenging as the initial number of classes may be unknown and a supervised learning algorithm may require the number of classes beforehand. In some embodiments, a classification algorithm may be provided with a fixed number of classes to which data may be grouped into, however, determining the fixed number of classes may be difficult. For example, upon examining FIG. 46A it may be determined that data points 4600 organized into four classes 4601 may result in a best outcome. Or that organizing data points 4600 into five classes 4602, as illustrated in FIG. 46B, may result in a good classification. However, for an unknown image or an unknown environment, determining the fixed number of classes beforehand is more challenging. Further, prior probabilities for each class P(ω_j) for j=1, 2, . . . may need to be known as well. In some embodiments, the processor may approximate how many of a total number of data points scanned belong to each class based on the angular resolution of sensors, the number of scans per second, and the angular displacement of the robot relative to the size of the environment. In some embodiments, the processor may assume class conditional probability densities P(x|ω_j, θ_j) are known for j=1, . . . , c. In some embodiments, the values of c parameter vectors θ₁, . . . , θ_c and class labels may be unknown. In some embodiments, the processor may use the mixture density function

[0254] $P\left(x|\theta \right)=\sum _{j=1}^{c}P\left(x|{\omega }_j,{\theta }_j\right)P\left({\omega }_j\right),$
wherein θ=(θ₁, . . . , θ_c)^t, conditional density P(x|ω_j, θ_j) is a component density, and priori P(ω_j) is a mixing parameter, to estimate the parameter vector θ. In some embodiments, the processor may draw samples from the mixture densities to estimate the parameter vector θ. In some embodiments, given that θ is known, the processor may decompose the mixture densities into components and may use a maximum a posteriori classifier on the derived densities. In some embodiments, for a set of data D={x₁, . . . , x_n} with n unlabeled data points independently drawn from a mixture density

[0255] $P\left(x|\theta \right)=\sum _{j=1}^{c}P\left(x|{\omega }_j,{\theta }_j\right)P\left({\omega }_j\right),$
wherein the parameter vector θ is unknown but fixed, the processor may determine the likelihood of the observed sample as the joint density P(D|θ)=Π_k=1ⁿP(x_k|θ). In some embodiments, the processor determines the maximum likelihood estimate {circumflex over (θ)} for θ as the value of θ that maximizes the probability of D given θ. In some embodiments, it may be assumed that the joint density P(D|θ) is differentiable from θ. In some embodiments, the processor may determine the logarithm of the likelihood,

[0256] $l=\sum _{k=1}^n\ln P\left(x_k|\theta \right),$
and the gradient of l with respect to

[0257] ${\theta }_i,{\nabla }_{{\theta }_i}l=\sum _{k=1}^n\frac{1}{P\left(x_k|\theta \right)}{\nabla }_{{\theta }_i}\left[\sum _{j=1}^{c}P\left(x_k|{\omega }_j,{\theta }_j\right)P\left({\omega }_j\right)\right].$
If θ_i and θ_j are independent and i≠j then

[0258] $P\left({\omega }_i|x_k,\theta \right)=\frac{P\left(x_k|{\omega }_i,{\theta }_i\right)P\left({\omega }_i\right)}{P\left(x_k|\theta \right)}$
and the processor may determine the gradient of the log likelihood using

[0259] ${\nabla }_{{\theta }_i}l=\sum _{k=1}^{n}P\left({\omega }_i|x_k,\theta \right){\nabla }_{{\theta }_i}\ln P\left(x_k|{\omega }_i,{\theta }_i\right).$
Since the gradient must vanish as the value of θ_i that maximizes l, the maximum likelihood estimate {circumflex over (θ)}_i must satisfy the conditions

[0260] $\sum _{k=1}^{n}P\left({\omega }_i|x_k,\theta \right){\nabla }_{{\theta }_i}\ln P\left(x_k|{\omega }_i,{\theta }_i\right)=0$
for i=1, . . . , c. In some embodiments, the processor finds the maximum likelihood solution among the solutions the equations for {circumflex over (θ)}_i. In some embodiments, the results may be generalized to include prior probabilities P(ω_i) among the unknown quantities. In such a case, the search for the maximum values of P(D|θ) extends over θ and P(ω_i), wherein P(ω_i)≥θ for i=1, . . . , c and

[0261] $\sum _{i=1}^{c}P\left({\omega }_i\right)=1.$
In some embodiments, {circumflex over (P)}(ω_i) may be the maximum likelihood estimate for P(ω_i) and {circumflex over (θ)}_i may be the maximum likelihood estimate for θ_i. If the likelihood function is differentiable and if {circumflex over (P)}(ω_i)≠0 for any i, then {circumflex over (P)}(ω_i) and {circumflex over (θ)}_i satisfy

[0262] $\hat{P}\left({\omega }_i\right)=\frac{1}{n}\sum _{k=1}^n\hat{P}\left({\omega }_i|x_k,\hat{\theta }\right)$
and

[0263] $\sum _{k=1}^n\hat{P}\left({\omega }_i|x_k,\hat{\theta }\right){\nabla }_{{\theta }_i}\ln P\left(x_k|{\omega }_i,{\hat{\theta }}_i\right)=0,$
wherein

[0264] $\hat{P}\left({\omega }_i|x_k,\hat{\theta }\right)=\frac{P\left(x_k|{\omega }_i,{\hat{\theta }}_i\right)\hat{P}\left({\omega }_i\right)}{\sum _{j=1}^{c}P\left(x_k|{\omega }_j,{\hat{\theta }}_i\right)\hat{P}\left({\omega }_j\right)}.$
This states that the maximum likelihood estimate of the probability of a category is the average over the entire data set of the estimate derived from each same, wherein each sample is weighted equally. The latter equation is related to Bayes Theorem, however the estimate for the probability for class ω_i depends on {circumflex over (θ)}_i and not the full {circumflex over (θ)} directly. Since {circumflex over (P)}≠0, and for the case wherein

[0265] $n=1,\sum _{k=1}^n\hat{P}\left({\omega }_i|x_k,\hat{\theta }\right){\nabla }_{{\theta }_i}\ln P\left(x_k|{\omega }_i,{\hat{\theta }}_i\right)=0$
states that the probability density is maximized as a function of θ_i.

[0266] In some embodiments, clustering may be challenging due to the continuous collection data that may differ at different instances and changes in the location from which data is collected. For example, FIG. 47A illustrates data points 4700 observed from a point of view 4701 of a sensor and FIG. 47B illustrates data points 4700 observed from a different point of view 4702 of the sensor. This exemplifies that data points 4700 appear differently depending on the point of view of the sensor. In some embodiments, the processor may use stability-plasticity trade-off to help in solving such challenges. The stability-plasticity dilemma is a known constraint for artificial neural systems as a neural network must learn new inputs from the environment without being disrupted by them. The neural network may require plasticity for the integration of new knowledge, but also stability to prevent forgetting previous knowledge. In some embodiments, too much plasticity may result in catastrophic forgetting, wherein a neural network may completely forget previously learned information when exposed to new information. Neural networks, such as backpropagation networks, may be highly sensitive to catastrophic forgetting because of highly distributed internal representations of the network. In such cases, catastrophic forgetting may be minimized by reducing the overlap among internal representations stored in the neural network. Therefore, when learning input patterns, such networks may alternate between them and adjust corresponding weights by small increments to correctly associate each input vector with the related output vector. In some embodiments, a dual-memory system, i.e., a short-term and a long-term memory, may be used to avoid catastrophic forgetting, wherein information may be initially consolidated on a short-term memory within a long-term memory. In some embodiments, too much stability may result in the entrenchment effect which may contribute to age-limited learning effects. In some embodiments, the entrenchment effect may be minimized by varying the loss of plasticity as a function of the transfer function and the error. In some embodiments, the processor may use Fahlman offset to modulate the plasticity of neural networks by adding a constant number to the derivative of the sigmoid function such that it does not go to zero and avoids the flat spots in the sigmoid function where weights may become entrenched.

[0267] In some embodiments, distance measuring devices used in observing the environment may have different field of views (FOVs) and angular resolutions may be used. For example, a depth sensor may provide depth readings within a FOV ranging from zero to 90 degrees with a one degree angular resolution. Another distance sensor may provide distance readings within a FOV ranging from zero to 180 degrees, with a 0.5 degrees angular resolution. In another case, a LIDAR may provide a 270 or 360 degree FOV.

[0268] In some embodiments, the immunity of a distance measuring device may be related to an illumination power emitted by the device and a sensitivity of a receiver of the device. In some instances, an immunity to ambient light may be defined by lux. For example, a LIDAR may have a typical immunity of 500 lux and a maximum immunity of 1500 lux. Another LIDAR may have a typical immunity of 2000 lux and a maximum immunity of 4500 lux. In some embodiments, scan frequency, given in Hz, may also influence immunity of distance measuring devices. For example, a LIDAR may have a minimum scan frequency of 4 Hz, typical scan frequency of 5 Hz, and a maximum scan frequency of 10 Hz. In some instances, Class I laser safety standards may be used to cap the power emitted by a transmitter. In some embodiments, a laser and optical lens may be used for the transmission and reception of a laser signal to achieve high frequency ranging. In some cases, laser and optical lens cleanliness may have some adverse effects on immunity as well. In some embodiments, the processor may use particular techniques to distinguish the reflection of illumination light from ambient light, such as various software filters. For example, once depth data is received it may be processed to distinguish the reflection of illumination light from ambient light.

[0269] In some embodiments, the center of the rotating core of a LIDAR used to observe the environment may be different than the center of the robot. In such embodiments, the processor may use a transform function to map the readings of the LIDAR sensor to the physical dimension of the robot. In some embodiments, the LIDAR may rotate clockwise or counterclockwise. In some embodiments, the LIDAR readings may be different depending on the motion of the robot. For example, the readings of the LIDAR may be different when the robot is rotating in a same direction as a LIDAR motor than when the robot is moving straight or rotating in an opposite direction to the LIDAR motor. In some instances, a zero angle of the LIDAR may not be the same as a zero angle of the robot.

[0270] In some embodiments, data may be collected using a proprioceptive sensor and an exteroceptive sensor. In some embodiments, the processor may use data from one of the two types of sensors to generate or update the map and may use data from the other type of sensor to validate the data used in generating or updating the map. In some embodiments, the processor may enact both scenarios, wherein the data of the proprioceptive sensor is used to validate the data of the exteroceptive sensor and vice versa. In some embodiments, the data collected by both types of sensors may be used in generating or updating the map. In some embodiments, the data collected by one type of sensor may be used in generating or updating a local map while data from the other type of sensor may be used for generating or updating a global map. In some embodiments, data collected by either type of sensor may include depth data (e.g., depth to perimeters, obstacles, edges, corners, objects, etc.), raw image data, or a combination.

[0271] In some embodiments, there may be possible overlaps in data collected by an exteroceptive sensor. In some embodiments, a motion filter may be used to filter out small jitters the robot may experience while taking readings with an image sensor or other sensors. FIG. 48 illustrates a flow path of an image, wherein the image is passed through a motion filter before processing. In some embodiments, the processor may vertically align captured images in cases where images may not be captured at an exact same height. FIG. 49A illustrates unaligned images 4900 due to the images being captured at different heights. FIG. 49B illustrates the images 4900 after alignments. In some embodiments, the processor detects overlap between data at a perimeter of the data. Such an example is illustrated in FIG. 50, wherein an area of overlap 5000 at a perimeter of the data 5001 is indicated by the arrow 5002. In some embodiments, the processor may detect overlap between data in other ways. An example of an alternative area of overlap 3403 between data 5001 is illustrated in FIG. 51. In some embodiments, there may be no overlap between data 5001 and the processor may use a transpose function to create a virtual overlap based on an optical flow or an inertia measurement. FIG. 52 illustrates a lack of overlap between data.

[0272] In some embodiments, the movement of the robot may be measured and tracked by an encoder, IMU, and/or optical tracking sensor (OTS) and images captured by an image sensor may be combined together to form a spatial representation based on overlap of data and/or measured movement of the robot. In some embodiments, the processor determines a logical overlap between data and does not represent data twice in a spatial representation output. For example, FIG. 53 illustrates a path 5300 of the robot and an amount of overlap 5301. In some embodiments, overlapping parts may be used for combining images, however, the spatial representation may only include one set (or only some sets) of the overlapping data or in other cases may include all sets of the overlapping data. In some embodiments, the processor may employ a convolution to obtain a single set of data from the two overlapping sets of data. In such cases, the spatial representation after collecting data during execution of the path 5300 in FIG. 53 may appear as in FIG. 54, as opposed to the spatial representation in FIG. 55 wherein spatial data is represented twice. During discovery, a path of the robot may overlap frequently, as in the example of FIG. 56, however, the processor may not use each of the overlapping data collected during those overlapping paths when creating the spatial representation.

[0273] In some embodiments, sensors of the robot used in observing the environment may have a limited FOV. In some embodiments, the FOV is 360 or 180 degrees. In some embodiments, the FOV of the sensor may be limited vertically or horizontally or in another direction or manner. In some embodiments, sensors with larger FOVs may be blind to some areas. In some embodiments, blind spots of robots may be provided with complementary types of sensors that may overlap and may sometimes provide redundancy. For example, a sonar sensor may be better at detecting a presence or a lack of presence of an obstacle within a wider FOV whereas a camera may provide a location of the obstacle within the FOV. In one example, a sensor of a robot with a 360 degree linear FOV may observe an entire plane of an environment up to the nearest objects (e.g., perimeters or furniture) at a single moment, however some blind spots may exist. While a 360 degree linear FOV provides an adequate FOV in one plane, the FOV may have vertical limitations. FIG. 57 illustrates a robot 5700 observing an environment 5701, with blind spot 5702 that sensors of robot 5700 cannot observe. With a limited FOV, there may be areas that go unobserved as the robot moves. For example, FIG. 58 illustrates robot 5800 and fields of view 5801 and 5802 of a sensor of the robot as the robot moves from a first position to a second position, respectively. Because of the small FOV or blind spot, object 5803 within area 5804 goes unnoticed as the robot moves from observing FOV 5801 to 5802. In some cases, the processor of the robot fits a line 5805 and 5806 to the data captured in FOVs 5801 and 5802, respectively. In some embodiments, the processor fits a line 5807 to the data captured in FOVs 5801 and 5802 that aligns with lines 5805 and 5806, respectively. In some embodiments, the processor aligns the data observed in different FOVs to generate a map. In some embodiments, the processor connects lines 5805 and 5806 by a connecting line or by a line fitted to the data captured in FOVs 5801 and 5802. In some embodiments, the line connecting lines 5805 and 5806 has lower certainty as it corresponds to an unobserved area 5804. For example, FIG. 59 illustrates estimated perimeter 5900, wherein perimeter line 5900 is fitted to the data captured in FOVs 5801 and 5802. The portion of perimeter line 5900 falling within area 5804, to which sensors of the robot were blind, may be estimated based on a line that connects lines 5805 and 5806 as illustrated in FIG. 58. However, since area 5804 is unobserved by sensors of the robot, the processor is less certain of the portion of the perimeter 5900 falling within area 5804. For example, the processor is uncertain if the portion of perimeter 5900 falling within area 5804 is actually perimeter 5901. Such a perimeter estimation approach may be used when the speed of data acquisition is faster than the speed of the robot.

[0274] In some embodiments, layered maps may be used in avoiding blind spots. In some embodiments, the processor may generate a map including multiple layers. In some embodiments, one layer may include areas with high probability of being correct (e.g., areas based on observed data) while another may include areas with lower probability of being correct (e.g., areas unseen and predicted based on observed data). In some embodiments, a layer of the map or another map generated may only include areas unobserved and predicted by the processor of the robot. At any time, the processor may subtract maps from one another, add maps with one another (e.g., by layering maps), or may hide layers.

[0275] In some embodiments, a layer of a map may be a map generated based solely on the observations of a particular sensor type. For example, a map may include three layers and each layer may be a map generated based solely on the observations of a particular sensor type. In some embodiments, maps of various layers may be superimposed vertically or horizontally, deterministically or probabilistically, and locally or globally. In some embodiments, a map may be horizontally filled with data from one (or one class of) sensor and vertically filled using data from a different sensor (or class of sensor).

[0276] In some embodiments, different layers of the map may have different resolutions. For example, a long range limited FOV sensor of a robot may not observe a particular obstacle. As a result, the obstacle is excluded from a map generated based on data collected by the long range limited FOV sensor. However, as the robot approaches the obstacle, a short range obstacle sensor may observe the obstacle and add it to a map generated based on the data of the obstacle sensor. The processor may layer the two maps and the obstacle may therefore be observed. In some cases, the processor may add the obstacle to a map layer corresponding to the obstacle sensor or to a different map layer. In some embodiments, the resolution of the map (or layer of a map) depends on the sensor from which the data used to generate the map came from. In some embodiments, maps with different resolutions may be constructed for various purposes. In some embodiments, the processor chooses a particular resolution to use for navigation based on the action being executed or settings of the robot. For example, if the robot is travelling at a slow driving speed, a lower resolution map layer may be used. In another example, the robot is driving in an area with high obstacle density at an increased speed therefore a higher resolution map layer may be used. In some cases, the data of the map is stored in a memory of the robot. In some embodiments, data is used with less accuracy or some floating points may be excluded in some calculations for lower resolution maps. In some embodiments, maps with different resolutions may all use the same underlying raw data instead of having multiple copies of that raw information stored.

[0277] In some embodiments, the processor executes a series of procedures to generate layers of a map used to construct the map from stored values in memory. In some embodiments, the same series of procedures may be used construct the map at different resolutions. In some embodiments, there may be dedicated series of procedures to construct various different maps. In some embodiments, a separate layer of a map may be stored in a separate data structure. In some embodiments, various layers of a map or various different types of maps may be at least partially constructed from the same underlying data structures.

[0278] In some embodiments, the processor identifies gaps in the map (e.g., due to areas blind to a sensor or a range of a sensor). In some embodiments, the processor may actuate the robot to move towards and investigates the gap, collecting observations and mapping new areas by adding new observations to the map until the gap is closed. However, in some instances, the gap or an area blind to a sensor may not be detected. In some embodiments, a perimeter may be incorrectly predicted and may thus block off areas that were blind to the sensor of the robot. For example, FIG. 60 illustrates actual perimeter 6000, blind spot 6001, and incorrectly predicted perimeter 6002, blocking off blind spot 6001. A similar issue may arise when, for example, a bed cover or curtain initially appears to be a perimeter when in reality, the robot may navigate behind the bed cover or curtain.

[0279] Issues related to incorrect perimeter prediction may be eradicated with thorough inspection of the environment and training. For example, data from a second type of sensor may be used to validate a first map constructed based on data collected by a first type of sensor. In some embodiments, additional information discovered by multiple sensors may be included in multiple layers or different layers or in the same layer. In some embodiments, a training period of the robot may include the robot inspecting the environment various times with the same sensor or with a second (or more) type of sensor. In some embodiments, the training period may occur over one session (e.g., during an initial setup of the robot) or multiple sessions. In some embodiments, a user may instruct the robot to enter training at any point. In some embodiments, the processor of the robot may transmit the map to the cloud for validation and further machine learning processing. For example, the map may be processed on the cloud to identify rooms within the map. In some embodiments, the map including various information may be constructed into a graphic object and presented to the user (e.g., via an application of a communication device). In some embodiments, the map may not be presented to the user until it has been fully inspected multiple times and has high accuracy. In some embodiments, the processor disables a main brush and/or a side brush of the robot when in training mode or when searching and navigating to a charging station.

[0280] In some embodiments, a gap in the perimeters of the environment may be due to an opening in the wall (e.g., a doorway or an opening between two separate areas). In some embodiments, exploration of the undiscovered areas within which the gap is identified may lead to the discovery of a room, a hallway, or any other separate area. In some embodiments, identified gaps that are found to be, for example, an opening in the wall may be used in separating areas into smaller subareas. For example, the opening in the wall between two rooms may be used to segment the area into two subareas, where each room is a single subarea. This may be expanded to any number of rooms. In some embodiments, the processor of the robot may provide a unique tag to each subarea and may use the unique tag to order the subareas for coverage by the robot, choose different work functions for different subareas, add restrictions to subareas, set cleaning schedules for different subareas, and the like. In some embodiments, the processor may detect a second room beyond an opening in the wall detected within a first room being covered and may identify the opening in the wall between the two rooms as a doorway. Methods for identifying a doorway are described in U.S. patent application Ser. Nos. 16/163,541 and 15/614,284, the entire contents of which are hereby incorporated by reference. For example, in some embodiments, the processor may fit depth data points to a line model and any deviation from the line model may be identified as an opening in the wall by the processor. In some embodiments, the processor may use the range and light intensity recorded by the depth sensor for each reading to calculate an error associated with deviation of the range data from a line model. In some embodiments, the processor may relate the light intensity and range of a point captured by the depth sensor using

[0281] $I\left(n\right)=\frac{a}{{r\left(n\right)}^4},$
wherein I(n) is the intensity of point n, r(n) is the distance of the particular point on an object and a=E(I(n)r(n)⁴) is a constant that is determined by the processor using a Gaussian assumption.

[0282] Given d_min, the minimum distance of all readings taken, the processor may calculate the distance

[0283] $r\left(n\right)=\frac{d_{\min }}{\sin \left(-\theta \left(n\right)\right)}$
corresponding to a point n on an object at any angular resolution θ(n). In some embodiments, the processor may determine the horizon

[0284] $\alpha =a\sin \frac{d_{\min }}{d_{\max }}$
of the depth sensor given d_min and d_max, the minimum and maximum readings of all readings taken, respectively. The processor may use a combined error

[0285] $e=\sum ^{}{\left(I\left(n\right){r\left(n\right)}^4-a\right)}^2+{\left(r\left(n\right)-\left(\frac{d_{\min }}{\sin \left(-\theta \left(n\right)\right)}\right)\right)}^2$
of the range and light intensity output by the depth sensor to identify deviation from the line model and hence detect an opening in the wall. The error e is minimal for walls and significantly higher for an opening in the wall, as the data will significantly deviate from the line model. In some embodiments, the processor may use a threshold to determine whether the data points considered indicate an opening in the wall when, for example, the error exceeds some threshold value. In some embodiments, the processor may use an adaptive threshold wherein the values below the threshold may be considered to be a wall.

[0286] In some embodiments, the processor may not consider openings with width below a specified threshold as an opening in the wall, such as openings with a width too small to be considered a door or too small for the robot to fit through. In some embodiments, the processor may estimate the width of the opening in the wall by identifying angles φ with a valid range value and with intensity greater than or equal to

[0287] $\frac{a}{d_{\max }}.$
The difference between the smallest and largest angle among all

[0288] $\phi =\left\{\theta \left(n\right)\bigvee \left(\left\{r\left(n\right)\ne \infty \right\}\right)\bigwedge \left(I\left(n\right)\ge {\left(\frac{a}{d_{\max }}\right)}^4\right)\right\}$
angles may provide an estimate of the width of the opening. In some embodiments, the processor may also determine the width of an opening in the wall by identifying the angle at which the measured range noticeably increases and the angle at which the measured range noticeably decreases and taking the difference between the two angles.

[0289] In some embodiments, the processor may detect a wall or opening in the wall using recursive line fitting of the data. The processor may compare the error (y−(ax+b))² of data points n₁ to n₂ to a threshold T₁ and summates the number of errors below the threshold. The processor may then compute the difference between the number of points considered (n₂−n₁) and the number of data points with errors below threshold T₁. If the difference is below a threshold T₂, i.e.,

[0290] $\left(\left(n_2-n_1\right)-\sum _{n_1}^{n_2}{\left(y-\left(ax+b\right)\right)}^2<T_1\right)<T_2,$
then the processor assigns the data points to be a wall and otherwise assigns the data points to be an opening in the wall.

[0291] In another embodiment, the processor may use entropy to predict an opening in the wall, as an opening in the wall results in disordered measurement data and hence larger entropy value. In some embodiments, the processor may mark data with entropy above a certain threshold as an opening in the wall. In some embodiments, the processor determines entropy of data using

[0292] $\begin{array}{cc}H\left(X\right)=-\sum _{i=1}^{n}P\left(x_i\right)\log P\left(x_i\right)& \end{array}$
wherein X=(x₁, x₂, . . . , x_n) is a collection of possible data, such as depth measurements. P(x_i) is the probability of a data reading having value x_i. P(x_i) may be determined by, for example, counting the number of measurements within a specified area of interest with value x_i and dividing that number by the total number of measurements within the area considered. In some embodiments, the processor may compare entropy of collected data to entropy of data corresponding to a wall. For example, the entropy may be computed for the probability density function (PDF) of the data to predict if there is an opening in the wall in the region of interest. In the case of a wall, the PDF may show localization of readings around wall coordinates, thereby increasing certainty and reducing entropy.

[0293] In some embodiments, the processor may apply a probabilistic method by pre-training a classifier to provide a priori prediction. In some embodiments, the processor may use a supervised machine learning algorithm to identify features of openings and walls. A training set of, for example, depth data may be used by the processor to teach the classifier common features or patterns in the data corresponding with openings and walls such that the processor may identify walls and openings in walls with some probability distribution. In this way, a priori prediction from a classifier combined with real-time data measurement may be used together to provide a more accurate prediction of a wall or opening in the wall. In some embodiments, the processor may use Bayes theorem to provide probability of an opening in the wall given that the robot is located near an opening in the wall,

[0294] $P\left(A|B\right)=\frac{P\left(B|A\right)P\left(A\right)}{P\left(B\right)}.P\left(A|B\right)$
is the probability of an opening in the wall given that the robot is located close to an opening in the wall, P(A) is the probability of an opening in the wall, P(B) is the probability of the robot being located close to an opening in the wall, and P(B|A) is the probability of the robot being located close to an opening in the wall given that an opening in the wall is detected.

[0295] The different methods described for detecting an opening in the wall above may be combined in some embodiments and used independently in others. Examples of methods for detecting a doorway are described in, for example, U.S. patent application Ser. Nos. 15/615,284 and 16/163,541, the entire contents of which are hereby incorporated by reference. In some embodiments, the processor may mark the location of doorways within a map of the environment. In some embodiments, the robot may be configured to avoid crossing an identified doorway for a predetermined amount of time or until the robot has encountered the doorway a predetermined number of times. In some embodiments, the robot may be configured to drive through the identified doorway into a second subarea for cleaning before driving back through the doorway in the opposite direction. In some embodiments, the robot may finish cleaning in the current area before crossing through the doorway and cleaning the adjacent area. In some embodiments, the robot may be configured to execute any number of actions upon identification of a doorway and different actions may be executed for different doorways. In some embodiments, the processor may use doorways to segment the environment into subareas. For example, the robot may execute a wall-follow coverage algorithm in a first subarea and rectangular-spiral coverage algorithm in a second subarea, or may only clean the first subarea, or may clean the first subarea and second subarea on particular days and times. In some embodiments, unique tags, such as a number or any label, may be assigned to each subarea. In some embodiments, the user may assign unique tags to each subarea, and embodiments may receive this input and associate the unique tag (such as a human-readable name of a room, like “kitchen”) with the area in memory. Some embodiments may receive instructions that map tasks to areas by these unique tags, e.g., a user may input an instruction to the robot in the form of “vacuum kitchen,” and the robot may respond by accessing the appropriate map in memory that is associated with this label to effectuate the command. In some embodiments, the robot may assign unique tags to each subarea. The unique tags may be used to set and control the operation and execution of tasks within each subarea and to set the order of coverage of each subarea. For example, the robot may cover a particular subarea first and another particular subarea last. In some embodiments, the order of coverage of the subareas is such that repeat coverage within the total area is minimized. In another embodiment, the order of coverage of the subareas is such that coverage time of the total area is minimized. The order of subareas may be changed depending on the task or desired outcome. The example provided only illustrates two subareas for simplicity but may be expanded to include multiple subareas, spaces, or environments, etc. In some embodiments, the processor may represent subareas using a stack structure, for example, for backtracking purposes wherein the path of the robot back to its starting position may be found using the stack structure.

[0296] In some embodiments, a map may be generated from data collected by sensors coupled to a wearable item. For example, sensors coupled to glasses or lenses of a user walking within a room may, for example, record a video, capture images, and map the room. For instance, the sensors may be used to capture measurements (e.g., depth measurements) of the walls of the room in two or three dimensions and the measurements may be combined at overlapping points to generate a map using SLAM techniques. In such a case, a step counter may be used instead of an odometer (as may be used with the robot during mapping, for example) to measure movement of the user. In some embodiments, the map may be generated in real-time. In some embodiments, the user may visualize a room using the glasses or lenses and may draw virtual objects within the visualized room. In some embodiments, the processor of the robot may be connected to the processor of the glasses or lenses. In some embodiments, the map is shared with the processor of the robot. In one example, the user may draw a virtual confinement line in the map for the robot. The processor of the glasses may transmit this information to the processor of the robot. Or, in another case, the user may draw a movement path of the robot or choose areas for the robot to operate within.

[0297] In some embodiments, the processor may determine an amount of time for building the map. In some embodiments, an Internet of Things (IoT) subsystem may create and/or send a binary map to the cloud and an application of a communication device. In some embodiments, the IoT subsystem may store unknown points within the map. In some embodiments, the binary maps may be an object with methods and characteristics such as capacity, raw size, etc. having data types such as a byte. In some embodiments, a binary map may include the number of obstacles. In some embodiments, the map may be analyzed to find doors within the room. In some embodiments, the time of analysis may be determined. In some embodiments, the global map may be provided in ASCII format. In some embodiments, a Wi-Fi command handler may push the map to the cloud after compression. In some embodiments, information may be divided into packet format. In some embodiments, compressions such as zlib may be used. In some embodiments, each packet may be in ASCII format and compressed with an algorithm such as zlib. In some embodiments, each packet may have a timestamp and checksum. In some embodiments, a handler such as a Wi-Fi command handler may gradually push the map to the cloud in intervals and increments. In some embodiments, the map may be pushed to the cloud after completion of coverage wherein the robot has examined every area within the map by visiting each area implementing any required corrections to the map. In some embodiments, the map may be provided after a few runs to provide an accurate representation of the environment. In some embodiments, some graphic processing may occur on the cloud or on the communication device presenting the map. In some embodiments, the map may be presented to a user after an initial training round. In some embodiments, a map handle may render an ASCII map. Rendering time may depend on resolution and dimension. In some embodiments, the map may have a tilt value in degrees.

[0298] In some embodiments, images or other sensor readings may be stitched and linked at both ends such that there is no end to the stitched images, such as in FIG. 61, wherein data A₁ to A₅ are stitched as are data A₁ and data A₅. For example, a user may use a finger to swipe in a leftwards direction across a screen of a mobile phone displaying a panorama image to view and pass past the right side of the panorama image and continue on to view the opposite side of the panorama image, in a continuous manner. In some embodiments, the images or other sensor readings may be two dimensional or three dimensional. For example, three dimensional readings may provide depth and hence spatial reality.

[0299] The robot may, for example, use the map to autonomously navigate the environment during operation, e.g., accessing the map to determine that a candidate route is blocked by an obstacle denoted in the map, to select a path with a path planning algorithm from a current point to a target point, or the like. It should be emphasized, though, that embodiments are not limited to techniques that construct maps in the ways described herein, as the present techniques may also be used for plane finding in augmented reality, barrier detection in virtual reality applications, outdoor mapping with autonomous drones, and other similar applications, which is not to suggest that any other description is limiting. Further details of mapping methods that may be used are described in U.S. patent application Ser. Nos. 16/048,179, 16/048,185, 16/163,541, 16/163,562, 16/163,508, and 16/185,000, the entire contents of which are hereby incorporated by reference.

[0300] In some embodiments, the processor localizes the robot during mapping or during operation. In some embodiments, methods of localization are inherently independent from mapping and path planning but may be used in tandem with any mapping or path planning method or may be used independently to localize the robot irrespective of the path or map of the environment. In some embodiments, the processor uses quantum SLAM.

[0301] In some embodiments, the processor may localize the robot within the environment represented by a phase space or Hilbert space. In some embodiments, the space may include all possible states of the robot within the space. In some embodiments, a probability distribution may be used by the processor of the robot to approximate the likelihood of the state of the robot being within a specific region of the space. In some embodiments, the processor of the robot may determine a phase space probability distribution over all possible states of the robot within the phase space using a statistical ensemble including a large collection of virtual, independent copies of the robot in various states of the phase space. In some embodiments, the phase space may consist of all possible values of position and momentum variables. In some embodiments, the processor may represent the statistical ensemble by a phase space probability density function ρ(p, q, t), q and p denoting position and velocity vectors. In some embodiments, the processor may use the phase space probability density function ρ(p, q, t) to determine the probability ρ(p, q, t)dq dp that the robot at time t will be found in the infinitesimal phase space volume dq dp. In some embodiments, the phase space probability density function ρ(p, q, t) may have the properties ρ(p, q, t)≥0 and ∫ρ(p, q, t)d(p, q)=1, ∀t≥0, and the probability of the position q lying within a position interval a, b is

[0302] $P\left[a\le q\le b\right]={\int }_a^b\int \rho \left(p,q,t\right)\mathrm{dpd}q.$
Similarly, the probability of the velocity p lying within a velocity interval c, d is

[0303] $P\left[c\le q\le d\right]={\int }_c^d\int \rho \left(p,q,t\right)\mathrm{dqd}p.$
In some embodiments, the processor may determine values by integration over the phase space. For example, the processor may determine the expectation value of the position q by (q)=∫qρ(p,q,t)d(p,q).

[0304] In some embodiments, the processor may evolve each state within the ensemble over time t according to an equation of motion. In some embodiments, the processor may model the motion of the robot using a Hamiltonian dynamical system with generalized coordinates q, p wherein dynamical properties may be modeled by a Hamiltonian function H. In some embodiments, the function may represent the total energy of the system. In some embodiments, the processor may represent the time evolution of a single point in the phase space using Hamilton's equations

[0305] $\frac{\mathrm{dp}}{\mathrm{dt}}=-\frac{\partial H}{\partial q},\frac{\mathrm{dq}}{\mathrm{dt}}=\frac{\partial H}{\partial p}.$
In some embodiments, the processor may evolve the entire statistical ensemble of phase space density function ρ(p, q, t) under a Hamiltonian H using the Liouville equation

[0306] $\frac{\partial \rho }{\partial t}=-\left\{\rho ,H\right\},$
wherein {⋅,⋅} denotes the Poisson bracket and H is the Hamiltonian of the system. For two functions ƒ, g on the phase space, the Poisson bracket may be given by

[0307] $\left\{f,g\right\}=\sum _{i=1}^N\left(\frac{\partial f}{\partial q_i}\frac{\partial g}{\partial p_i}-\frac{\partial f}{\partial p_i}\frac{\partial g}{\partial q_i}\right).$
In this approach, the processor may evolve each possible state in the phase space over time instead of keeping the phase space density constant over time, which is particularly advantageous if sensor readings are sparse in time.

[0308] In some embodiments, the processor may evolve the phase space probability density function ρ(p, q, t) over time using the Fokker-Plank equation which describes the time evolution of a probability density function of a particle under drag and random forces. In comparison to the behavior of the robot modeled by both the Hamiltonian and Liouville equations, which are purely deterministic, the Fokker-Planck equation includes stochastic behaviour. Given a stochastic process with dX_t=μ(X_t,t)dt+σ(X_t,t)dW_t, wherein X_t and μ(X_t,t) are M-dimensional vectors, σ(X_t, t) is a M×P matrix, and W_t is a P-dimensional standard Wiener process, the probability density ρ(x t) for X_t satisfies the Fokker-Planck equation

[0309] $\frac{\partial \rho \left(x,t\right)}{\partial t}=-\sum _{i=1}^M\frac{\partial }{\partial x_i}\left[{\mu }_i\left(x,t\right)\rho \left(x,t\right)\right]+\sum _{i=1}^M\sum _{j=1}^M\frac{{\partial }^2}{\partial x_i\partial x_j}\left[D_{\mathrm{ij}}\left(x,t\right)\rho \left(x,t\right)\right]$
with drift vector μ=(μ₁, . . . , μ_M) and diffusion tensor

[0310] $D=\frac{1}{2}\sigma {\sigma }^T.$
In some embodiments, the processor may add stochastic forces to the motion of the robot governed by the Hamiltonian H and the motion of the robot may then be given by the stochastic differential equation

[0311] $d{X}_t=\left(\begin{array}{c}dq\\ dp\end{array}\right)=\left(\begin{array}{c}+\frac{\partial H}{\partial p}\\ -\frac{\partial H}{\partial q}\end{array}\right)\mathrm{dt}=\left(\begin{array}{c}{0}_N\\ {\sigma }_N\left(p,q,t\right)\end{array}\right){\mathrm{dW}}_t,$
wherein σ_N is a N×N matrix and dW_t is a N-dimensional Wiener process. This leads to the Fokker-Plank equation wherein

[0312] $\frac{\partial \rho }{\partial t}=-\left\{\rho ,H\right\}+{\nabla }_p·\left(D{\nabla }_p\rho \right),$
∇_p denotes the gradient with respect to position p, ∇·denotes divergence, and

[0313] $D=\frac{1}{2}{\sigma }_N{\sigma }_N^T$
is the diffusion tensor.

[0314] In other embodiments, the processor may incorporate stochastic behaviour by modeling the dynamics of the robot using Langevin dynamics, which models friction forces and perturbation to the system, instead of Hamiltonian dynamics. The Langevian equations may be given by M{umlaut over (q)}=−∇_qu(q)−γp+√{square root over (2γk_BTM)}R(t), wherein (−γp) are friction forces, R(t) are random forces with zero-mean and delta-correlated stationary Gaussian process, T is the temperature, k_B is Boltzmann's constant, γ is a damping constant, and M is a diagonal mass matrix. In some embodiments, the Langevin equation may be reformulated as a Fokker-Planck equation

[0315] $\frac{\partial \rho }{\partial t}=-\left\{\rho ,H\right\}+{\nabla }_p·\left(\gamma p\rho \right)+k_{B}T{\nabla }_p.$
(γM∇_pφ that the processor may use to evolve the phase space probability density function over time. In some embodiments, the second order term ∇_p·(γM∇_pρ) is a model of classical Brownian motion, modeling a diffusion process. In some embodiments, partial differential equations for evolving the probability density function over time may be solved by the processor of the robot using, for example, finite difference and/or finite element methods.

[0316] FIG. 62A illustrates an example of an initial phase space probability density of a robot, a Gaussian in (q, p) space. FIG. 62B illustrates an example of the time evolution of the phase space probability density after four time units when evolved using the Liouville equation incorporating Hamiltonian dynamics,

[0317] $\frac{\partial \rho }{\partial t}=-\left\{\rho ,H\right\}$
with Hamiltonian

[0318] $H=\frac{1}{2}{p}^2.$
FIG. 62C illustrates an example of the time evolution of the phase space probability density after four time units when evolved using the Fokker-Planck equation incorporating Hamiltonian dynamics,

[0319] $\frac{\partial \rho }{\partial t}=-\left\{\rho ,H\right\}+{\nabla }_p·\left(D{\nabla }_p\rho \right)$
with D=0.1. FIG. 62D illustrates an example of the time evolution of the phase space probability density after four time units when evolved using the Fokker-Planck equation incorporating Langevin dynamics,

[0320] $\frac{\partial \rho }{\partial t}=-\left\{\rho ,H\right\}+{\nabla }_p·\left(\gamma p\rho \right)+k_{B}T{\nabla }_p·\left(\gamma M{\nabla }_p\rho \right)$
with γ=0.5, T=0.2, and k_B=1. FIG. 62B illustrates that the Liouville equation incorporating Hamiltonian dynamics conserves momentum over time, as the initial density in FIG. 62A is only distorted in the q-axis (position). In comparison, FIGS. 62C and 62D illustrate diffusion along the p-axis (velocity) as well, as both evolution equations account for stochastic forces. With the Fokker-Planck equation incorporating Hamiltonian dynamics the density spreads more equally (FIG. 62C) as compared to the Fokker-Planck equation incorporating Langevin dynamics where the density remains more confined (FIG. 62D) due to the additional friction forces.

[0321] In some embodiments, the processor of the robot may update the phase space probability distribution when the processor receives readings (or measurements or observations). Any type of reading that may be represented as a probability distribution that describes the likelihood of the state of the robot being in a particular region of the phase space may be used. Readings may include measurements or observations acquired by sensors of the robot or external devices such as a Wi-Fi™ camera. Each reading may provide partial information on the likely region of the state of the robot within the phase space and/or may exclude the state of the robot from being within some region of the phase space. For example, a depth sensor of the robot may detect an obstacle in close proximity to the robot. Based on this measurement and using a map of the phase space, the processor of the robot may reduce the likelihood of the state of the robot being any state of the phase space at a great distance from an obstacle. In another example, a reading of a floor sensor of the robot and a floor map may be used by the processor of the robot to adjust the likelihood of the state of the robot being within the particular region of the phase space coinciding with the type of floor sensed. In an additional example, a measured Wi-Fi™ signal strength and a map of the expected Wi-Fi™ signal strength within the phase space may be used by the processor of the robot to adjust the phase space probability distribution. As a further example, a Wi-Fi™ camera may observe the absence of the robot within a particular room. Based on this observation the processor of the robot may reduce the likelihood of the state of the robot being any state of the phase space that places the robot within the particular room. In some embodiments, the processor generates a simulated representation of the environment for each hypothetical state of the robot. In some embodiments, the processor compares the measurement against each simulated representation of the environment (e.g., a floor map, a spatial map, a Wi-Fi map, etc.) corresponding with a perspective of each of the hypothetical states of the robot. In some embodiments, the processor chooses the state of the robot that makes the most sense as the most feasible state of the robot. In some embodiments, the processor selects additional hypothetical states of the robot as a backup to the most feasible state of the robot.

[0322] In some embodiments, the processor of the robot may update the current phase space probability distribution ρ(p, q, t₁) by re-weighting the phase space probability distribution with an observation probability distribution m(p, q, t_i) according to

[0323] $\overline{\rho }\left(p,q,t_i\right)=\frac{\rho \left(p,q,t_i\right)·m\left(p,q,t_i\right)}{\int \rho \left(p,q,t_i\right)·m\left(p,q,t_i\right)d\left(p,q\right)}.$
In some embodiments, the observation probability distribution may be determined by the processor of the robot for a reading at time t_i using an inverse sensor model. In some embodiments, wherein the observation probability distribution does not incorporate the confidence or uncertainty of the reading taken, the processor of the robot may incorporate the uncertainty into the observation probability distribution by determining an updated observation probability distribution

[0324] $\hat{m}=\frac{1-\alpha }{c}+\alpha m$
αm that may be used in re-weighting the current phase space probability distribution, wherein α is the confidence in the reading with a value of 0≤α≤1 and c=∫∫dpdq. At any given time, the processor of the robot may estimate a region of the phase space within which the state of the robot is likely to be given the phase space probability distribution at the particular time.

[0325] To further explain the localization methods described, examples are provided. In a first example, the processor uses a two-dimensional phase space of the robot, including position q and velocity p. The processor confines the position of the robot q to an interval [0, 10] and the velocity p to an interval [−5, +5], limited by the top speed of the robot, therefore the phase space (p, q) is the rectangle D=[−5, 5]×[0, 10]. The processor uses a Hamiltonian function

[0326] $H=\frac{p^2}{2m},$
with mass m and resulting equations of motion {dot over (p)}=0 and

[0327] $\stackrel{.}{q}=\frac{p}{m}$
to delineate the motion of the robot. The processor adds Langevin-style stochastic forces to obtain motion equations {dot over (p)}=−γp+√{square root over (2γmk_BT)}R(t) and

[0328] $\stackrel{.}{q}=\frac{p}{m},$
wherein R(t) denotes random forces and m=1. The processor of the robot initially generates a uniform phase space probability distribution over the phase space D. FIGS. 63A-63D illustrate examples of initial phase space probability distributions the processor may use. FIG. 63A illustrates a Gaussian distribution over the phase space, centered at q=5, p=0. The robot is estimated to be in close proximity to the center point with high probability, the probability decreasing exponentially as the distance of the point from the center point increases. FIG. 63B illustrates uniform distribution for q∈[4.75, 5.25], p∈[−5, 5] over the phase space, wherein there is no assumption on p and q is equally likely to be in [4.75, 5.25]. FIG. 63C illustrates multiple Gaussian distributions and FIG. 63D illustrates a confined spike at q=5, p=0, indicating that the processor is certain of the state of the robot.

[0329] In this example, the processor of the robot evolves the phase space probability distribution over time according to Langevin equation

[0330] $\frac{\partial \rho }{\partial t}=-\left\{\rho ,H\right\}+\left(\gamma \frac{\partial }{\partial p}\right)·(\mathrm{p\rho })+\gamma k_{b}T\frac{{\partial }_{\rho }^2}{\partial p^2},$
wherein

[0331] $\left\{\rho ,H\right\}=p\frac{\partial \rho }{\partial q}$
and m=1. Thus, the processor solves

[0332] $\frac{\partial \rho }{\partial t}=-p\frac{\partial \rho }{\partial q}+\gamma \left(\rho +p\frac{\partial \rho }{\partial p}\right)+\gamma k_{b}T\frac{{\partial }_{\rho }^2}{\partial p^2}\mathrm{for}t>0$
with initial condition ρ(p, q, 0)=ρ₀ and homogenous Neumann perimeters conditions. The perimeter conditions govern what happens when the robot reaches an extreme state. In the position state, this may correspond to the robot reaching a wall, and in the velocity state, it may correspond to the motor limit. The processor of the robot may update the phase space probability distribution each time a new reading is received by the processor. FIGS. 64A and 64B illustrate examples of observation probability distributions for odometry measurements and distance measurements, respectively. FIG. 64A illustrates a narrow Gaussian observation probability distribution for velocity p, reflecting an accurate odometry sensor. Position q is uniform as odometry data does not indicate position. FIG. 64B illustrates a bimodal observation probability distribution for position q including uncertainty for an environment with a wall at q=0 and q=10. Therefore, for a distance measurement of four, the robot is either at q=4 or q=6, resulting in the bi-modal distribution. Velocity p is uniform as distance data does not indicate velocity. In some embodiments, the processor may update the phase space at periodic intervals or at predetermined intervals or points in time. In some embodiments, the processor of the robot may determine an observation probability distribution of a reading using an inverse sensor model and the phase space probability distribution may be updated by the processor by re-weighting it with the observation probability distribution of the reading.

[0333] The example described may be extended to a four-dimensional phase space with position q=(x, y) and velocity p=(p_x,p_y). The processor solves this four dimensional example using the Fokker-Planck equation

[0334] $\frac{\partial \rho }{\partial t}=-\left\{\rho ,H\right\}+{\nabla }_p·\left(\gamma p\rho \right)+k_{B}T{\nabla }_p·\left(\gamma M{\nabla }_p\rho \right)$
with M=I₂ (2D identity matrix), T=0.1, γ=0.1, and k_B=1. In alternative embodiments, the processor uses the Fokker-Planck equation without Hamiltonian and velocity and applies velocity drift field directly through odometry which reduces the dimension by a factor of two. The map of the environment for this example is given in FIG. 65, wherein the white space is the area accessible to the robot. The map describes the domain for q₁, q₂∈D. In this example, the velocity is limited to p₁, p₂∈[−1, 1]. The processor models the initial probability density ρ(p, q, 0) as Gaussian, wherein ρ is a four-dimensional function. FIGS. 66A-66C illustrate the evolution of ρ reduced to the q₁, q₂ space at three different time points (i.e., the density integrated over p₁,p₂, ρ_red=∫∫ρ(p₁, p₂, q₁, q₂)dp₁dp₂). With increased time, the initial density focused in the middle of the map starts to flow into other rooms. FIGS. 67A-67C illustrate the evolution of ρ reduced to the p₁, q₁ space and 68A-68C illustrate the evolution of ρ reduced to the p₂, q₂ space at the same three different time points to show how velocity evolves over time with position. The four-dimensional example is repeated but with the addition of floor sensor data observations. FIG. 69 illustrates a map of the environment indicating different floor types 6900, 6901, 6902, and 6903 with respect to q₁, q₂. Given that the sensor has no error, the processor may strongly predict the area within which the robot is located based on the measured floor type, at which point all other hypothesized locations of the robot become invalid. For example, the processor may use the distribution

[0335] $m\left(p_1,p_2,q_1,q_2\right)=\{\begin{array}{c}\mathrm{const}>0,q_1{q}_2\mathrm{with}\mathrm{the}\mathrm{observed}\mathrm{floor}\mathrm{type}\\ 0,\mathrm{else}\end{array}.$
If the sensor has an average error rate ϵ, the processor may use the distribution

[0336] $m\left(p_1,p_2,q_1,q_2\right)=\{\begin{array}{c}{c}_1>0,q_1{q}_2\mathrm{with}\mathrm{the}\mathrm{observed}\mathrm{floor}\mathrm{type}\\ c_2>0,\mathrm{else}\end{array}.$
with c₁, c₂ chosen such that ∫_p∫_Dobsmd(q₁, q₂)d(p₁, p₂)=1−ϵ and ∫_p∫_Dobscmd(q₁, q₂)d(p₁, p₂)=ϵ. D_obs is the q₁, q₂ with the observed floor type and D_obs^c is its complement. By construction, the distribution m has a probability 1−ϵ for q₁, q₂ ∈D_obs and probability ϵ for q₁, q₂ ∈D_obs^c. Given that the floor sensor measures floor type 5302, the processor updates the probability distribution for position as shown in FIG. 70. Note that the corners of the distribution were smoothened by the processor using a Gaussian kernel, which corresponds to an increased error rate near the borders of an area. Next, Wi-Fi signal strength observations are considered. Given a map of the expected signal strength, such as that in FIG. 71, the processor may generate a density describing the possible location of the robot based on a measured Wi-Fi signal strength. The darker areas in FIG. 71 represent stronger Wi-Fi signal strength and the signal source is at q₁, q₂=4.0, 2.0. Given that the robot measures a Wi-Fi signal strength of 0.4, the processor generates the probability distribution for position shown in FIG. 72. The likely area of the robot is larger since the Wi-Fi signal does not vary much. A wall distance map, such as that shown in FIG. 73 may be used by the processor to approximate the area of the robot given a distance measured. Given that the robot measures a distance of three distance units, the processor generates the probability distribution for position shown in FIG. 74. For example, the processor evolves the Fokker-Planck equation over time and as observations are successively taken, the processor re-weights the density function with each observation wherein parts that do not match the observation are considered less likely and parts that highly match the observations relatively increase in probability. An example of observations over time may be, t=1: observe p₂=0.75; t=2: observe p₂=0.95 and Wi-Fi signal strength 0.56; t=3: observe wall distance 9.2; t=4: observe floor type 2; t=5: observe floor type 2 and Wi-Fi signal strength 0.28; t=6: observe wall distance 3.5; t=7: observe floor type 4, wall distance 2.5, and Wi-Fi signal strength 0.15; t=8: observe floor type 4, wall distance 4, and Wi-Fi signal strength 0.19; t=8.2: observe floor type 4, wall distance 4, and Wi-Fi signal strength 0.19.

[0337] In another example, the robot navigates along a long floor (e.g., x-axis, one-dimensional). The processor models the floor using Liouville's equation

[0338] $\frac{\partial \rho }{\partial t}=-\left\{\rho ,H\right\}$
with Hamiltonian

[0339] $H=\frac{1}{2}{p}^2$
wherein q∈[−10,10] and p∈[−5, 5]. The floor has three doors at q₀=−2.5, q₁=0, and q₂=5.0 and the processor of the robot is capable of determining when it is located at a door based on sensor data observed and the momentum of the robot is constant, but unknown. Initially the location of the robot is unknown, therefore the processor generates an initial state density such as that in FIG. 75. When the processor determines the robot is in front of a door, the possible location of the robot is narrowed down, but not the momentum. Therefore, the processor may update the probability density to that shown in FIG. 76. The processor evolves the probability density, and after five seconds the probability is as shown in FIG. 77, wherein the uncertainty in the position space has spread out again given that the momentum is unknown. However, the evolved probability density keeps track of the correlation between position and momentum. When the processor determines the robot is in front of a door again, the probability density is updated to FIG. 78, wherein the density has significantly narrowed down, indicating a number of peaks representing possible location and momentum combinations of the robot. For the left door, there is equal likelihood for p=0, p=−0.5, and p=−1.5. These momentum values correspond with the robot travelling from one of the three doors in five seconds. This is seen for the other two doors as well.

[0340] In some embodiments, the processor may model motion of the robot using equations {dot over (x)}=ν cos ω, {dot over (y)}=ν sin ω, and {dot over (θ)}=ω, wherein ν and ω are translational and rotational velocities, respectively. In some embodiments, translational and rotational velocities of the robot may be computed using observed wheel angular velocities ω_l and ω_r using

[0341] $\left(\begin{array}{c}v\\ \omega \end{array}\right)=J\left(\begin{array}{c}{\omega }_l\\ {\omega }_r\end{array}\right)=\left(\begin{array}{cc}{r}_l/2& r_r/2\\ -r_l/b& r_r/b\end{array}\right),$
wherein J is the Jacobian, r_l and r_r are the left and right wheel radii, respectively and b is the distance between the two wheels. Assuming there are stochastic forces on the wheel velocities, the processor of the robot may evolve the probability density