US 6,789,640 B1Grant
Yaw control for a personal transporter
Issue Date:2004-09-14
•7 Claims
•9 Drawing Sheets
Abstract
A device and method for providing yaw control for a balancing transporter that has two laterally disposed ground-contacting wheels. The method has the steps of receiving a user input of a desired yaw value; comparing an instantaneous yaw value with the desired yaw value to generate a yaw error value; processing the yaw error value to obtain a yaw command signal; and applying the yaw command signal in conjunction with a pitch command signal based on a pitch error in such a manner as to maintain balance of the transporter in the course of executing yaw control. The yaw command signal may include component terms quadratic in the pitch error and/or a function of a common wheel rotational velocity. A control input mechanism is wirelessly coupled to the controller of the balancing transporter so as to maintain the sealed integrity of a user interface.
Metadata
Assignee
- DEKA Products Limited Partnership
Inventors
- Richard W. Arling
- W. Patrick Kelly
- Philip LeMay
- John B. Morrell
- Jonathan B. Pompa
- David W. Robinson
Application Information
Application Number:US 10/308,850
Filing Date:2002-12-03
Priority Date:2000-10-13
Art Unit:7
Classifications
IPC:
B60K 2814
Field of Search:
180 41180171180170180218180271180 71180 21180282180338280 5513280 5507318586318584
Patent Drawings (9 sheets)
Description
[0002] The present application is a continuation-in-part of copending U.S. patent application Ser. No. 09/687,789, filed Oct. 13, 2000, now U.S. Pat. No. 6,581,714, and additionally claims priority from U.S. Provisional Patent Application No. 60/388,846, filed Jun. 14, 2002, both of which applications are incorporated herein by reference.
Field of the Invention
[0003] The present application is directed to modes for jointly controlling the yaw and pitch of a dynamically balanced personal transporter.
Background of the Invention
[0004] Dynamically stabilized transporters refer to personal transporters having a control system that actively maintains the stability of the transporter while the transporter is operating. The control system maintains the stability of the transporter by continuously sensing the orientation of the transporter, determining the corrective action to maintain stability, and commanding the wheel motors to make the corrective action.
[0005] For vehicles that maintain a stable footprint, coupling between steering control, on the one hand, and control of the forward motion of the vehicles is not an issue of concern since, under typical road conditions, stability is maintained by virtue of the wheels being in contact with the ground throughout the course of a turn. In a balancing transporter, however, any torque applied to one or more wheels affects the stability of the transporter.
Summary of the Invention
[0006] In accordance with preferred embodiments of the present invention, there is provided a method for providing yaw control for a balancing transporter that has two laterally disposed ground-contacting wheels. The method has the steps of receiving a user input of a desired yaw value; comparing an instantaneous yaw value with the desired yaw value to generate a yaw error value; processing the yaw error value to obtain a yaw command signal; and applying the yaw command signal in conjunction with a pitch command signal based on a pitch error in such a manner as to maintain balance of the transporter in the course of executing yaw control.
[0007] In accordance with further embodiments of the invention, the yaw command signal may include component terms quadratic in the pitch error and/or a function of a common wheel rotational velocity.
[0008] In accordance with yet further embodiments of the invention, a yaw controller is provided. The yaw controller has an input for receiving a user-specified yaw value and a summer for differencing an instantaneous yaw value from the user-specified yaw value to generate a yaw error value. The yaw controller also has a processor for generating a yaw command signal based at least on the yaw error value in conjunction with a pitch command signal based on a pitch error in such a manner as to maintain balance of the transporter in the course of executing yaw control. The input for receiving a user-specified yaw value may be wirelessly coupled to the processor, and may have a grip coupled to a user interface such that the grip is rotatable about an axis fixed with respect to the user interface. The grip may also include a magnet moveable with respect to a sensor coupled to the user interface.
Brief Description of the Drawings
[0009] The foregoing features of the invention will be more readily understood by reference to the following detailed description, taken with reference to the accompanying drawings, in which:
[0010] FIG. 1 depicts one embodiment of a human transporter to which the present invention may advantageously be applied;
[0011] FIG. 2 shows a block diagram of the system architecture of an embodiment of the present invention;
[0012] FIG. 3 is a block diagram of the power drive module of an embodiment of the present invention;
[0013] FIG. 4 is a basic block diagram of a controller of a transporter, in accordance with embodiments of the invention;
[0014] FIG. 5 is a block diagram depicting the coupling of pitch and yaw controller outputs for generation of wheel amplifier commands;
[0015] FIG. 6 is a block diagram showing the constitutive inputs of a pitch command in accordance with of the present invention;
[0016] FIG. 7A is a block diagram showing the constitutive inputs of a yaw command in accordance with of the present invention;
[0017] FIGS. 7B and 7C are block diagrams of different embodiments of a yaw controller in accordance with the present invention;
[0018] FIG. 8A is an exploded view of components of a yaw control mechanism showing a yaw control grip coupled to a user interface of a personal transporter, in accordance with an embodiment of the present invention;
[0019] FIG. 8B shows a detailed exploded view of the yaw control grip of FIG. 8A; and
[0020] FIG. 8C shows the integral yaw control sensor of the yaw control mechanism of FIG. 8A.
Description of Preferred Embodiments
[0021] A personal transporter may be said to act as ‘balancing’ if it is capable of operation on one or more wheels but would be unable to stand on the wheels but for operation of a control loop governing operation of the wheels. A balancing personal transporter lacks static stability but is dynamically balanced. The wheels, or other ground-contacting elements, that provide contact between such a personal transporter and the ground or other underlying surface, and minimally support the transporter with respect to tipping during routine operation, are referred to herein as ‘primary ground-contacting elements.’
[0022] An embodiment of a balancing personal transporter in accordance with the present invention is depicted in FIG. 1 and designated generally by numeral 10. User 8 is shown in FIG. 1, standing on platform (or ‘base’) 12 of ground-contacting module 26. Wheels 21 and 22 are shown as coaxial about the Y axis. Steering or other control may be provided by one or more thumbwheels 32 and 34, or by any other user input mechanisms. A variety of steering devices which are further examples of user input mechanisms that may be employed within the scope of the present invention are described in U.S. Pat. No. 6,288,505, which is incorporated herein by reference. A user interface (or ‘handle’) 14 may be provided on control shaft (or ‘stalk’) 16 for gripping by the user and for supporting user instruments such as control grips, discussed below.
[0023] Referring now to FIG. 2, a block diagram is shown of the system architecture of an embodiment of the present invention. A left motor 110 drives a left wheel 20 (shown in FIG. 1) and a right motor 120 drives a right wheel 21. Motors 110 and 120 are preferably DC brushless but may be either AC or DC motors and either brushed or brushless. Each motor is energized by a redundant set of windings 111, 112, 121, 122. Each winding is capable of energizing the motor in the event the complimentary winding is unable to energize the motor. In the discussion below, each redundant component is distinguished by a two letter group identifying either the left (L) or right (R) side of the transporter and either the A group or B group of redundant components. For example, the left motor winding energized by the A group of components is designated as the LA winding.
[0024] Each of motor windings 111, 112, 121, 122 is driven by a motor amplifier 132, 133, 142, 143. The A-group amplifiers 132, 133 are supplied by the A-group power supply 131 and the B-group amplifiers 142, 143 are supplied by the B-group power supply 141. The electrical connections between the power supplies and amplifiers and between the amplifiers and motor windings are expected to carry large currents up to 20 to 40 Amperes and are identified by thick lines 105 in FIG. 2.
[0025] Each motor 110, 120 has a shaft feedback device (SFD) 113, 123 that measures the position or angular velocity of the motor shaft. The SFD is in signal communication with the motor amplifiers driving the motor associated with the SFD. For example, the right SFD 123 associated with the right motor 120 is in signal communication with the RA amplifier 133 and the RB amplifier 143. The SFD is preferably a Hall sensor that determines the position of the shaft, however the SFD may be selected from a variety of sensors such as encoders, resolvers, and tachometers, all listed without limitation for purposes of example. Certain sensors, such as tachometers, may also be used to measure the shaft velocity. Conversion of a signal representing instantaneous shaft velocity to or from a signal representing position is accomplished by integrating or differentiating the signal, respectively.
[0026] The A-group amplifiers 132, 133 are commanded by the A processor 135 while the B-group amplifiers 142, 143 are commanded by the B processor 145. Power is supplied to the A processor from the A power source 131 through the A-group DC-DC converter 136. Similarly, the B power source 141 supplies power to the B processor 146 through the B-group DC-DC converter 145. The A-group amplifiers 132, 133, A-group converter 136, and A processor 135 are preferably grouped together into a compartment or tray 130 that is at least partially isolated by a barrier 150 from the B-tray 140 containing the B-group amplifiers, B-group converter, and B processor. Physically separating the A tray 130 and B tray 140 reduces the probability of a common point failure. The barrier 150 acts to delay the propagation of a failure, in one tray to the other tray such that the transporter has sufficient time to put the rider in a safe condition to exit the transporter. Similarly, the A power supply 131 is physically separated from the B power supply 141. The A power supply 131 and the components in the A tray 130 are capable of driving both motors 110, 120 for a short period of time, on the order of a few seconds, in the event of a failure in any one of the B-group components. Conversely, the B power supply 141 and the components in the B tray 140 are capable of driving both motors 110, 120 for a short period of time if an A-group component fails.
[0027] Although the processors 135, 145 are physically isolated from each other, signal communication is maintained between the processors via communication channels 137, 147. Communication channels 137, 147 are preferably electrical conductors but may also be electromagnetic such as optical, infrared, microwave, or radio. The A channel 137 transmits signals from the A processor 135 to the B processor 145 and the B channel 147 transmits signals from the B processor 145 to the A processor 135. Optical isolators 139, 149 are incorporated into channels 137, 147 to prevent over-voltages from propagating from a shorted processor to the other processor.
[0028] Each processor receives signals from a plurality of sensors that monitor the state of the transporter and the input commands of the rider. The processor uses the sensor signals to determine and transmit the appropriate command to the motor amplifiers. The information transmitted to the processors by the sensors include the spatial orientation of the transporter provided by an inertial measurement unit (IMU) 181, 182, the rider directed turn command provided by a yaw input device (YID) 132, 142, and the presence of a rider on the transporter provided by a rider detector (RD) 161, 162, 163, 164. Other inputs to the processor may include a rider operated pitch trim device (PTD) 148 for adjusting the pitch of the transporter to a more comfortable pitch and a stop button (not shown) for bringing the transporter to a stop quickly. Depending on the importance of the sensor to the operation of the transporter, the sensors may or may not be duplicated for redundancy. For example, the spatial orientation of the transporter is central to the operation of the transporter, as is described below, and therefore an A-group IMU 181 supplies transporter orientation information to the A processor 135 and a B-group IMU 182 supplies transporter orientation information to the B-processor 145. On the other hand, the transporter may still be operated in a safe manner without the PTD 148 so only one such device is typically provided. Similarly, an output device such as a display 138 does not require redundancy. A non-redundant device such as a display 138 or a PTD 148 may be connected to either processor.
[0029] In the embodiment depicted in FIG. 2, display 138 is controlled by the A processor 136 and the PTD 148 is in direct signal communication with the B processor 145. The information provided by the PTD 148 is transmitted by the B processor 145 to the A processor 135 via the B channel 147.
[0030] Additionally, each processor 135, 145 communicates with one of the user interface processors (UIPs) 173, 174. Each UIP 173, 174 receives steering commands from the user through one of the yaw input devices 171, 172. A A-group UIP 173 also communicates to the non-redundant UIDs such as the display 138, brake switch 175, and pitch trim control 148. Other user interface devices that are not provided redundantly in the embodiment shown in FIG. 2, such as a sound warning device, lights, and an on/off switch, may also be connected to the A-group UIP 173. The A-group UIP 173 may also pass along information provided by the user interface devices to the B-group UIP 174.
[0031] In accordance with preferred embodiments of the invention, the A-group UIP 173 compares calculations of the A-group processor with calculations of the B-group processor and queries the A-group processor 135 with a ‘watchdog’ calculation to verify operation of the A-group processor. Similarly, the B-group UIP 174 queries the B-group processor 145 to verify normal operation of the B-group processor.
[0032] FIG. 3 shows a block schematic of a power module 300 of one embodiment of the present invention. A balancing processor 310 generates a command signal to motor amplifier 320 that, in turn, applies the appropriate power to motor 330. Balancing processor 310 receives inputs from the user and system sensors and applies a control law, as discussed in detail below, to maintain balance and to govern motion of the transporter in accordance with user commands. Motor 330, in turn, rotates a shaft 332 that supplies a torque, τ, at an angular velocity, ω, to a wheel 20, 21 (shown in FIG. 1) that is attached to shaft 332. In some embodiments, a transmission, not shown, may be used to scale the wheel speed in relation to the angular velocity of the shaft 332. In a preferred embodiment of the present invention, motor 330 is a three-coil brushless DC motor. In that embodiment, motor 330 has three sets of stator coils although any number of coils may be used. The stator coils are electrically connected to a power stage 324 by coil leads 337 capable of conducting large currents or high voltages. It is understood that the large currents and high voltages are relative to the currents and voltages normally used in signal processing and cover the range above 1 ampere or 12 volts, respectively.
[0033] Motor amplifier 320 itself contains both an amplifier processor 322 and a power amplification stage 324. Amplifier controller 322 may be configured to control either current or voltage applied to the motor 330. These control modes may be referred to as current control mode and voltage control mode, respectively. Power stage 324 switches the power source 340 into or out of connection with each coil, with the switching of the power stage 324 controlled by the amplifier controller 322. An inner loop 326 senses whether the output of power stage 324 is as commanded and feeds back an error signal to amplifier controller 322 at a closed loop bandwidth, preferably on the order of 500 Hz or higher, typically in the range of 500 Hz to 1 kHz. Additionally, control by amplifier controller 322 is based, in part, on a feedback signal from shaft feedback sensor (SFS) 335.
[0034] Shaft feedback sensor 335 is also in signal communication with the processor 310 and provides information related to the shaft position or motion to the processor. The shaft feedback sensor 335 may be any sensor known in the sensor art capable of sensing the angular position or velocity of a rotating shaft and includes tachometers, encoders, and resolvers. In a preferred embodiment, a Hall sensor is used to sense the position of the rotating shaft 332. An advantage of a Hall sensor is the low cost of the sensor. In order to obtain a measure of shaft rotation velocity from a position signal provided by shaft feedback sensor 335, the position signal is differentiated by differentiator 308. The outer feedback loop 342 operates at a bandwidth characteristic of the balance control provided by balance processor 310 and may be as low as 20-30 Hz.
[0035] While current and voltage may be equivalent in certain applications, voltage control is advantageously applied in embodiments of transporter control where the outer loop bandwidth is more than 3-4 times slower than the inner closed loop bandwidth, for reasons discussed in U.S. patent application Ser. No. 09/687,789.
[0036] A simplified control algorithm for achieving balance in the embodiment of the invention according to FIG. 1 when the wheels are active for locomotion is shown in the block diagram of FIG. 3. The plant 61 is equivalent to the equations of motion of a system with a ground contacting module driven by a single motor, before the control loop is applied. T identifies the wheel torque. The remaining portion of the figure is the control used to achieve balance. The boxes 62 and 63 indicate differentiation. To achieve dynamic control to insure stability of the system, and to keep the system in the neighborhood of a reference point on the surface, the wheel torque T in this embodiment is governed by the following simplified control equation:
[0037] T=K1(θ−θ0)+K2({dot over (θ)}−{dot over (θ)}0)+K3(x−x0)+K4({dot over (x)}−{dot over (x)}0), (1)
[0038] where:
[0039] T denotes a torque applied to a ground-contacting element about its axis of rotation;
[0040] θ is a quantity corresponding to the lean of the entire system about the ground contact, with θ0representing the magnitude of a system pitch offset, all as discussed in detail below;
[0041] x identifies the fore-aft displacement along the surface relative to a fiducial reference point, with x0representing the magnitude of a specified fiducial reference offset;
[0042] a dot over a character denotes a variable differentiated with respect to time; and
[0043] a subscripted variable denotes a specified offset that may be input into the system as described below; and
[0044] K1, K2, K3, and K4are gain coefficients that may be configured, either in design of the system or in real-time, on the basis of a current operating mode and operating conditions as well as preferences of a user. The gain coefficients may be of a positive, negative, or zero magnitude, affecting thereby the mode of operation of the vehicle, as discussed below. The gains K1, K2, K3, and K4are dependent upon the physical parameters of the system and other effects such as gravity. The simplified control algorithm of FIG. 2 maintains balance and also proximity to the reference point on the surface in the presence of disturbances such as changes to the system's center of mass with respect to the reference point on the surface due to body motion of the subject or contact with other persons or objects. It should be noted that the amplifier control may be configured to control motor current (in which case torque T is commanded, as shown in FIG. 4) or, alternatively, the voltage applied to the motor may be controlled, in which case the commanded parameter is velocity.
[0045] The effect of θ0in the above control equation (Eqn. 1) is to produce a specified offset θ0from the non-pitched position, θ=0. Adjustment of θ0will adjust the vehicle's offset from a non-pitched position. In some embodiments, pitch offset may be adjusted by the user, for example, by means of a thumb wheel 32, shown in FIG. 1. An adjustable pitch offset is useful under a variety of circumstances. For example, when operating the vehicle on an incline, it may be desirable for the operator to stand erect with respect to gravity when the vehicle is stationary or moving at a uniform rate. On an upward incline, a forward torque on the wheels is required in order to keep the wheels in place. This requires that the user push the handle further forward, requiring that the user assume an awkward position. Conversely, on a downward incline, the handle must be drawn back in order to remain stationary. Under these circumstances, θ0may advantageously be manually offset to allow control with respect to a stationary pitch comfortable to the user.
[0046] Alternatively, θ0can be set by the control system of the vehicle as a method of limiting the speed and/or the performance of the vehicle.
[0047] The magnitude of K3determines the extent to which the vehicle will seek to return to a given location. With a non-zero K3, the effect of x0is to produce a specified offset x0from the fiducial reference by which x is measured. When K3is zero, the vehicle has no bias to return to a given location. The consequence of this is that if the vehicle is caused to lean in a forward direction, the vehicle will move in a forward direction, thereby maintaining balance.
[0048] The term “lean” is often used with respect to a system balanced on a single point of a perfectly rigid member. In that case, the point (or line) of contact between the member and the underlying surface has zero theoretical width. In that case, furthermore, lean may refer to a quantity that expresses the orientation with respect to the vertical (i.e., an imaginary line passing through the center of the earth) of a line from the center of gravity (CG) of the system through the theoretical line of ground contact of the wheel. While recognizing, as discussed above, that an actual ground-contacting member is not perfectly rigid, the term “lean” is used herein in the common sense of a theoretical limit of a rigid ground-contacting member. The term “system” refers to all mass caused to move due to motion of the ground-contacting elements with respect to the surface over which the vehicle is moving.
[0049] “Stability” as used in this description and in any appended claims refers to the mechanical condition of an operating position with respect to which the system will naturally return if the system is perturbed away from the operating position in any respect.
[0050] In order to accommodate two wheels instead of the one-wheel system illustrated for simplicity in FIG. 4, separate motors may be provided for left and right wheels of the vehicle and the torque desired from the left motor and the torque to be applied by the right motor can be governed in the general manner described below in connection with FIG. 4. Additionally, tracking both the left wheel motion and the right wheel motion permits adjustments to be made to prevent unwanted turning of the vehicle and to account for performance variations between the two drive motors.
[0051] Referring now to FIG. 5, steering, or yaw control, of the transporter is accomplished by adding a turning command to the wheel amplifiers and have the following form. Inputs (described below) corresponding to values of transporter parameters are used by Pitch Controller 500 and Yaw Controller 502 to derive a balance control signal BalCmd and a yaw control signal YawCmd according to algorithms discussed in the succeeding paragraphs.
[0052] LeftCmd=BalCmd+YawCmd (2)
[0053] RightCmd=BalCmd−YawCmd (3)
[0054] The LeftCmd and RightCmd are the command sent by the controller to the left and right motor amplifiers, respectively, after differentiation or other conditioning as appropriate. The LeftCmd and RightCmd represent voltage if the amplifiers are in voltage control mode, current if the amplifiers are in current control mode, or duty cycle if the amplifiers are in duty cycle control mode. BalCmd is the command sent by the controller to each amplifier to maintain the transporter in a balanced state while moving or while at rest. The YawCmd causes the transporter to turn by reducing the command to one of the wheels while increasing the command to the other wheel. For example, a positive YawCmd increases the command to the left wheel while decreasing the command to the right wheel thereby causing the transporter to execute a right turn. The YawCmd may be generated by a yaw-input device described above with no feedback loop or in a closed cycle loop to correct yaw position errors as described in U.S. Pat. No. 6,288,505.
[0055] Pitch controller 500 is described in detail with reference to FIG. 6. The inputs include the desired transporter pitch θdesired, the actual measured pitch θ, the pitch rate {dot over (θ)}, and the component of the wheel rotation velocity that is common to the two primary wheels, ωcom. Both θ and {dot over (θ)} are typically derived from inertial sensing, as described in U.S. Pat. No. 6,332,103, which is incorporated herein by reference.
[0056] Desired transporter pitch θdesiredand current instantaneous pitch θ are differenced in summer 520 to produce a pitch error θerr. A term quadratic in pitch error θerr(preserving the sign of the actual pitch error) may also be provided, thereby providing more intense response to large deviations in pitch as may result from encountering an obstacle, for example. In a voltage control mode, a term is needed proportional to the wheel rotational velocity to compensate for all or a portion of the back-emf generated in proportion to the rotational velocity of the motors.
[0057] Yaw controller 502 is described in detail with reference to FIGS. 7A-7C. FIG. 7A depicts the differencing, in summer 522, of the current yaw value Ψ with respect to the desired yaw value Ψdesiredto obtain the current yaw error Ψerr. Desired yaw value Ψdesiredis obtained from a user input such as the thumbwheel or other user input device employed for directional input as discussed above. The current value of yaw is derived from various state estimates, such as the differential wheel velocities, inertial sensing, etc. Derivation of the yaw command from the yaw error is provided by controller 524 according to various processing algorithms. Two examples of yaw control algorithms are shown in FIGS. 7B and 7C. Various controller transfer strategies may be implemented with proportional, derivative, and ‘three term’ ‘PID’ functions as depicted.
[0058] A yaw control mechanism for providing user input for the yaw control system described above is now described with reference to FIGS. 8A-8C. A user mounted on the transporter provides yaw control input to yaw controller 502 (shown in FIG. 5) by rotating yaw grip assembly 800, shown in detail in FIG. 8B. With particular reference to FIG. 8A, user interface 14 has twin hollow stalks 802, one on either side, either of which may serve interchangeably to support yaw grip assembly 800. Thus yaw may advantageously be controlled by a specified hand (right or left), either side of central control shaft 16. Yaw grip assembly 800 comprises a grip 804 which is rotated about an axis 806 coaxial with stalks 802. Spring damper 808 provides an opposing force to rotation of yaw grip 804 and returns yaw grip 804 to the central neutral position. Yaw grip 804 contains at least one magnet 810 (two are shown, in accordance with a preferred embodiment), the rotation of which about axis 806 allows the rotational orientation of grip 804 to be sensed by sensor unit 812 (shown in FIG. 8C) which is disposed within protruding stalk 802. Thus, user interface 14 may be sealed at its ends with fixed yaw grips 814 and the integral sealed nature of the user interface is not compromised by the yaw control input. Sensor unit 812 may contain Hall effect sensors which are preferably redundant to ensure fail-safe operation. Other magnetic sensors may also be employed within the scope of the present invention.
[0059] Spring damper 808 may also contain a viscous damper to provide a non-Hooke's Law counter force.
[0060] The use of a sensor within the sealed user interface may also advantageously provide for user input other than yaw control, such as activating a pedestrian alert signal, lights, etc., or throttling torque applied to the wheels of a transporter. Grips 814 may also be the source of sound, by placing an audio transducer (not shown) into one or both of the grips, coupled wirelessly to the unit, thereby maintaining the sealed integrity of the user interface.
[0061] The described embodiments of the invention are intended to be merely exemplary and numerous variations and modifications will be apparent to those skilled in the art. All such variations and modifications are intended to be within the scope of the present invention as defined in the appended claims.
Claims
What is claimed is:
1. A method for providing yaw control for a balancing transporter having two laterally disposed ground-contacting wheels, the method comprising:
a. receiving a user input of a desired yaw value;
b. comparing an instantaneous yaw value with the desired yaw value to generate a yaw error value;
c. processing the yaw error value to obtain a yaw command signal; and
d. applying the yaw command signal in conjunction with a pitch command signal based on a pitch error in such a manner as to maintain balance of the transporter in the course of executing yaw control.
2. The method according to claim 1, wherein the yaw command signal includes a component term quadratic in the pitch error.
3. The method according to claim 1, wherein the yaw command signal includes a component term that is a function of a common wheel rotational velocity.
4. A yaw controller for a balancing transporter having two laterally disposed ground-contacting wheels, the yaw controller comprising:
a. an input for receiving a user-specified yaw value;
b. a summer for differencing an instantaneous yaw value from the user-specified yaw value to generate a yaw error value; and
c. a processor for generating a yaw command signal based at least on the yaw error value in conjunction with a pitch command signal based on a pitch error in such a manner as to maintain balance of the transporter in the course of executing yaw control.
5. A yaw controller in accordance with claim 4, wherein the input for receiving a user-specified yaw value is wirelessly coupled to the processor.
6. A yaw controller in accordance with claim 5, wherein the input comprises a grip coupled to a user interface and rotatable about an axis fixed with respect to the user interface.
7. A yaw controller in accordance with claim 6, wherein the grip includes a magnet moveable with respect to a sensor coupled to the user interface.
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