Robot Gripper Control System Using PYDF Piezoelectric Sensors

The present invention relates to a robot gripper control system and more particularly to a control system which uses PVDF piezoelectric sensors to measure slippage or tangential forces as well as normal forces.

It is known in the prior art to use piezoelectric materials in robot manipulators. U.S. Pat. No. 4,539,554, issued to Jarvis et al. on Sep. 3, 1985, discloses pressure transducers capable of producing an analog output voltage representative of the applied pressure. Jarvis et al. discloses a piezoelectric material disposed between a ground plate and a silicon transducer. The amount of force applied through a compliant cover over the piezoelectric material to the silicon transducer is proportional to the sensing of the silicon transducer. The capacitance is stored at a node A associated with the transducing element, and may be interrogated by a sensing circuit located in the silicon substrate which yields a direct indication of the localized force applied to the sensor. Jarvis et al. discloses that the piezoelectric material may be the piezoelectric polymer polyvinylidene fluoride (hereinafter "PVDF").

U.S. Pat. No. 4,495,434, issued to Diepers et al on Jan. 22, 1985, discloses a pressure-sensitive transducer for robot grippers. Diepers et al. refers to the use of transducers of piezoceramics or piezoelectric polymers such as PVDF.

U.S. Pat. No. 3,285,074 issued to Elazar on Nov. 15, 1966, discloses a piezoelectric transducer (accelerometer) which is dampened by a series of diodes. The system includes a cross-feedback arrangement using the output of one crystal as a reference with respect to a zenner diode and another crystal

The present invention relates to a robot gripper system which senses tangential as well as normal forces to compensate for slippage. A rate-of-force signal can be utilized to actively damp an exerted force.

The apparatus including the features noted above and described in the preferred embodiment below relates to a robot gripper system operated by a motor, having a gripper mechanism used to engage an object. A force sensor provides a force signal proportional to the amount of force applied by the gripper mechanism to the object in both the tangential and the normal direction. A control circuit 30 receives the force signal and controls the gripper motor accordingly. Another sensor produces a rate-of-force signal proportional to the rate of the application of the gripper force to the object. A circuit is provided to utilize said rate-of-force signal as a negative feedback to the control circuit for the gripper motor.

In the preferred embodiment the sensor that provides the rate-of-force signal proportional to the rate of the application of the gripper force to the subject is a PVDF piezoelectric sensor.

The control system more specifically comprises a first sensor that provides a first signal proportional to the integrated force exerted by the gripper surface on the object being engaged. A second sensor means provides a second signal proportional to the rate-of-force exerted by the gripper surface on the object being engaged. These signals refer to the forces provided in the normal direction to the object being gripped. Similar signals are transmitted by sensors measuring tangential forces on the gripper mechanism.

The control operating the gripper motor includes amplifying means for providing a control signal to control the operation of the motor, first means for providing the first signal as a negative feedback, second means for providing the second signal as a negative feedback and mixer means connected to said amplifying means for providing a mixed signal to the amplifying means comprised of the first and second signals.

It should be understood that other objects and advantages of the present invention will be readily appreciated by reference to the following detailed description when considered in connection with the accompanying drawings

FIG. 1 is a schematic block diagram of a robot gripper control system according to one embodiment of the present invention.

FIG. 2 is an isometric view of a robot gripper according to one embodiment of the present invention.

FIG. 3a is an isometric view, with portions broken away, of a piezoelectric sensor according to one embodiment of the present invention.

FIG. 3b is an enlarged view of a portion of FIG. 3a.

FIG. 3c shows a rate-of-force sensor means according to one aspect of the present invention.

FIG. 4 is a graphic illustration of experimental open-loop step response of the gripper.

FIGS. 5a, 5b and 5c graphically illustrate the component of a model/according to the present invention.

FIG. 6 graphically illustrates the calculated openloop step response or he model.

FIG. 7a is a graph illustrating the experiment step response of a PVDF rate sensor using the pencil point break step response technique.

FIG. 7b is a graphic representation of the theoretical response of the PVDF sensor calculated from the model.

FIG. 8 is a graphical representation of the theoretical test of, the ability of the rate feedback sensor to suppress overshoot/with or without rate feedback.

FIG. 9 is a graphical representation of a theoretical test of the speed enhancement of an undamped response, a damped response using rate feedback, and a damped response using friction.

FIG. 10 is a graphical representation of the root loci of a proportional control system and a PD control system.

FIG. 11 is a graphical representation of an experimental test of the ability of the rate feedback sensor suppress overshoot with or without rate feedback.

FIG. 12 is a graphical representation of an experimental test of the speed enhancement response with the feedforward and feedback gains adjusted simultaneously and the best response without rate feedback.

FIG. 13 is a graphical representation of an experimental impact test showing step response with or with rate feedback.

Polyvinylidene fluoride ("PVDF") is a piezoelectric polymer which shows great promise as a sensor for robot systems. According to the present invention, this material is used for robot gripper control. The piezoelectric sensor functions as a rate-of-force sensor for derivative feedback, while a strain gauge senses both the integrated force exerted upon the entire gripping surface in the normal and tangential directions. The sensors are used together in a proportional and derivative (PD) control system. The benefits afforded by the additional sensory feedback have been evaluated by comparing the performance of a gripper with and without the piezoelectric sensor.

A particular advantage is obtained by measuring the tangential forces which may not be readily available to a mechanism sensing only normal forces. In those systems utilizing normal force measurement grippers operate to apply a force without the ability to sense slippage. If an object between robot fingers for example slips while the robot is maneuvering, the mechanism cannot measure this slip and make the necessary adjustments. By utilizing certain properties of PVDF films, this tangential force and thus the slip can be determined and compensated for.

Robot gripper control is the control of the force integrated over the gripping area. The integrated force is directly related to the issue of gripper compliance control. Most gripping problems are concerned with the fast, accurate application of force in one direction. Compliance control could also be defined in terms of the finger position and velocity, or in terms of both force and position. Gripper control may also depend on static variables such as object orientation.

We have found PVDF to be troublesome for absolute force feedback due to output drift and temperature sensitivity. Others have shown that use of extremely thin piezoelectric films and temperature compensation may make piezoelectric sensor practical for absolute force measurements See P. C. Chen, R.S. Muller and R.M. White, "Thin Film ZnO-MOS Transducers with virtually dc Response," Proceedings IEEE Ultrasonics Symposium, Nov. 1980; D.L. Polla, R.S. Muller and R.M. White, "Pyroelectric Properties and Application of Sputtered Zinc Oxide Thin Films," Proceedings IEEE Ultrasonics Symposium, San Francisco, CA 1985; A.J. Bur and S.C. Roth, "Development of a Polymer Pressure Gage with Temperature Compensation," National Bureau of Standards Interim Report, Contact No. 82-64, 1982. Piezoelectrics, however, function quite naturally as rate-of-force sensors. No current integration or high impedance voltage amplifiers are required. One must simply measure the voltage output of the transducer as the charge drains across a path of low resistance. If a piezoelectric sensor and an integrated force sensor are used together, force and damping should be simultaneously controllable as in a classical D control system where the position variable is force, and the velocity variable is rate-of-force.

The control problem addressed by our invention is the maximization of the rise time of a step change in force under the constraint of zero overshoot. This problem is specified in terms of step response rise time and overshoot, because the most demanding gripper applications require fast response time and generally cannot tolerate overshoot. The step function is the most difficult encountered in practice, and the most practical in view of speed maximization. The step response analysis presented here is confined to consideration of changes from one nonzero low level of force to another high force level However, experimental results are reported which demonstrate the possible extensibility of the results to the control of nonlinear impact forces.

The robot gripper, sensors, and control system are shown graphically in the block diagram in FIG. 1. The transfer function G(s)=(Output Force/Input Voltage) represents the dynamic coupling between the voltage input of a pulse-width-modulated power amplifier, DC permanent magnet motor, the robot gripper mechanism, and the force sensor. The pulsed power amplifier is required to boost the signal power and to reduce nonlinearities introduced by commutator voltage drop in the drive motor. The piezoelectric force sensor is represented by the transfer function R(s).sub.1 =(Output Voltage)/(Input Force). The gains K and e are the respective scalar feedforward and rate feedback gains. The same representation and gains apply to R(S).sub.2 for controlling the system based on tangential forces.

The gripper on a commercially available manipulator Rhino XR-1, selected for this experiment, is similar in design to many popular industrial grippers It is position locking in that forces exerted on the gripping surfaces are isolated from the dc electric drive motor when the motor is turned off. Position locking grippers tend to be more efficient than back-drivable grippers in which steady state forces are not isolated from the drive motor. The instrumented fingers of the gripper are shown with mounted sensors and an object C in FIG. 2. Only one piezoelectric B and one force sensor A are used experimentally, because the gripper applies forces symmetrically to both fingers The force sensor A is a silicon strain gauge commercially available from Transensory Devices. This sensor is selected for its excellent linearity, low hysteresis, absolute accuracy, and commercial availability.

The piezoelectric polymer PVDF is an ideal piezoelectric for rate-of-force sensing because of its strong low Q response, ease of use, and compliance, properties which are lacking in most non-polymeric piezoelectric. The sensor B is mechanically designed for stretch mode response as well as thickness (compression) mode response.

All but a small circular spot of a conductor 1 is etched away on one side of a rectangular piece of PVDF file 2 as shown in FIG. 3a. The opposite side of the film is completely covered by the conductor 3. The inner conductor 4 of a short piece of high gauge coaxial cable 5 is connected to the conducting support using conductive epoxy 6. A first edge 20 of the film is bent upward, and a portion of the outer conductor 7 of the coaxial cable 5 is attached to the front surface at the bend. The outer conductor 7 has another portion 24 attached to the front surface of a second edge 22 which is also bent upward. Finally, the sensor is potted in non-conducting epoxy 9 with the conducting surface of the film facing outward (downward) as shown in FIG. 3b. The coaxial cable 5 and grounded front surface provide excellent shielding (40 dB S/N), while the potting epoxy provides support for the cable connection and the film. This construction technique is a modification of the technique described by Dario for piezoelectric array sensors. See J.S. Schoenwald, "Strategies for Robotics Sensing Using Acoustics," Proceedings IEEE Ultrasonics Symposium, San Francisco, CA, Oct. 16-18, 1985. Dario's technique, however, requires a special feed-through circuit board for support and electrical connection.

One example of a band limited current amplifier as best illustrated in FIG. 3c, has a coaxial cable 5 connected to a nearby amplifier which buffers the voltage signal across a 1 megaohm input resistor 10. The capacitance of the film is approximately 10 pF. The input resistor 10 and this capacitance form a first-order bandpass network with a resonate frequency of approximately 20 kHz. Since the step response rise time of the sensor is 20 microseconds, the bandwidth of the bandpass network is only slightly wider than that of the sensor. This band-limiting damps high frequency noise, and places an upper limit on the rate at which the derivative can change if it is to be detected accurately. The wide bandwidth of the piezoelectric sensor is of importance in its application as a rate-of-force sensor. The output of the strain gauge, for instance, could not be differentiated and used for rate feedback because of its narrow bandwidth; regardless of noise issues It should be noted that the other designs for the band limited current amplifier can be used.

An output force to input voltage transfer function model for the gripper, G(s), and an input force to output voltage model of the rate sensor, R(s).sub.1 and R(s).sub.2 are obtained to permit the evaluation of the theoretical closed-loop performance Both models are determined from their step response in the time domain.

The transfer function of the gripping mechanism, G(s), was identified from experiments performed on the open loop plant and a closed-loop proportional (no rate feedback) control system. Closed loop experiments on the system indicated that two additional assumptions could be made. First, the system can track step inputs without steady state error. This indicates that the system is at least type 1. Secondly, the system is capable of closed loop instability. The feedforward gain level which causes instability is measured experimentally. This indicates that the order of the denominator of the transfer function should be at least three orders of magnitude higher then the numerator. Thus, the model should be of the form shown in Eq. (1). ##EQU1##

The force sensor output resulting from a 7-volt step input is shown in FIG. 4. The model is constructed in a step wise-iterative process to approximate the dominant response while incorporating the above-mentioned facts about the closed loop performance. First, the most important components of the response are modeled: the rise from zero to 50 millivolt and the rise from 50 to 100 millivolts. Those components are modeled as the sum of an exponential and an integral term as shown in FIGS. 5a and 5b.

FIGS. 5a and 5b can be represented in the frequency domain as the sum of the Laplace transforms of each part. Multiplying by s to account for the step input yields the preliminary transfer function shown in Eq. (2). ##EQU2##

The resulting response is shown in FIG. 5c. This figure has nearly the same form as FIG. 4, but lacks the slight initial curvature and final flattening. The final flattening is the result of torque saturation in the motor. If the force exerted by the gripper is confined to low levels, the motor torque will never saturate due to the position locking effect of the gripper mechanism. Therefore, in closed loop operation, this final flattening will never occur. The model could be extended to high levels of force near motor stall using an integral compensator with torque dependent gain. High level forces are not required for the experiments considered herein, so integral compensation is not required.

The model in Eq. (2) is not yet in the form required by Eq. (1). Since the numerator is first order two additional lo poles must be chosen. One pole is found by iteratively matching the initial curvature to that of FIG. 5a. The last pole is found using the Routh-Hurwitz stability criterion and the fact that the closed loop response becomes unstable when the feedforward gain K rises above 500. After scaling, the final transfer function is shown in Eq. (3). ##EQU3##

A plot of the theoretical step response is shown in FIG. 6. Note that the model given in Eq. (3) is already in its simplest form. No further simplifications are possible without sacrificing all ability to predict the relative stability of the closed loop system. Friction nonlinearities make higher order transfer function models meaningless.

The rate sensor R(s).sub.1 and R(s)2, is also modeled from its step response. The step response rise time of piezoelectrics is extremely fast. The simplest step actuation technique of sufficient speed available is the pencil point break technique first developed by Hsu to simulate a source of acoustic emission. See W. Sachse and N.N. Hsu, "Ultrasonic Transducers for Material Testing and Their Characteristics," in Physical Acoustics, Vol. 14, W.P. Mason and R.N. Thuston, eds., New York: Academic press, 1979. When a thin lead (0.5 mm) pencil point is broken, the force exerted by the lead drops to zero in less than a microsecond. Knowledge of the exact value of the input force is not essential because it can be identified later. The most important part of the response is the initial rise, as will be shown.

The step response of the PVDF film across a 1 megaohm resistor is shown in FIG. 7a. This response can be broken into two parts:

(1) a 25 kHz high-frequency mode, and

(2) a 2 kHz low-frequency mode.

The low frequency mode is associated with oscillation of the surface after the unloading process. In the gripper system, the sensor will be used to sense impact forces, and changes in force after contact is established. Therefore, the sensor will have some surface loading up until the object is to be released. Hence, the low frequency mode is ignored in the modeling procedure. The high-frequency response resembles the step response of a second order bandpass filter with an undamped natural frequency of 40.times.10.sup.3 rad/sec, and a damping ratio of 0.3. Using these facts as parameters, the transfer function of Eq. (4) is derived. ##EQU4## The response of this filter is plotted in FIG. 7b.

We have conducted tests which compare the performance of the gripper control system with and without rate feedback. The results are divided into theoretical and experimental parts. In both parts two basic tests are performed. The first test in each part demonstrates the ability of the additional feedback to prevent overshoot during a step transition in force. The second test compares the fastest achievable rise times with and without rate feedback. The description of the experimental results also reports an impact test using the PD control system.

Step responses are calculated using the transfer function models as discussed above.

The first test is designed to demonstrate the ability of the PD control system to prevent overshoot during a step response. The rate feedback gain e is first set to zero. The feedforward gain K is raised to a value (300) which causes overshoot in the response as shown in curve (a) of FIG. 8. At this feedforward gain, the overshoot is 25 percent, and the settling time is 200 ms. If the feedforward gain K were increased further, the overshoot would grow larger and the settling time would be longer. Next, without changing feedforward gain K, the rate feedback gain e is raised to a value (25) which reduces the overshoot to a smooth monotonic response as shown in curve (b) FIG. 8.

The rise time in both cases is the same, but because oscillation about the steady state value are eliminated the settling time is reduced to only 150 ms when rate feedback is included. Therefore, the models indicate that overshoot can be damped through rate feedback without sacrificing speed

This test demonstrates the response speed enhancement attainable using the PD control system. Since the PD control system allows the damping to be increased as the feedforward gain is increased, much higher feedforward gains may be used without overshoot. Curve (a) of FIG. 9 shows the step response of the proportional system (rate gain e=0) when the feedforward gain is set such that the response is nearly unstable (K=500). The overshoot force is 60 percent and the settling time is 700 ms. If the rate feedback is raised to 30 all overshoot is eliminated, the rise time is reduced to 60 ms as shown in curve (b) of FIG. 9. This is approximately the fastest rise time predicted by the theory.

Higher feedforward gains require significantly higher rate feedback gains which tend to overdamp the response to such an extent that longer rise times result. For purposes of comparison, curve (c) of FIG. 9 is included to show the fastest rise time achievable without any rate feedback. Here the rise time is 500 ms. Curve c is actually the fastest monotonically increasing response without rate feedback. (The constraint of monotonicity is added to make the results more realistic. In the actual control system, if no rate feedback is used, all damping must come from friction. In practice, most nonmonotonically increasing responses lead to actual overshoot due to friction nonlinearities.) A comparison of responses in curves b and c indicates that an order-of-magnitude improvement in response speed may be possible.

Test 1 indicate that if the feedforward gain was held constant, the feedback gain could be adjusted independently to set the damping to a desired level. In fact, the damping can be set over a wide range, and can even be used to reduce the friction inherent in the gripper by changing the sign. The stabilizing effect of the rate feedback is clear upon examination of the root loci of the two systems FIG. 10 shows the superimposed root loci with and without rate feedback for the above two cases. The dominant poles move significantly closer to the right half plane as the feedforward gain is raised from 300 to 500 in the proportional control system, while in the PD control system, the poles move away from the right half plane as the gain is raised.

This shows that the rise time of the system can be reduced with rate feedback Also note that the zeta of the dominant complex poles increases sharply from zeta=0.3219 to zeta=0.2132 as the gain is increased in the proportional control system. However, it is only from zeta=0.625 to zeta=0.608 slightly increased in the PD control system. This 550% difference accounts for the dramatic reduction of the overshoot by the use of a rate sensor.

The theoretical results reported above were experimentally tested using the hardware described in connection with FIGS. 1-3. This output force is detected by the feedback force sensor, recorded on a digital oscilloscope, and the results are plotted from the oscilloscope.

Curve (a) of FIG. 11 shows the step response when the feedforward gain is adjusted as in the first theoretical test without rate feedback. The response shows larger oscillations than were present in the theoretical test, but rise time and settling time are roughly the same. This discrepancy is probably caused by frictional effects which are not included in the model of the gripper.

When rate feedback is included (same feedforward gain), the oversheet is completely suppressed as shown in curve 9b) in FIG. 11. As in the theoretical response, the rise time is virtually unaffected by the additional feedback, and the settling time is reduced.

In this part, the maximum response speed with and without rate feedback is experimentally determined. First, the most rapid response without rate feedback is determined by the criteria outlined above in test 2 of the theoretical results. This response is shown in FIG. 12b to have a rise time of 2 seconds.

Next, the feedforward gain and rate feedback gain are increased together to achieve the minimum step response rise time of 90 mx as shown in FIG. 12a. Thus, experiment indicates that the response time can be improved by more than an order of magnitude using rate feedback.

We have conducted a nonlinear experiment which extends the above experimental results to real life gripping conditions. In the above tests, the gripper was always in contact with the object with some small initial contact force. In the actual gripping processes, however, the gripper would usually close unimpeded until it makes contact with the object to be grasped. Curve (a) of FIG. 13 shows the step response when the wide open gripper closes with proportional feedback onto an object placed symmetrically between the fingers. The initial part of the response is zero because no contact exists as the gripper closes. The response jumps to more than 300 percent in overshoot, breaks contact with the object, and impacts again. The second impact is at lower initial velocity, and the response is damped by friction after 2 seconds. The response finally reaches steady state (not shown) after 10 seconds.

In contrast, the curve (b) of FIG. 13 shows the step response when the system is adjusted with the same feedforward gain as above, but rate feedback is included. This response exhibits only a few percent overshoot, and the settling time is 300 ms (after impact). Thus, the rate feedback should provide significant improvement in the performance under practical gripping conditions.

A robot gripper control system has been constructed and analyzed to evaluate the usefulness of piezoelectric rate-of-force sensor feedback in gripper force control. Rate sensing was shown to provide a method of actively damping the force exerted by the gripper. Specifically the rate feedback was shown to be effective in suppressing overshoot occurring during step transition in force, and to improve the step response settling time by as much as an order of magnitude. A demonstration shows the possible extensibility of the results to the damping of impact forces. Overall, it is apparent that significant advantages exist in the use of piezoelectric rate-of-force sensors in the control of robot grippers.

The above tests were directed to measuring normal forces on the control system. The same relationship exists for measuring tangential forces The advantages of measuring tangential forces is the ability to compensate for slippage despite signals from PVDF in the normal direction that the object is being held properly.

For this purpose controller 30 includes a comparator and override system for controlling the gripper. In those instances where the signal sensed at R(s).sub.1 indicates satisfactory forces being applied, the controller will produce a signal for the gripper to provide the necessary force based on the feedback signal from R(s).sub.2. That is where tangential forces are sensed and the gripper will be operated to apply the additional force to overcome the slippage.

While preferred embodiments of the invention have been shown and described, it will be apparent to those skilled in the art that modifications can be made within the scope of the invention which is defined in the appended claims. Accordingly, the foregoing embodiments are to be considered illustrative only, rather than restricting the invention and those modifications which come within the meaning and range of equivalency of the claims are to be included herein.