Manuel Moreyra and Blake Hamaford

Transcription

1 Proceedings of the 1998 EEE nternational Conference on Robotics & Automation Leuven, Belgium * May 1998 OnSe Of Manuel Moreyra and Blake Hamaford Haptic Technologies nc th Ave. NE Seattle, WA (206) moreyra@cris.com * [corresponding author] Biorobotics Laboratory Dept. of Electrical Engineering University of Washington Seattle WA washington.edu/ BRL ABSTRACT A method is described to characterize and experimentally measure the dynamic performance of haptic display devices. The method characterizes the response to impulse inputs of various frequencies characteristic of simulating hard contacts in virtual environments. By comparing the experimentally measured vellocity just after the impulse with the actual velocity, a dimensionless measure of structural distortion is derived. The method is easy to apply because no additional sensors or test fixtures are required. This paper presents a derivation of the structural deformation ratio for the single degree of freedom case, generalization to N-dof spatial devices, and experimental results for a single axis of a rugged haptic device in our laboratory. Acknowledgments This project was supported by National Science Foundation Grant BCS , the Washington Technology Center, and a contract with Roeing nformation and Support Services. NTRODUCTON Haptic displays, also known as force feedback devices, have drawn increasing attentioln from engineering researchers as applications draw nearer. The design of a device which can reproduce sensations of contact and manipulation at the human hand is a demanding challenge as the number of degrees of freedom, workspace, and the force output capacity increases. There are many aspects to the performance of haptic display devices which are relevant to the fidelity of the haptic sensations it can produce. Although much work remains to be done to relate these measures to psychophysics, several criteria have emerged (Rosenberg, 1995, Hayward, 1995). There can be no doubt that one of the most important of these measures is the frequency response or dynamic performance of the device. These dynamics are determined by the interaction of the inertia, stiffness, and friction properties of the various elements making up a network of structure and transmission between the actuator and user. Thus, a crucial design issue is making the dynamic response of the mechanism good enough to convincingly reproduce the high frequency transient forces of hard contact impact events. Defining the bandwidth of a force display in terms of a force input-output transfer function is tricky, as pointed out by Townsend and Salisbury (1989), because this transfer function depends strongly on the boundary conditions encountered by the device. There is a need for an objective and quantitative method of measuring the dynamic performance of haptic display devices. Two difficulties are the conceptual problem of defining a meaningful measurement and the practical probllem of making the measurement. Such a performance measure should do at least the following things: 1) Characterize the distortion of force feedback information imposed by the device s dynamics. 2) Provide engineering insight SO that problems can be fixed with targeted re-design. 3) Be adaptable to differing devices with different numbers of degrees of freedom, workspace, etc. 4) Be able to be expressed spatially so that good and bad directions can be identified in the device s various coordinate systems. 5) Be inexpensive to experimentallly measure. This paper will describe recent measurements on a laboratory prototype and a novel rnethod of analysis, the Structural Deformation Ratio (SDR.), which makes it relatively easy to quantify some aspects of the high frequency performance of force displays. We built a 2-axis force display device in our laboratory with 350 Watt brushless DC motors, cable drive transmission, and a rugged structure (Figure 1). Selected performance specifications are given in Table 1 For more details see Moreyra n later work, we designed and built a ~-5/98 $ EEE 369

2 axis, wide range, load cell for the end effector with which to study the interaction forces at the users hand (Moreyra 1996). A mechanical schematic diagram of one of the two degrees of freedom (Figure 2) illustrates some of the mechanical elements potentially contributing to distortion of the force appearing at the human hand. An important dynamic feature of any mechanism is the lowest structural resonance frequency. This frequency for our device varies between Hz depending on the device position. This natural frequency, w, defines three key regions for the device in the frequency domain. Normal control system practice is to confine the operation to the first of these three regions, but the broad bandwidth of impact forces and the high frequency response of human receptors (Shimoga, 1993) creates a need to maxi- Workspace Force Output: continuous peak 300 x 400 mm2 100 N 380 N Friction: static and dynamic N inertia (x, y). with force sensor (4.4, 4.6) kg (4.9, 5.1) kg 1 Spatial resolution (x and y axis) mm Controller Pentium 75 MH~ Sampling rate Torque servo drive: type wont. current -peak current switching frequency PWM 6 A 12 A 20 khz Figure 1: Photo of 2 axis planar force display device built at University of Washington (see Table 1) mize w, and to carefully consider the system s behavior at all three frequency ranges. Figure 2: Eighth order model describing transmission of force from actuator to human hand along a single degree of freedom. 370

3 Structural Deformation Ratio: Theory We will now derive the structural deformation ratio (SDR) for the case of a single degree of freedom device. We assume that torque is accurately applied by the actuator and that position sensors are rigidly attached to the motor drive shaft. We also convert motor torque to force through a constant radius. f an impulse, f :: E P = F(t)dt (2) f z: 0 is applied to a rigid body at rest, the theoretical change in velocity is where m is the total moving mass. n our example (Figure 2) (3) m = m,+m2+m3+m4+mhand (4) This assumes that frictional losses are negligible during the impulse itself. We can reproduce this situation experimentally by driving the actuator with appropriate commands to generate an impulse, P. We can then use joint sensors to measure the velocity, v, = v(t = E) (5) (see Figure 2), just after the end of the applied impulse. f flexibility is present in the device, the actuator will not "see" the entire mass instantaneously and The ratio Vm S(E) = - h (7) is thus a dimensionless measure of the flexibility of the device. Consider the simplified dynamical model of a single degree of freedom shown in Figure 3. The flexible element divides the total mass, m, into two components r?z and m - rit. The response of this system will contain a mode determined by the "fast inertia" 1-1 mf = (;-- -7) (8) P = mvfh = ikv, (9) We can solve for the moving component, & by The mass ratio, r, may indicate the source of unwanted structural flexibility in the single degree of freedom case. The total mass, m is known from the design. Working from the actuator towards the end point, mass of each element is accumulated in the serial chain until rir is reached. The next link in the chain will be a candidate for the source of flexibility. Of course this method will only work for the case where one element in the chain provides a dominant compliance. Spatial SDR The SDR can be generalized from the scalar measurement given above to spatial mechanisms. First we will assume that the velocity is at or near zero so that centripetal and Coriolis terms and variations in the device configuration can be neglected. Second we will neglect the effects of gravity. n this case T = M(e)e (12) Where M(e) is the device inertia matrix, and 0, is the joint accelerations. f we apply impulses to the joints according to: Then eth(p) E P = T(^) dt (13) 0 =& = M-"(e)P f we perform a suitable experiment and measure the r"" f the frequency content of the force waveform is high compared to - - then only rit 21n&. will effect the initial transient response and we can neglect the momentum of the second mass. f the impulses are equal for the experimental and theoretical cases, and if losses are negligible during the impulse, we have Figure 3: Simplified model of a single degree of freedom force transmission illustrating the transiently moving and fixed masses. 37 1

4 actual joint velocities, 6,,we can then form the spatial structural deformation ratio as a diagonal matrix as follows (E) describes the unwanted deformation or distortion of the structure in the joint space. To identify the importance of these effects for the human operator s perception, we might want to see how that deformation is reflected into the task space through the kinematic model of the haptic device. We can derive a task-reflected deformation by considering the following mapping: Axs = J(k) AO, (16) where AOf is a hypothetical incremental deformation of the joint, Axs, is the corresponding deformation in the task space, and J(0) is the manipulator Jacobian matrix. Applying the singular value decomposition (SVD) to the mapping, J(0)S, describes an ellipsoid similar to the manipulability ellipsoid (Yoshikawa, 1990). This ellipsoid characterizes the effects of structural distortion relative to the human operator space. Eigenvectors corresponding to large eigenvalues describe the direction along which the effects of mechanism deformation should be the most noticeable. EXPERMENTAL METHODS To measure one aspect of the dynamic performance of our device, we conducted an experiment in which torque impulses were applied to the device through its motors and the resulting force was measured at lhe human hand. The impulses were defined by F(k) = Asin($) Where E is the impulse duration in integer milliseconds, and k = 0, 1, 2,..., E is the sample number (sample rate = 1000 samples per second). The amplitude, A, was 100 Newtons, Our experiment chose impulse durations corresponding to frequencies in the three ranges described above (Table 2). The force response can be expected to depend strongly on load on the end effector and/or the human operator dynamics. To study some of this dependence, we simulated the inertial effects of the human operator on the system by adding weights of 0.67kg and 1.2kg corresponding to bent arm and extended arm postures. We measured the weight of the forearm of seven volunteers with body mass between 75kg and 93kg. The average weight of the hand and about one half of the forearm was 0.67kg (minimum 0.5kg, maximum 0.9kg). With the arm fully extended and relaxed, the average weight of the hand and about one half of the arm was 1.2kg (minimum 1.Okg, maximum 1.4kg). RESULTS Force mpulse Responses Force impulses were applied to the High Bandwidth Force Display which was set to a position in the middle of the x axis travel (the worst case for mechanical stiffness). The force response to each of the three impulses with each of the masses was highly oscillatory (Figure 4). The peak force measured at the handle increases from about 2.5 N with no additional mass and a 5ms impulse to 10 N for 1310 gr. of added mass and a 51ms impulse. t is interesting to note that the peak actuator force amplitude was loon in all cases so that considerable attenuation is evident with the shorter impulses. n an additional experiment, a human operator grasped the handle and the response with 675 gr. payload is plotted as a control (Figure 5 ). Because the effective inertia of the arm depends on posture, the experiment was repeated with two poses: straight arm and bent arm. For a more comfortable user posture, this experiment was performed with the device near a corner of its workspace so the natural frequency was slightly higher. With both grasp postures, the responses are much less oscillatory than the inertially loaded control case (Figure Sa,b,c). Structural Distortion Ratio Using the method described above, the SDR was measured for the different impulse durations and applied payloads (Table 2). The frequency of the sinusoid corresponding to each impulse given by equation (17) is listed to give a basic idea of the frequency content of each impulse. The SDR approaches 1 as the frequency content Table 2: Structural distortion ratio. LD. Trequ- ruct. distortion ratio V,JV,* of the impulse goes down Payloads (gr) 372

5 U 5 0 h -5 a) 5 ms force input, Fn = 700 sm(@/6), k= 0, Time (ms) [ b) 17 ms force input, f,, = 700 sir)(@/78), k = 0,,.. 78 v 2101 a) 5 ms force input, F,n = 700 sin(kp/6), k = 0,7,..6-5 c Time (m) b) 17 ms force nput, f,,, = 00 sin(kp/78), k = 0,, ":A c) E5 51ms force input, f, = 700 sin(kp/52), k = 0,7, t Time lmsl ( Time (ms) Figure 4: Reaction forces to various sinusoidal shaped force impulses. The payloads on the handle weigh 0,675, and 1310 gr, handle weighs 195 gr. Reaction force increases with heavier payload Time (ms) 675 gr payload - bent arm extended arm Figure 5: Arm reaction forces to various sinusoidal shape force impulses. DSCUSSON This paper has presented a new technique for the measurement of dynamic properties of haptic display devices. Dynamic response is important to the perception of high frequency haptic information such as texture interaction or making hard contact. The technique was applied to a Cartesian, 2-axis force display device, and theoretically extended to serial kinematic chains of arbitrary dynamics and geometry. mpulse responses with pure inertial loads were highly oscillatory but the oscillation was almost totally suppressed by normal human hand contact. mpulse amplitudes were greatly attenuated (by as much as 40:1, 32db) depending on frequency content. This is to be expected due to the inertia of the device. For transient forces it is reasonable to approximate where FHO is the amplitude of the impulse felt by the operator, FA the amplitude of the actuator impulse, and MHO, MFD are the masses of the human operator and force display respectively. We measured the SDR for our device with impulses whose frequency content was a factor of three above, approximately equal to, and a factor of three below the device natural frequency. SDR was as high as 3.23 for the shortest impulse and the largest added mass, and as low as 0.98 for the longest impulse and 1-10 added mass. SDR of less than one is possible because frictional losses may "absorb" some of the impulse even before it is over. n the derivation above we neglected the effects of gravity. Gravity can be easily handled with one of the fol- 373

6 lowing approaches. First, it may be possible to ignore the effects of gravity. This would be the case if a dynamic simulation of the device with gravitational effects but without the applied impulses showed that gravitational acceleration results in a velocity after the impulse duration which is insignificant compared to the measured post-impulse velocity, V,. This could also be measured experimentally by letting the device fall from its initial position. Second, if necessary, it could be compensated for by subtracting the computed or measured gravitationally induced velocity from V,. To evaluate the dynamic performance of a force display with this method the following steps can be performed: Set up the device as normal but attach a mass to the endpoint approximately that of the appropriate human limb (i.e. the finger, hand, arm etc.). Using modified control software, apply single impulses of different durations to the joint motors and record joint velocity immediately after the end of the impulse. A torque impulse can be applied to either one joint at a time or to more that one joint. However, all joint velocities must be measured and computed. Further research is necessary to determine the effect of these different possible stimulus patterns. Compute the theoretical joint velocities, erh using (14). Compute S, the structural deformation ratio matrix for various impulse durations. Compute the deformation Jacobian, J( 0)s using (1 5) Compute and plot the deformation ellipsoid in task space. This method can be applied to all serial, impedance controlled, haptic devices and does not require any additional sensors or test fixtures. To evaluate the results, the system should be tested with impulses of varying durations (i.e. various frequency content). As was done in our experiment, the pulse durations should be selected to span the frequency range which includes the device structural modes when they are known. When the SDR is close to unity the manipulator is perfoming well. The shorter the maximum impulse which causes the SDR to exceed unity, the higher the device bandwidth. n the spatial case, the axes of the deformation ellipsoid show the directions in the operator s workspace which are most affected by dynamic limitations of the device. Desirable performance is represented by a deformation ellipsoid which is equal to the manipulability ellipsoid, i.e, for which qe)s = qe)r. (19) The principle advantage of this method is its simplicity. Although it does not provide a complete characterization of the device, the method has the following advantages. No external sensor or test fixture are required. Existing sensors (joint position and derived or measured velocity) and interface electronics are used. The SDR is dimensionless and can be compared among haptic devices of different size, force outputs, etc. The method applies to any number of degrees of freedom. t is independent of the human operator dynamics (the added mass to represent the human operator can be easily standardized). By using the SDR to estimate the ratio of moving mass to stationary mass, it may be possible to locate unwanted flexibility in the mechanism. Further research is needed to determine the psychophysical importance of non-uniformity of the deformation ellipsoid. There may be directions for which the human is more or less sensitive to haptic device flexibility. REFERENCES V. Hayward, O.R. Astley, Performance Measures for Haptic nterfaces, Proceedings 7th ntl. Symposium on Robotics Research, Herrshing, Germany, Oct , 1995 Moreyra, M., Design of a Planar High Bandwidth Force Display with Force Sensing, MSEE Thesis, Department of Electrical Engineering, University of Washington, Seattle, WA Rosenberg, L. How to Assess the Quality of Force- Feedback Systems, The Journal of Medicine and Virtual Reality. Vol 1, No 1. Spring Shimoga, K., A survey of perceptual feedback issues in dexterous telemanipulation. 11. Finger touch feedback, Proceedings EEE VRAS-93, pp , Seattle, WA, September 1993 Townsend, WT, Salisbury, JK, Mechanical bandwidth as a guideline to high-performance manipulator design, Proceedings EEE nternational Conference on Robotics and Automation, Scottsdale, AZ, USA.vol.3., pp ,14-19 May Townsend, WT, The Effect of Transmission Design on Force-Controlled Manipulator Performance, Ph.D. Thesis, Artificial ntelligence Laboratory, Massachusetts nstitute of Technology, Massachusetts, Yoshikawa, T. Foundations of Robotics, Analysis and Control MT Press, Cambridge MA,