1. Identification of Human Grasp Dynamics and the Effects of Displacement Quantization and Zero-Order Hold on the Limit Cycle Behavior of Haptic Knobs Doctoral Dissertation Defense Christopher J. Hasser November 19, 2001

2. System IDSimulation TheoryHardwareDiscussion 2 Reading Committee J. Kenneth Salisbury Mark R. Cutkosky J. Christian Gerdes

3. System IDSimulation TheoryHardwareDiscussion 3 Acknowledgements Stanford faculty and staff Immersion Corporation Haptic research community Fellow students Family

4. System IDSimulation TheoryHardwareDiscussion 4 Haptic Greek origin – “of or pertaining to the sense of touch”

5. System IDSimulation TheoryHardwareDiscussion 5 Common Haptic System Architecture Illustration: Immersion Corporation

6. System IDSimulation TheoryHardwareDiscussion 6 Haptic Knobs Illustrations: BMW/ Immersion Corporation

7. System IDSimulation TheoryHardwareDiscussion 7 Nissan Concept Haptic Scroll Wheel in Nissan Concept Car Close-up of Haptic Scroll Wheel Illustrations: Nissan/ Immersion Corporation

8. System IDSimulation TheoryHardwareDiscussion 8 Often occur during contact with a virtual barrier Distracting, unacceptable user experience Relevant factors: –Zero-order hold delays –Displacement signal –Velocity signal –Physical damping –Virtual barrier stiffness Limit Cycle Oscillations

9. System IDSimulation TheoryHardwareDiscussion 9 Goal Understand the effect of displacement quantization on limit cycle oscillations in sampled data haptic systems.

10. System IDSimulation TheoryHardwareDiscussion 10 Approach 1.Identify the dynamics of the human hand grasping a haptic knob 2.Model and simulate the effects of displacement quantization 3.Analyze using nonlinear control theory 4.Empirically confirm simulation and theory 5.Discuss effect origins and design implications

11. System IDSimulation TheoryHardwareDiscussion 11 Why Simulate? Easily observable, repeatable conditions Precise control over experiment parameters Physically impossible configurations Analysis of hardware yet to be constructed

12. System IDSimulation TheoryHardwareDiscussion 12 EE Student to EE Professor: “But how do you *get* the plant model?” EE Professor: “You hire a mechanical engineer.” Why System Identificaton?

13. System IDSimulation TheoryHardwareDiscussion 13 Why System Identificaton? Simulation requires a plant model Two choices for obtaining model: –Analytic construction –System identification System identification most attractive for complex human hand under well- constrained conditions

14. System IDSimulation TheoryHardwareDiscussion 14 Apparatus Design and drawing: B. Schena For system ID and simulation verification 25 mm brushed DC motor Knob with grip force load cell 640,000 count per revolution optical encoder

15. System IDSimulation TheoryHardwareDiscussion 15 Pinch Grasp Nine subjects – five male, four female Subject squeezed knob slowly 20 ms torque pulse applied when grip force reached threshold

16. System IDSimulation TheoryHardwareDiscussion 16 Second-Order Lumped Parameter Model finger finger, knob, & motor rotor

17. System IDSimulation TheoryHardwareDiscussion 17 Torque, Acceleration, Velocity, and Displacement Input Torque (upper left), Acceleration (upper right) Velocity (lower left), and Displacement (lower right)

18. System IDSimulation TheoryHardwareDiscussion 18 Torque Contributions and Model Check

19. System IDSimulation TheoryHardwareDiscussion 19 Model Performance Pulse (Step) Responses for Various Grip Forces

20. System IDSimulation TheoryHardwareDiscussion 20 Results Across All Subjects Moment of Inertia (J), Damping (B), Stiffness (K), and Damping Ratio (ζ) J K B ζ

21. System IDSimulation TheoryHardwareDiscussion 21 Fourth-Order Model Block Diagram fingerfingerpad/knob/motor Fourth-order model explains moment of inertia variation at high grip forces Low grip forces are the most interesting for studying chatter Details in dissertation

22. System IDSimulation TheoryHardwareDiscussion 22 Other Grasp Postures

23. System IDSimulation TheoryHardwareDiscussion 23 1.Identify the dynamics of the human hand grasping a haptic knob 2.Model and simulate the effects of displacement quantization 3.Analyze using nonlinear control theory 4.Empirically confirm simulation and theory 5.Discuss effect origins and design implications Approach

24. System IDSimulation TheoryHardwareDiscussion 24 Finger/Manipulandum/Wall Model Gillespie's Model of a Finger/Manipulandum Contacting a Virtual Wall (from Gillespie, 1996)

25. System IDSimulation TheoryHardwareDiscussion 25 Block Diagram Gillespie and Cutkosky, 1996

26. System IDSimulation TheoryHardwareDiscussion 26 Energy Leaks Plot of modeled manipulandum position and control effort (from Gillespie and Cutkosky, 1996).

27. System IDSimulation TheoryHardwareDiscussion 27 Encoder Quantization Continuous-Time Simulation with Encoder Displacement Quantization

28. System IDSimulation TheoryHardwareDiscussion 28 Simulation with Hand Stiffness and Damping Simulation of Hand Lightly Pressing Knob Against Stiff Virtual Wall, with Lines Fitted to Steady State Peaks and Troughs to Measure Limit Cycle Magnitude (2000 Hz, 8192 encoder counts/revolution)

29. System IDSimulation TheoryHardwareDiscussion 29 Simulation with Hand Stiffness and Damping Oscillation Magnitude as a Function of Sample Rate and Displacement Resolution (Log Magnitude for Growth Rate)

30. System IDSimulation TheoryHardwareDiscussion 30 Simulation with Hand Stiffness and Damping Peak-to-Peak Oscillation Magnitude, Expressed in Units of Encoder Counts UnsaturatedSaturated

31. System IDSimulation TheoryHardwareDiscussion 31 Oscillation Frequency Oscillation Frequency as a Function of Sample Rate and Displacement Resolution

32. System IDSimulation TheoryHardwareDiscussion 32 Summary of Simulation Results Displacement quantization possesses no inherent energy leak Limit cycle magnitude scales directly with displacement quantization and ZOH delay Limit cycle frequency relatively unaffected by displacement quantization but sharply affected by ZOH delay For great majority of cases, limit cycle oscillations are smaller than ±1 encoder count

33. System IDSimulation TheoryHardwareDiscussion 33 1.Identify the dynamics of the human hand grasping a haptic knob 2.Model and simulate the effects of displacement quantization 3.Analyze using nonlinear control theory 4.Empirically confirm simulation and theory 5.Discuss effect origins and design implications Approach

34. System IDSimulation TheoryHardwareDiscussion 34 Describing Function Analysis Assumptions: Single nonlinear element Nonlinear element is time-invariant Linear component has low-pass properties Nonlinearity is odd Describing Function: The ratio of the fundamental component of the nonlinear element to the input sinusoid Slotine & Li, 1991

35. System IDSimulation TheoryHardwareDiscussion 35 Describing Function Analysis Nyquist Plot Relay nonlinearity Slotine & Li, 1991

36. System IDSimulation TheoryHardwareDiscussion 36 Describing Function Analysis Nyquist Plot with Describing Function at Various Phase Delays

37. System IDSimulation TheoryHardwareDiscussion 37 DFA Results -- Amplitude -- Oscillation Magnitude as a Function of Sample Rate and Displacement Resolution

38. System IDSimulation TheoryHardwareDiscussion 38 DFA Compared to Simulation -- Amplitude -- Oscillation Magnitude as a Function of Sample Rate and Displacement Resolution DFA Simulation

39. System IDSimulation TheoryHardwareDiscussion 39 Mean: -54% Std. Dev.: ±15% Range: -75% to -17% Difference Between DFA and Simulation Magnitudes as a Percentage of Simulation Magnitudes DFA Compared to Simulation -- Amplitude --

40. System IDSimulation TheoryHardwareDiscussion 40 DFA Results -- Frequency -- Oscillation Frequency as a Function of Sample Rate and Displacement Resolution

41. System IDSimulation TheoryHardwareDiscussion 41 DFA Compared to Simulation -- Frequency -- Oscillation Frequency as a Function of Sample Rate and Displacement Resolution DFA Simulation

42. System IDSimulation TheoryHardwareDiscussion 42 Mean: 4% Std. Dev.: ±14% Range: -21% to +30% Difference Between DFA and Simulation Frequencies as a Percentage of Simulation Frequencies DFA Compared to Simulation -- Frequency --

43. System IDSimulation TheoryHardwareDiscussion 43 Summary of Describing Function Results Relay nonlinearity with phase delay provides good approximation of quantized displacement with ZOH delay DFA does excellent job of predicting magnitude and frequency sensitivities DFA underestimates simulated oscillation magnitude, but provides close prediction of simulated oscillation frequency

44. System IDSimulation TheoryHardwareDiscussion 44 1.Identify the dynamics of the human hand grasping a haptic knob 2.Model and simulate the effects of displacement quantization 3.Analyze using nonlinear control theory 4.Empirically confirm simulation and theory 5.Discuss effect origins and design implications Approach

45. System IDSimulation TheoryHardwareDiscussion 45 Hardware Testing Limit Cycle Oscillations for Various Encoder Resolutions and Sample Rates Worsening Encoder Resolution Worsening Sample Rate 455 Hz1 kHz 2 kHz5 kHz 256 cts/rev 512 cts/rev 1024 cts/rev 2048 cts/rev

46. System IDSimulation TheoryHardwareDiscussion 46 Hardware Testing - Amplitude Results - Oscillation Magnitude as a Function of Sample Rate and Displacement Resolution

47. System IDSimulation TheoryHardwareDiscussion 47 Hardware Testing - Frequency Results - Oscillation Frequency as a Function of Sample Rate and Displacement Resolution

48. System IDSimulation TheoryHardwareDiscussion 48 Hardware Tests Compared to Simulation (Frequency) Oscillation Frequency as a Function of Sample Rate and Displacement Resolution Hardware Simulation

49. System IDSimulation TheoryHardwareDiscussion 49 Summary of Hardware Testing Results Simulations, approximation, and analysis provide reasonable predictions of amplitude sensitivities Hardware oscillation frequencies deviate from simulation and analytic predictions

50. System IDSimulation TheoryHardwareDiscussion 50 1.Identify the dynamics of the human hand grasping a haptic knob 2.Model and simulate the effects of displacement quantization 3.Analyze using nonlinear control theory 4.Empirically confirm simulation and theory 5.Discuss effect origins and design implications Approach

51. System IDSimulation TheoryHardwareDiscussion 51 Displacement Quantization Effect Explained Illustration of Barrier Penetration and Resultant Torque Outputs for a Traditional ZOH System and a ZOH System with Displacement Quantization resolution sample rate Oscillation Magnitude

52. System IDSimulation TheoryHardwareDiscussion 52 Amplitude Approximation Simulation ResultsPredictions Hardware ResultsPredictions For limit cycles of form: Approximate amplitude:

53. System IDSimulation TheoryHardwareDiscussion 53 Potential Limit Cycle Mitigation Approaches Increase displacement resolution Physical damping & friction Electromechanical damping Virtual damping using velocity sensor Corrective torque pulses Phase estimation damping Velocity-adaptive low-pass filtering Goal: Decrease amplitude without increasing frequency

54. System IDSimulation TheoryHardwareDiscussion 54 Design Implications ZOH and displacement quantization effects interact – they are not independent Avoid increasing oscillation frequency Increasing sample rate is often not the answer Pick the highest acceptable sample rate and then work to maximize position resolution

55. System IDSimulation TheoryHardwareDiscussion 55 Design Implications (cont.) Other factors in addition to chatter discourage low- resolution displacement sensing Potential but speculative role for oscillation mitigation schemes Supports approaches such as nonlinear springs with increasing stiffness

56. System IDSimulation TheoryHardwareDiscussion 56 Design Implications Notional Optimization Surface QF = max(logmag norm, freq norm,.45)

57. System IDSimulation TheoryHardwareDiscussion 57 Conclusions Human hand grasping a haptic knob can be modeled as a second-order system –Stiffness and damping increase with grip force –Model breaks down for high grip forces Displacement quantization increases magnitude of limit cycle oscillations by exacerbating effect of delays in control law updating Described design implications for displacement resolution and sample rate selection Two tools: –Simple approximation (magnitude) –Describing function analysis (magnitude & frequency)

58. System IDSimulation TheoryHardwareDiscussion 58 Questions?

59. System IDSimulation TheoryHardwareDiscussion 59 Results for One Subject

60. System IDSimulation TheoryHardwareDiscussion 60 Results for All Subjects

61. System IDSimulation TheoryHardwareDiscussion 61 Comparison to Hajian DampingStiffness

62. System IDSimulation TheoryHardwareDiscussion 62 Fourth-Order Model Block Diagram fingerfingerpad/knob/motor J1J1 grip force J2J2 Assumptions: Finger stiffness 10x greater than finger pad stiffness Finger damping 10x greater than fingerpad damping Springs act in series Dampers act in series

63. System IDSimulation TheoryHardwareDiscussion 63 Fourth-Order Model Performance Acceleration Responses of Estimated 4th and 2nd-Order Systems Compared to Measured Response finger fingerpad/ knob/motor

64. System IDSimulation TheoryHardwareDiscussion 64 Equal Loudness Curves Equal Loudness Curves for the Human Sense of Hearing