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Doctoral Dissertation Defense Christopher J. Hasser November 19, 2001

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. Reading Committee. Mark R. Cutkosky J. Christian Gerdes.

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Doctoral Dissertation Defense Christopher J. Hasser November 19, 2001

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  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. Reading Committee Mark R. CutkoskyJ. Christian Gerdes J. Kenneth Salisbury

  3. Acknowledgements • Stanford faculty and staff • Immersion Corporation • Haptic research community • Fellow students • Family

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

  5. Common Haptic System Architecture Illustration: Immersion Corporation

  6. Haptic Knobs Illustrations: BMW/ Immersion Corporation

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

  8. Limit Cycle Oscillations • 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

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

  10. Approach • Identify the dynamics of the human hand grasping a haptic knob • Model and simulate the effects of displacement quantization • Analyze using nonlinear control theory • Empirically confirm simulation and theory • Discuss effect origins and design implications

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

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

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

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

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

  18. Torque Contributions and Model Check

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

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

  21. finger fingerpad/knob/motor Fourth-Order Model Block Diagram • 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. Other Grasp Postures

  23. Approach • Identify the dynamics of the human hand grasping a haptic knob • Model and simulate the effects of displacement quantization • Analyze using nonlinear control theory • Empirically confirm simulation and theory • Discuss effect origins and design implications

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

  25. Block Diagram Gillespie and Cutkosky, 1996

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

  27. Encoder Quantization Continuous-Time Simulation with Encoder Displacement Quantization

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

  30. Simulation with Hand Stiffness and Damping Peak-to-Peak Oscillation Magnitude, Expressed in Units of Encoder Counts Unsaturated Saturated

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

  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. Approach • Identify the dynamics of the human hand grasping a haptic knob • Model and simulate the effects of displacement quantization • Analyze using nonlinear control theory • Empirically confirm simulation and theory • Discuss effect origins and design implications

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

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

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

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

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

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

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

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

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

  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. Approach • Identify the dynamics of the human hand grasping a haptic knob • Model and simulate the effects of displacement quantization • Analyze using nonlinear control theory • Empirically confirm simulation and theory • Discuss effect origins and design implications

  45. WorseningSample Rate 455 Hz 1 kHz 2 kHz 5 kHz 256 cts/rev 512 cts/rev WorseningEncoderResolution 1024 cts/rev 2048 cts/rev Hardware Testing Limit Cycle Oscillations for Various Encoder Resolutions and Sample Rates

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

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

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

  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. Approach • Identify the dynamics of the human hand grasping a haptic knob • Model and simulate the effects of displacement quantization • Analyze using nonlinear control theory • Empirically confirm simulation and theory • Discuss effect origins and design implications

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