Identification of Human Grasp Dynamics and the Effects of Displacement Quantization and Zero-Order Hold on the Limit Cycle Behavior of Haptic Knobs

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

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Haptic
Greek origin of or pertaining to the sense
of touch
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Common Haptic System Architecture
Illustration Immersion Corporation
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Haptic Knobs
Illustrations BMW/ Immersion Corporation
7
Nissan Concept
Illustrations Nissan/ Immersion Corporation
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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

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

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

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

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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

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Pinch Grasp

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

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Second-Order Lumped Parameter Model
finger, knob, motor rotor
finger
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Torque, Acceleration, Velocity, and Displacement
Input Torque (upper left), Acceleration (upper
right) Velocity (lower left), and Displacement
(lower right)
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Torque Contributions and Model Check
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Model Performance
Pulse (Step) Responses for Various Grip Forces
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Results Across All Subjects
J
B
K
?
Moment of Inertia (J), Damping (B), Stiffness
(K), and Damping Ratio (?)
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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

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Other Grasp Postures
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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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Finger/Manipulandum/Wall Model
Gillespie's Model of a Finger/Manipulandum
Contacting a Virtual Wall (from Gillespie, 1996)
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Block Diagram
Gillespie and Cutkosky, 1996
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Energy Leaks
Plot of modeled manipulandum position and control
effort (from Gillespie and Cutkosky, 1996).
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Encoder Quantization
Continuous-Time Simulation with Encoder
Displacement Quantization
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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)
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Simulation with Hand Stiffness and Damping
Oscillation Magnitude as a Function of Sample
Rate and Displacement Resolution (Log Magnitude
for Growth Rate)
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Simulation with Hand Stiffness and Damping
Peak-to-Peak Oscillation Magnitude, Expressed in
Units of Encoder Counts
Unsaturated
Saturated
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Oscillation Frequency
Oscillation Frequency as a Function of Sample
Rate and Displacement Resolution
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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

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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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Describing Function Analysis
Slotine Li, 1991
Describing Function The ratio of the
fundamental component of the nonlinear element to
the input sinusoid

• Assumptions
• Single nonlinear element
• Nonlinear element is time-invariant
• Linear component has low-pass properties
• Nonlinearity is odd

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Describing Function Analysis
Slotine Li, 1991
Relay nonlinearity
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Describing Function Analysis
Nyquist Plot with Describing Function at Various
Phase Delays
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DFA Results-- Amplitude --
Oscillation Magnitude as a Function of Sample
Rate and Displacement Resolution
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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
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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
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DFA Results-- Frequency --
Oscillation Frequency as a Function of Sample
Rate and Displacement Resolution
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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
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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
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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

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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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Hardware Testing
Limit Cycle Oscillations for Various Encoder
Resolutions and Sample Rates
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Hardware Testing- Amplitude Results -
Oscillation Magnitude as a Function of Sample
Rate and Displacement Resolution
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Hardware Testing - Frequency Results -
Oscillation Frequency as a Function of Sample
Rate and Displacement Resolution
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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
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Summary of Hardware Testing Results

• Simulations, approximation, and analysis provide
  reasonable predictions of amplitude sensitivities
• Hardware oscillation frequencies deviate from
  simulation and analytic predictions

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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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Displacement Quantization Effect Explained
Illustration of Barrier Penetration and Resultant
Torque Outputs for a Traditional ZOH System and a
ZOH System with Displacement Quantization
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Amplitude Approximation
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Potential Limit Cycle Mitigation Approaches
Goal Decrease amplitude without increasing
frequency

• Increase displacement resolution
• Physical damping friction
• Electromechanical damping
• Virtual damping using velocity sensor
• Corrective torque pulses
• Phase estimation damping
• Velocity-adaptive low-pass filtering

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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

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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

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Design Implications
QF max(logmagnorm, freqnorm, .45)
Notional Optimization Surface
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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)

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Questions?
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Results for One Subject
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Results for All Subjects
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Comparison to Hajian
Damping
Stiffness
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Fourth-Order Model
Block Diagram
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Fourth-Order Model Performance
Acceleration Responses of Estimated 4th and
2nd-Order Systems Compared to Measured Response
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Equal Loudness Curves
Equal Loudness Curves for the Human Sense of
Hearing