Title: Identification of Human Grasp Dynamics and the Effects of Displacement Quantization and Zero-Order Hold on the Limit Cycle Behavior of Haptic Knobs
1Identification 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
2Reading Committee
Mark R. CutkoskyJ. Christian Gerdes
J. Kenneth Salisbury
3Acknowledgements
- Stanford faculty and staff
- Immersion Corporation
- Haptic research community
- Fellow students
- Family
4Haptic
Greek origin of or pertaining to the sense
of touch
5Common Haptic System Architecture
Illustration Immersion Corporation
6Haptic Knobs
Illustrations BMW/ Immersion Corporation
7Nissan Concept
Illustrations Nissan/ Immersion Corporation
8Limit 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
9Goal
Understand the effect of displacement
quantization on limit cycle oscillations in
sampled data haptic systems.
10Approach
- 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
11Why Simulate?
- Easily observable, repeatable conditions
- Precise control over experiment parameters
- Physically impossible configurations
- Analysis of hardware yet to be constructed
12Why System Identificaton?
EE Student to EE Professor But how do you
get the plant model?
EE Professor You hire a mechanical engineer.
13Why 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
14Apparatus
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
15Pinch Grasp
- Nine subjects five male, four female
- Subject squeezed knob slowly
- 20 ms torque pulse applied when grip force
reached threshold
16Second-Order Lumped Parameter Model
finger, knob, motor rotor
finger
17Torque, Acceleration, Velocity, and Displacement
Input Torque (upper left), Acceleration (upper
right) Velocity (lower left), and Displacement
(lower right)
18Torque Contributions and Model Check
19Model Performance
Pulse (Step) Responses for Various Grip Forces
20Results Across All Subjects
J
B
K
?
Moment of Inertia (J), Damping (B), Stiffness
(K), and Damping Ratio (?)
21Fourth-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
22Other Grasp Postures
23Approach
- 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
24Finger/Manipulandum/Wall Model
Gillespie's Model of a Finger/Manipulandum
Contacting a Virtual Wall (from Gillespie, 1996)
25Block Diagram
Gillespie and Cutkosky, 1996
26Energy Leaks
Plot of modeled manipulandum position and control
effort (from Gillespie and Cutkosky, 1996).
27Encoder Quantization
Continuous-Time Simulation with Encoder
Displacement Quantization
28Simulation 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)
29Simulation with Hand Stiffness and Damping
Oscillation Magnitude as a Function of Sample
Rate and Displacement Resolution (Log Magnitude
for Growth Rate)
30Simulation with Hand Stiffness and Damping
Peak-to-Peak Oscillation Magnitude, Expressed in
Units of Encoder Counts
Unsaturated
Saturated
31Oscillation Frequency
Oscillation Frequency as a Function of Sample
Rate and Displacement Resolution
32Summary 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
33Approach
- 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
34Describing 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
35Describing Function Analysis
Slotine Li, 1991
Relay nonlinearity
36Describing Function Analysis
Nyquist Plot with Describing Function at Various
Phase Delays
37DFA Results-- Amplitude --
Oscillation Magnitude as a Function of Sample
Rate and Displacement Resolution
38DFA 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
39DFA 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
40DFA Results-- Frequency --
Oscillation Frequency as a Function of Sample
Rate and Displacement Resolution
41DFA 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
42DFA 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
43Summary 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
44Approach
- 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
45Hardware Testing
Limit Cycle Oscillations for Various Encoder
Resolutions and Sample Rates
46Hardware Testing- Amplitude Results -
Oscillation Magnitude as a Function of Sample
Rate and Displacement Resolution
47Hardware Testing - Frequency Results -
Oscillation Frequency as a Function of Sample
Rate and Displacement Resolution
48Hardware 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
49Summary of Hardware Testing Results
- Simulations, approximation, and analysis provide
reasonable predictions of amplitude sensitivities - Hardware oscillation frequencies deviate from
simulation and analytic predictions
50Approach
- 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
51Displacement Quantization Effect Explained
Illustration of Barrier Penetration and Resultant
Torque Outputs for a Traditional ZOH System and a
ZOH System with Displacement Quantization
52Amplitude Approximation
53Potential 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
54Design 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
55Design 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
56Design Implications
QF max(logmagnorm, freqnorm, .45)
Notional Optimization Surface
57Conclusions
- 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)
58Questions?
59Results for One Subject
60Results for All Subjects
61Comparison to Hajian
Damping
Stiffness
62Fourth-Order Model
Block Diagram
63Fourth-Order Model Performance
Acceleration Responses of Estimated 4th and
2nd-Order Systems Compared to Measured Response
64Equal Loudness Curves
Equal Loudness Curves for the Human Sense of
Hearing