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

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

2System ID Simulation Theory Hardware Discussion

Reading Committee

J. Kenneth Salisbury

Mark R. CutkoskyJ. Christian Gerdes


Acknowledgements

• Stanford faculty and staff

• Immersion Corporation

• Haptic research community

• Fellow students

• Family


Haptic

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


Common Haptic System Architecture

Illustration: Immersion Corporation


Haptic Knobs

Illustrations: BMW/ Immersion Corporation


Nissan Concept

Haptic Scroll Wheel in Nissan Concept Car

Close-up of Haptic Scroll Wheel

Illustrations: Nissan/ Immersion Corporation


• 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


Goal

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


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


Why Simulate?

• Easily observable, repeatable conditions

• Precise control over experiment parameters

• Physically impossible configurations

• Analysis of hardware yet to be constructed


EE Student to EE Professor:

“But how do you *get* the plant model?”

EE Professor:

“You hire a mechanical engineer.”

Why System Identificaton?


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


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


Pinch Grasp

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

threshold


Second-Order Lumped Parameter Model

finger finger, knob, & motor rotor


Torque, Acceleration, Velocity, and Displacement

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


Torque Contributions and Model Check


Model Performance

Pulse (Step) Responses for Various Grip Forces


Results Across All Subjects

Moment of Inertia (J), Damping (B), Stiffness (K), and Damping Ratio (ζ)

J

K

B

ζ


Fourth-Order Model

Block Diagramfinger fingerpad/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


Other Grasp Postures







Approach


Finger/Manipulandum/Wall Model

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


Block Diagram

Gillespie and Cutkosky, 1996


Energy Leaks

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


Encoder Quantization

Continuous-Time Simulation with Encoder Displacement Quantization


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)



Oscillation Magnitude as a Function of Sample Rate and Displacement Resolution (Log Magnitude for Growth Rate)



Peak-to-Peak Oscillation Magnitude, Expressed in Units of Encoder Counts

Unsaturated Saturated


Oscillation Frequency

Oscillation Frequency as a Function of Sample Rate and Displacement Resolution


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







Approach


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 Slotine & Li, 1991



Nyquist PlotRelay nonlinearity

Slotine & Li, 1991



Nyquist Plot with Describing Function at Various Phase Delays


DFA Results-- Amplitude --

Oscillation Magnitude as a Function of Sample Rate and Displacement Resolution


DFA Compared to Simulation-- Amplitude --



DFA Simulation


• 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 --


DFA Results-- Frequency --



DFA Compared to Simulation-- Frequency --



DFA Simulation


• 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 --


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







Approach


Hardware Testing

Limit Cycle Oscillations for Various Encoder Resolutions and Sample Rates

Wor

seni

ngE

ncod

erR

esol

utio

n

WorseningSample Rate

455 Hz 1 kHz 2 kHz 5 kHz

256 cts/rev

512 cts/rev

1024 cts/rev

2048 cts/rev


Hardware Testing- Amplitude Results -



Hardware Testing - Frequency Results -



Hardware Tests Compared to Simulation (Frequency)



Hardware Simulation


Summary of Hardware Testing Results

• Simulations, approximation, and analysis provide reasonable predictions of amplitude sensitivities

• Hardware oscillation frequencies deviate from simulation and analytic predictions







Approach


Displacement Quantization Effect Explained

Illustration of Barrier Penetration and Resultant Torque Outputs for a Traditional ZOH System and a ZOH System with Displacement Quantization

resolutionsample rate

Oscillation Magnitude

2

1

)()(t

t

errorleak dtttTE

)()(1

kkTEN

kerrorleak


Amplitude Approximation

Simulation Results Predictions

Hardware Results Predictions

)sin( tAt

tCA

For limit cycles of form:

Approximate amplitude:


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


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


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


Design Implications

Notional Optimization Surface

QF = max(logmagnorm, freqnorm, .45)


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)


Questions?

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

Documents

system identificaton

threshold slide

motor rotor slide

christian gerdes slide

sense of touch slide

haptic knobs illustrations

haptic greek origin

plant model