Technical Report No. VSR-04.02

End-of-Year Technical Report

For Project

Digital Human Modeling and Virtual Reality for FCS

DYNAMIC MOTION PREDICTION OF GAIT AND LIFTING

By

Hyung Joo Kim

Emily Horn

YuJiang Xiang

Karim Abdel Malek

Jasbir S. Arora

Dated: October 25, 2004

Table of Content

Abstract.. 4

1. Introduction.. 5

1.1 Problem Description.. 5

1.2 Relevant Literature on Gait Analyses. 5

1.3 Scope of the Study.. 7

1.4 Overview of the Report. 7

2. Dynamic Equilibrium and Stability.. 8

2.1 Center of Pressure. 9

2.2 Foot Support Region.. 12

2.3 Zero Moment Point (ZMP) 13

2.4 Dynamic Stability.. 15

2.5 Foot-ground Contact Modes. 16

2.6 Foot-ground Contact Mode Function.. 16

3. Function Approximation using B-splines. 18

3.1 B-spline Approximation.. 18

3.2 B-spline Basis Functions. 19

3.3 B-spline Approximation with Non-Repeated Knots. 20

3.4 Flexible Gait Stage Durations using Knot Distribution.. 21

3.5 Sample Time Frame. 21

4. Optimization Formulation for Dynamic Motion Prediction.. 23

4.1 Inverse Dynamics with Optimization.. 23

4.2 Kinematic Model and Formulation.. 24

4.2.1 Denavit-Hartenberg Method. 24

4.2.2 Kinematic Quantities. 28

4.2.2 Derivatives of Kinematic Quantities. 29

4.3 13-DOF Human Model. 30

4.4 Cost Functions and Constraints for Optimization.. 31

4.5 Human Performance Measures. 34

4.5.1 Joint Angle Limits. 34

4.5.2 Foot Slippage. 34

4.5.3 Ground Penetration. 35

4.5.4 Dynamic Equilibrium.. 35

4.5.5 Dynamic Stability. 37

4.5.6 Initial and Final Position Constraints. 37

5. Dynamic Motion Prediction Examples. 39

5.1 Walking.. 39

5.2 Pushing an Object. 42

5.3 Climbing.. 43

5.4 Pick-up and delivery.. 43

6. Conclusion and Future Opportunities. 45

References. 46

Abstract

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