Learning-Based Inverse Dynamics for Human Motion Analysis

Produktbeschreibung

This dissertation deals with machine learning techniques for inverse dynamics of human motion. Inverse
dynamics refers to the derivation of acting forces and moments from the motion of a kinematic model. More precisely, the objective is to estimate joint torques, ground reaction forces and ground reaction moments at both feet based on the three-dimensional input motion of a skeletal model. The problem is solved using a data-driven machine learning approach, proposing several regression models that are particularly suitable with respect to limited data availability. The goal is to exploit the inherent strengths of machine learning, such as fast and noiseresistant data analysis. The described methods are able to predict underlying joint torques and exterior forces with high precision (on gait sequences: relative root mean squared errors of 7.0 %, 16.1 % and 11.9 % for reaction forces, reaction moments and joint moments which correspond to Pearson‘s correlation coefficients of 0.91, 0.83 and 0.82), while reducing computation times by two orders of magnitude compared to traditional optimization.

Contents

1 Introduction 1
1.1 Applications and Challenges of Inverse Dynamics . . . . . . . . . . . . . . 1
1.2 Learning Inverse Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Structure of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Related work 15
2.1 Inverse Dynamics by Physical Simulation . . . . . . . . . . . . . . . . . . . 15
2.1.1 Inverse Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.2 Forward Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.3 Implicit Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Learning-Based Inverse Dynamics . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Decreasing Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Fundamentals 23
3.1 Rigid Body Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.1 Representation of Position . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.2 Representation of Orientation . . . . . . . . . . . . . . . . . . . . . 24
3.1.3 Homogeneous Transformations . . . . . . . . . . . . . . . . . . . . . 26
3.2 Kinematics of a Rigid Body System . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Kinematic Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.2 The Denavit-Hartenberg Convention . . . . . . . . . . . . . . . . . 28
3.2.3 Velocity and Acceleration Kinematics . . . . . . . . . . . . . . . . . 30
3.3 Dynamics of a Rigid Body System . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 TMT-Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.1 Terminology and General Concepts . . . . . . . . . . . . . . . . . . 45
3.4.2 Support Vector Machines . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4.3 Ridge Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.4 Random Forests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4.5 Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.4.6 Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.7 Transfer Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4 Human motion dataset 62
4.1 Motion Capture and Kinematic Optimization . . . . . . . . . . . . . . . . 62
4.2 Force Plate Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Estimation of Inertial Properties . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4 Optimization of Joint Torques . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.5 Data Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.6 Generation of Training Data Points . . . . . . . . . . . . . . . . . . . . . . 73
5 Supervised learning of inverse dynamics 76
5.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.1.1 End-to-End Regression . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.1.2 Multi-Stage Regression . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2 Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2.1 Predictive Dynamics Dataset . . . . . . . . . . . . . . . . . . . . . 82
5.2.2 Public Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.3 Application to Reconstructed Motions . . . . . . . . . . . . . . . . 90
5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6 Self-supervision by dynamics-based layers 95
6.1 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 Dynamics Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.1 Forward Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2.2 Inverse Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.2.3 Contact Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2.4 Training Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3 Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.3.1 Comparison in the Supervised Setting . . . . . . . . . . . . . . . . . 105
6.3.2 Semi-Supervision with Small Labeled Datasets . . . . . . . . . . . . 106
6.3.3 Domain Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.3.4 Ablation of Input Structure . . . . . . . . . . . . . . . . . . . . . . 115
6.3.5 Effect of Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7 Conclusions 123
a Appendix 127
a.1 Evaluation Based on Additional Metrics . . . . . . . . . . . . . . . . . . . 127
a.2 Data-Driven Inverse Dynamics Optimization . . . . . . . . . . . . . . . . . 127
Bibliography 130

Keywords: inverse Dynamik, maschinelles Lernen, menschliche Bewegung, Gelenkmomente, Ganganalyse, künstliche neuronale Netze, selbstüberwachtes Lernen, inverse dynamics, machine learning, human motion, joint moments, gait analysis, artificial neural networks, self-supervised learning