Contents
Abstract i
Contents xiii
List of Figures xv
List of Tables xviii
Abbreviations xix
1 Introduction 1
1.1 State of the art in mono-wheel robots . . . 1
1.2 First attempt at building a monocycle robot . . . 4
1.3 Motivation and aim of thesis . . . 7
1.4 Roadmap of thesis . . . 8
2 Theoretical Preliminaries 9 2.1 Coordinate frames and transformations . . . 9
2.2 Dynamical systems . . . 12
2.3 Optimal control . . . 17
2.4 Convex optimisation, SOS polynomials . . . 18
3 The Acrover 21 3.1 Kinematics . . . 21
3.2 Equations of motion . . . 24
3.3 Longitudinal plane dynamics . . . 33
3.4 Lateral plane dynamics . . . 38
4 Control System 44 4.1 Speed control (block 3 ) . . . 45
4.1.1 Linear parameter-varying model . . . 45
4.1.2 Robust LQR for speed tracking . . . 47
4.1.3 Controller implementation . . . 50
4.1.4 Region of attraction analysis . . . 52
4.2 Tilt control (block 4 ) . . . 54
4.2.1 Descriptor form linear parameter-varying model . . . 57
4.2.2 Gain scheduling for tilt tracking . . . 59
4.2.3 Controller implementation . . . 61
4.3 Motion control . . . 63 xiii
Contents xiv
4.3.1 Point-to-point motion . . . 64
4.3.2 Path planning (block 1 ) . . . 65
4.3.3 Path following (block 2 ) . . . 65
5 Drives and Sensors 67 5.1 Rotary drive (blocks 5 and 6 ) . . . 68
5.1.1 Linear model of a DC motor . . . 68
5.1.2 Transmission . . . 69
5.1.3 Nonlinear model of friction . . . 70
5.1.4 Drive velocity estimation . . . 74
5.1.5 Torque control with friction compensation . . . 79
5.2 Orientation and twist estimation (blocks 7, 8 and 9 ) . . . 81
5.3 Localisation (block 10 ) . . . 82
6 Simulations 86 6.1 Non-realtime simulations of partial models . . . 86
6.1.1 General structure . . . 87
6.1.2 Partial dynamics subsystem . . . 87
6.1.3 Drive subsystem . . . 88
6.1.4 GMS friction subsystem . . . 89
6.1.5 Luenberger observer subsystem . . . 90
6.1.6 Controller subsystem . . . 90
6.1.7 Exemplary results . . . 91
6.2 Realtime simulation of the complete system . . . 96
6.2.1 Software structure . . . 97
6.2.2 Unique features implemented for the Acrover . . . 99
6.2.3 Exemplary results . . . 99
7 Prototype 103 7.1 Mechanical design . . . 104
7.2 Electronics . . . 106
7.3 Software architecture . . . 107
7.4 Park and recovery mechanism . . . 108
7.5 Setup used in experiments . . . 109
7.6 Parameters of mathematical models . . . 110
7.6.1 Identification of GMS friction . . . 111
8 Experimental Validation 115 8.1 Upright stabilisation and tilt tracking . . . 115
8.2 Cartesian motion . . . 119
9 Conclusions 124 9.1 Contributions . . . 124
9.2 Future works . . . 128
