"Robot Dynamics Algorithms, Second Edition" presents the subject of computational rigid-body dynamics through the medium of spatial (6D) vector notation. It explains how to model a rigid-body system and how to analyze it. The book is a comprehensive collection of the best rigid-body dynamics algorithms in a single source. This second edition includes nearly twice the content of the previous edition with algorithms shown explicitly in pseudocode and laid out in tables for easy implementation. It also has more algorithms than the previous edition including algorithms that exploit sparse matrices and ones for kinematic loops. New material on the mathematics of spatial (6D) vectors and how to analyze rigid-body systems using spatial vectors is covered. Finally there is an entire chapter devoted to how to build computer-oriented models of rigid-body systems.This book is for engineers with knowledge of rigid-body dynamics who are interested in calculating the dynamics of a rigid-body system. It is both an algorithms recipe book as well as a guide to the analysis and deeper understanding of rigid-body systems.
Author(s): Roy Featherstone
Edition: 1
Year: 2007
Language: English
Pages: 228
Contents......Page 7
Preface......Page 5
1.1 Dynamics Algorithms......Page 10
1.2 Spatial Vectors......Page 12
1.3 Units and Notation......Page 13
1.4 Readers' Guide......Page 14
1.5 Further Reading......Page 15
2.1 Mathematical Preliminaries......Page 16
2.2 Spatial Velocity......Page 19
2.3 Spatial Force......Page 22
2.4 Plücker Notation......Page 24
2.5 Line Vectors and Free Vectors......Page 25
2.6 Scalar Product......Page 26
2.7 Using Spatial Vectors......Page 27
2.8 Coordinate Transforms......Page 29
2.9 Spatial Cross Products......Page 32
2.10 Differentiation......Page 34
2.11 Acceleration......Page 37
2.12 Momentum......Page 40
2.13 Inertia......Page 41
2.14 Equation of Motion......Page 44
2.15 Inverse Inertia......Page 45
2.16 Planar Vectors......Page 46
2.17 Further Reading......Page 47
3. Dynamics of Rigid Body Systems......Page 48
3.1 Equations of Motion......Page 49
3.2 Constructing Equations of Motion......Page 51
3.3 Vector Subspaces......Page 55
3.4 Classification of Constraints......Page 59
3.5 Joint Constraints......Page 62
3.6 Dynamics of a Constrained Rigid Body......Page 66
3.7 Dynamics of a Multibody System......Page 69
4. Modelling Rigid Body Systems......Page 74
4.1 Connectivity......Page 75
4.2 Geometry......Page 82
4.3 Denavit-Hartenberg Parameters......Page 84
4.4 Joint Models......Page 87
4.5 Spherical Motion......Page 93
4.6 A Complete System Model......Page 96
5.1 Algorithm Complexity......Page 97
5.2 Recurrence Relations......Page 98
5.3 The Recursive Newton-Euler Algorithm......Page 100
5.4 The Original Version......Page 105
5.5 Additional Notes......Page 107
6. Forward Dynamics — Inertia Matrix Methods......Page 109
6.1 The Joint-Space Inertia Matrix......Page 110
6.2 The Composite-Rigid-Body Algorithm......Page 112
6.3 A Physical Interpretation......Page 116
6.4 Branch-Induced Sparsity......Page 118
6.5 Sparse Factorization Algorithms......Page 120
6.6 Additional Notes......Page 125
7.1 Articulated-Body Inertia......Page 127
7.2 Calculating Articulated-Body Inertias......Page 131
7.3 The Articulated-Body Algorithm......Page 136
7.4 Alternative Assembly Formulae......Page 139
7.5 Multiple Handles......Page 144
8.1 Equations of Motion......Page 148
8.2 Loop Constraint Equations......Page 150
8.3 Constraint Stabilization......Page 152
8.4 Loop Joint Forces......Page 155
8.5 Solving the Equations of Motion......Page 156
8.6 Algorithm for C – T[sup(a)]......Page 159
8.7 Algorithm for K and k......Page 161
8.8 Algorithm for G and g......Page 163
8.9 Exploiting Sparsity in K and G......Page 165
8.10 Some Properties of Closed-Loop Systems......Page 166
8.11 Loop Closure Functions......Page 168
8.12 Inverse Dynamics......Page 171
8.13 Sparse Matrix Method......Page 173
9.1 Hybrid Dynamics......Page 177
9.2 Articulated-Body Hybrid Dynamics......Page 182
9.3 Floating Bases......Page 185
9.4 Floating-Base Forward Dynamics......Page 187
9.5 Floating-Base Inverse Dynamics......Page 189
9.6 Gears......Page 192
9.7 Dynamic Equivalence......Page 195
10. Accuracy and Efficiency......Page 200
10.1 Sources of Error......Page 201
10.2 The Sensitivity Problem......Page 204
10.3 Efficiency......Page 206
10.4 Symbolic Simplification......Page 214
11.1 Single Point Contact......Page 218
11.2 Multiple Point Contacts......Page 221
11.3 A Rigid-Body System with Contacts......Page 224
11.4 Inequality Constraints......Page 227
11.5 Solving Contact Equations......Page 229
11.6 Contact Geometry......Page 232
11.7 Impulsive Dynamics......Page 235
11.8 Soft Contact......Page 240
11.9 Further Reading......Page 244
A.1 Simple Planar Arithmetic......Page 245
A.2 Simple Spatial Arithmetic......Page 247
A.3 Compact Representations......Page 249
A.4 Axial Screw Transforms......Page 253
A.5 Some Efficiency Tricks......Page 256
Bibliography......Page 261
Symbols......Page 269
C......Page 271
E......Page 272
I......Page 273
M......Page 274
R......Page 275
Z......Page 276
