Humanoid Robots: Modelling and Control

Cover......Page 1
HUMANOID
ROBOTS:
Modeling and Control
......Page 3
Copyright
......Page 4
Dedication......Page 5
Preface......Page 6
Acknowledgments......Page 8
1.1 Historical Development......Page 9
1.2.1 Human Likeness of a Humanoid Robot......Page 10
1.2.3 Human-Friendly Humanoid Robot Design......Page 11
1.3 Characteristics of Humanoid Robots......Page 12
1.4.2 Constrained Multibody Systems and Contact Modeling......Page 13
 Single-Leg, Multilegged, and Multilimb Robots......Page 14
1.5 Prerequisite and Structure......Page 15
 References......Page 16
2.2 Kinematic Structure......Page 23
2.3 Forward and Inverse Kinematic Problems......Page 26
2.4.1 Twist, Spatial Velocity, and Spatial Transform......Page 27
 Multi-DoF Joint Models......Page 30
 Parametrization of Instantaneous Rotation......Page 32
2.4.3 Inverse Differential Kinematic Relations......Page 33
2.5 Differential Kinematics at Singular Configurations......Page 34
2.7 Kinematic Redundancy......Page 40
2.7.1 Self-Motion......Page 41
2.7.2 General Solution to the Inverse Kinematics Problem......Page 43
2.7.3 Weighted Generalized Inverse......Page 45
 Singularity Avoidance Subtask via the Manipulability Measure......Page 46
2.7.5 Redundancy Resolution via the Extended Jacobian Technique......Page 47
2.8 Inverse Kinematics Solution Under Multiple Task Constraints......Page 48
2.8.1 Motion-Task Constraints......Page 49
 Restricted Generalized Inverse and Task Prioritization......Page 50
 Multiple Tasks With Fixed Priorities......Page 51
 Variable Task Priorities With Smooth Task Transitions......Page 53
2.8.3 Iterative Optimization Methods......Page 54
 Introducing a Hierarchical Structure With Fixed Task Priorities......Page 55
 Introducing Inequality Constraints......Page 56
2.8.4 Summary and Discussion......Page 57
2.9 Motion Constraints Through Contacts......Page 58
2.9.1 Contact Joints......Page 59
2.9.2 Contact Coordinate Frames......Page 60
2.9.3 Kinematic Models of Frictionless Contact Joints......Page 61
2.10 Differential Kinematics of Chains With Closed Loops......Page 62
2.10.1 Instantaneous Motion Analysis of Chains With Closed Loops......Page 63
 Limb Velocities......Page 65
 Velocities Within the Closed Chain......Page 66
2.10.2 Inverse Kinematics Solution......Page 68
2.10.3 Forward Kinematics Solution......Page 69
2.11.1 Quasivelocity, Holonomic and Nonholonomic Contact Constraints......Page 70
2.11.2 First-Order Differential Motion Relations Expressed in Terms of Base Quasivelocity......Page 71
 Constraint-Consistent Joint Velocity......Page 73
 Constraint-Consistent Generalized Velocity......Page 74
2.11.3 Second-Order Differential Motion Constraints and Their Integrability......Page 75
2.11.4 First-Order Differential Motion Relations With Mixed Quasivelocity......Page 78
 Implementation Example......Page 81
 References......Page 83
3.2 Wrench and Spatial Force......Page 91
3.3 Contact Joints: Static Relations......Page 92
3.3.1 Static Models of Frictionless Contact Joints......Page 93
 Point-Contact Model......Page 94
 Soft-Finger Contact Model......Page 95
 Polyhedral Convex Cone Model......Page 96
 Plane-Contact Model: the Contact Wrench Cone......Page 97
3.3.3 Motion/Force Duality Relations Across Contact Joints......Page 98
 Summary and Discussion......Page 100
3.4 Kinetostatic Relations in Independent Closed-Loop Chains......Page 101
3.4.2 Orthogonal Decomposition of the Loop-Closure and Root Link Wrenches......Page 102
3.4.3 Decomposition of the Limb Joint Torque......Page 103
3.5 The Wrench Distribution Problem......Page 104
3.5.1 General Solution to the Wrench Distribution Problem......Page 105
 Internal Forces......Page 106
 Internal Moments......Page 107
 Internal Wrench......Page 108
3.5.4 Which Generalized Inverse?......Page 110
3.5.5 Priorities Among the Joint Torque Components......Page 111
3.6.1 The Composite Rigid Body (CRB) and the CRB Wrench......Page 112
3.6.2 Interdependent Closed Loops......Page 114
3.6.3 Independent Closed Loops......Page 115
3.6.4 Determining the Joint Torques......Page 116
 Double Stance on Flat Floor in 2D (Lateral Plane)......Page 117
 Double Stance on Flat Floor With Friction......Page 119
 Double Stance With Noncoplanar Contacts......Page 120
3.6.6 Summary and Discussion......Page 121
3.7 Static Posture Stability and Optimization......Page 122
3.7.1 Static Posture Stability......Page 123
 An Example......Page 124
 Joint Torque Limit Test......Page 125
3.7.2 Static Posture Optimization......Page 126
3.8 Posture Characterization and Duality Relations......Page 127
 References......Page 129
4.1 Introduction......Page 133
4.2 Underactuated Robot Dynamics......Page 134
4.3.1 The Linear Inverted Pendulum Model......Page 136
 Linearized IP-on-Foot Model......Page 138
 IP-on-Cart Model......Page 139
 LIP-on-Cart Model......Page 140
4.3.3 Linear Reaction Wheel Pendulum Model and Centroidal Moment Pivot......Page 141
4.3.4 Reaction Mass Pendulum Model......Page 144
4.4.1 3D Inverted Pendulum With Variable Length......Page 145
4.4.2 Spherical IP-on-Foot and Sphere-on-Plane Models......Page 147
4.4.3 The 3D Reaction Wheel Pendulum Model......Page 148
4.4.4 The 3D Reaction Mass Pendulum Model......Page 149
4.5.1 Dynamic Model in Joint-Space Coordinates......Page 150
4.5.2 Dynamic Model in Spatial Coordinates......Page 152
 Operational Space Method [60]......Page 153
 Constrained Dynamics in Spatial Coordinates......Page 154
 Complete Dynamic Decoupling via the KD-JSD Method [116]......Page 155
4.5.3 Null-Space Dynamics With Dynamically Decoupled Hierarchical Structure......Page 156
4.6 Spatial Momentum of a Manipulator Floating Freely in Zero Gravity......Page 157
4.6.2 Spatial Momentum......Page 158
4.6.3 Locked Joints: the Composite Rigid Body......Page 159
4.6.4 Joints Unlocked: Multibody Notation......Page 161
4.6.5 Instantaneous Motion of a Free-Floating Manipulator......Page 164
4.7.1 The Momentum Equilibrium Principle......Page 166
 Coupling Spatial Momentum Conservation: the Reaction Null Space......Page 167
4.7.3 Angular Momentum-Based Redundancy Resolution......Page 168
 System Angular Momentum Conservation......Page 169
4.7.4 Motion of a Free-Floating Humanoid Robot in Zero Gravity......Page 170
4.8 Equation of Motion of a Free-Floating Manipulator in Zero Gravity......Page 171
4.8.1 Representation in Terms of Base Quasivelocity......Page 172
 In the Presence of External Forces......Page 173
4.8.2 Representation in Terms of Mixed Quasivelocity......Page 175
4.8.3 Representation in Terms of Centroidal Quasivelocity......Page 176
4.9 Reaction Null Space-Based Inverse Dynamics......Page 178
4.10 Spatial Momentum of a Humanoid Robot......Page 179
4.11 Equation of Motion of a Humanoid Robot......Page 181
4.12 Constraint-Force Elimination Methods......Page 183
4.12.1 Gauss\' Principle of Least Constraint......Page 184
4.12.2 Direct Elimination......Page 186
4.12.3 Maggi\'s Equations (Null-Space Projection Method)......Page 187
4.12.4 Range-Space Projection Method......Page 190
4.12.5 Summary and Conclusions......Page 191
4.13.1 Joint-Space Dynamics-Based Representation......Page 192
4.13.2 Spatial Dynamics-Based Representation (Lagrange-d\'Alembert Formulation)......Page 193
 Adjoining the Object Dynamics......Page 194
4.13.3 Equation of Motion in End-Link Spatial Coordinates......Page 195
 System Dynamics Projection Along the Unconstrained Motion Directions......Page 196
 Projection Along the Constrained and Unconstrained Motion Directions......Page 197
4.13.4 Summary and Discussion......Page 198
4.14.1 Based on the Direct Elimination/Gauss/Maggi/Projection Methods......Page 200
4.14.3 Based on the Joint-Space Dynamics Elimination Approach......Page 202
4.14.4 Summary and Conclusions......Page 203
 References......Page 204
5.1 Overview......Page 211
5.2 Dynamic Postural Stability......Page 213
5.3.1 The Extrapolated CoM and the Dynamic Stability Margin......Page 215
5.3.2 Extrapolated CoM Dynamics......Page 217
5.3.3 Discrete States With Transitions......Page 218
5.3.4 Dynamic Stability Region in 2D......Page 219
5.4 ZMP Manipulation-Type Stabilization on Flat Ground......Page 220
5.4.1 The ZMP Manipulation-Type Stabilizer......Page 222
5.4.2 Velocity-Based ZMP Manipulation-Type Stabilization in 3D......Page 223
5.4.3 Regulator-Type ZMP Stabilizer......Page 225
5.4.4 ZMP Stabilization in the Presence of GRF Estimation Time Lag......Page 227
5.4.5 Torso Position Compliance Control (TPCC)......Page 228
5.5.1 Capture Point (CP) and Instantaneous Capture Point (ICP)......Page 230
5.5.2 ICP-Based Stabilization......Page 231
5.5.3 ICP Stabilization in the Presence of GRF Estimation Time Lag......Page 232
5.5.4 ICP Dynamics and Stabilization in 2D......Page 233
5.6.1 Stability Analysis Based on the LRWP Model......Page 234
5.6.2 Stability Analysis in 3D: the Divergent Component of Motion......Page 236
5.6.3 DCM Stabilizer......Page 239
5.6.4 Summary and Conclusions......Page 240
5.7 Maximum Output Admissible Set Based Stabilization......Page 241
5.8.1 Fundamental Functional Dependencies in Balance Control......Page 243
5.8.3 Whole-Body Balance Control With Relative Angular Momentum/Velocity......Page 245
 Relative Angular Momentum/Velocity (RAM/V) Balance Control......Page 247
 Special Cases: Balance Control That Conserves the System or the Coupling Angular Momentum......Page 249
5.8.4 RNS-Based Stabilization of Unstable Postures......Page 250
 Summary and Conclusions......Page 251
5.8.5 An Approach to Contact Stabilization Within the Resolved Momentum Framework......Page 252
5.8.6 Spatial Momentum Rate Stabilization Parametrized by the CMP/VRP......Page 254
5.8.7 CRB Motion Trajectory Tracking With Asymptotic Stability......Page 255
5.9 Task-Space Controller Design for Balance Control......Page 256
5.9.1 Generic Task-Space Controller Structure......Page 257
5.9.2 Optimization Task Formulation and Constraints......Page 258
5.10.1 Pseudoinverse-Based Body-Wrench Distribution......Page 261
5.10.2 The ZMP Distributor......Page 262
5.10.3 Proportional Distribution Approach......Page 263
5.10.4 The DCM Generalized Inverse......Page 264
 Vertical GRF Force Distribution Policy......Page 265
 Friction Policy......Page 266
 CoP Allocation Policy......Page 267
 Final Result......Page 268
 Implementation Example......Page 269
5.10.5 The VRP Generalized Inverse......Page 270
5.10.6 Joint Torque-Based Contact Wrench Optimization......Page 272
5.11.1 Independent Motion Optimization With CRB Wrench-Consistent Input......Page 274
5.11.2 Stabilization With Angular Momentum Damping......Page 275
5.11.3 Motion Optimization With Task-Based Hand Motion Constraints......Page 278
5.12.1 Multicontact Motion/Force Controller Based on the Closed-Chain Model......Page 279
5.12.2 Motion/Force Optimization Based on the Operational-Space Formulation......Page 281
 Example......Page 283
5.13 Reactive Balance Control in Response to Weak External Disturbances......Page 286
5.13.1 Gravity Compensation-Based Whole-Body Compliance With Passivity......Page 287
5.13.2 Whole-Body Compliance With Multiple Contacts and Passivity......Page 288
5.13.3 Multicontact Motion/Force Control With Whole-Body Compliance......Page 291
5.14 Iterative Optimization in Balance Control......Page 292
5.14.1 A Brief Historical Overview......Page 293
5.14.2 SOCP-Based Optimization......Page 294
5.14.3 Iterative Contact Wrench Optimization......Page 295
 Sequential Approach......Page 296
 Nonsequential Approach......Page 297
 Hierarchical Multiobjective Optimization With Hard Constraints......Page 298
 Penalty-Based Multiobjective Optimization With Soft Constraints......Page 299
5.14.6 Mixed Iterative/Noniterative Optimization Approaches......Page 300
 Hierarchical Task Formulation With Decoupling......Page 301
5.14.7 Computational Time Requirements......Page 302
 References......Page 303
6.1 Introduction......Page 311
6.2.1 Grasp Matrix and Hand Jacobian Matrix......Page 312
6.2.3 Constraint Types......Page 315
6.2.4 Form Closure......Page 316
 Case Study......Page 317
 Definition of Force Closure......Page 318
 Case Study......Page 319
6.3.1 Background of Multiarm Object Manipulation......Page 321
6.3.2 Kinematics and Statics of Multiarm Cooperation......Page 322
6.3.3 Force and Moment Applied to the Object......Page 324
 Case Study......Page 325
6.3.5 Control of the External and Internal Wrenches......Page 326
 Virtual Linkage [28] (see also Section 3.5.2)......Page 327
 Virtual Stick [25,27]......Page 330
 Cooperation Among Three Robot Arms......Page 331
 Cooperation Between Two Humanoid Robots......Page 332
 Cooperation Among Four Humanoid Robots......Page 334
6.3.6 Hybrid Position/Force Control......Page 336
 Hybrid Position/Force Controller......Page 337
6.4.1 On-Line Footstep Planning......Page 338
6.4.2 Coordinated Movement of Hands and Feet......Page 339
6.4.4 Leader-Follower-Type Cooperative Object Manipulation......Page 341
 Concept of a Leader-Follower-Type Cooperative Object Manipulation......Page 342
 Experiment of Object Transportation......Page 343
 Simulation of Symmetry-Type Cooperation......Page 344
 Simulation Results......Page 345
6.4.6 Comparison Between Leader-Follower-Type and Symmetry-Type Cooperation......Page 346
6.5.1 Equation of Motion of the Object......Page 348
6.5.2 Controller......Page 349
 References......Page 353
7.1 Overview......Page 355
7.2.1 CP-Based Walking Control......Page 357
7.2.2 CP-Based Gait Generation......Page 358
7.2.3 ICP Controller......Page 361
7.2.4 CP-Based Gait Generation and ZMP Control......Page 362
7.3.1 Landing Position Control for Walking on Sand......Page 363
7.3.2 Experiments of Walking on Sand......Page 364
7.3.3 Summary and Discussion......Page 369
7.4.1 Continuous Double-Support (CDS) Gait Generation......Page 370
7.4.2 Heel-to-Toe (HT) Gait Generation......Page 372
7.4.3 Simulation......Page 373
7.5 Synergy-Based Motion Generation......Page 374
7.5.2 Combinations of Primitive Synergies......Page 376
7.6 Synergy-Based Reactive Balance Control With Planar Models......Page 378
 Lateral Plane......Page 379
7.6.3 Sagittal-Plane Ankle/Hip Synergies......Page 381
7.6.4 Lateral Plane Ankle, Load/Unload and Lift-Leg Synergies......Page 385
7.6.5 Transverse-Plane Twist Synergy......Page 387
7.6.6 Complex Reactive Synergies Obtained by Superposition of Simple Ones......Page 388
7.6.7 Summary and Discussion......Page 389
7.7.1 Reactive Synergies Generated With a Simple Dynamic Torque Controller......Page 390
7.7.2 The Load/Unload and Lift-Leg Strategies Revisited......Page 391
7.7.3 Compliant-Body Response......Page 392
7.7.4 Impact Accommodation With Angular Momentum Damping From the RNS......Page 394
 Anticipatory-Type Impact Accommodation......Page 396
 Nonanticipatory-Type Impact Accommodation......Page 397
7.7.5 Reactive Stepping......Page 398
 Impact Phase......Page 400
 Simulation......Page 401
7.7.6 Accommodating a Large Impact Without Stepping......Page 404
7.8.1 Historical Background......Page 407
7.8.2 Considering the Effects of the Reduction Gear Train......Page 408
7.8.3 Ground Reaction Force and Moment......Page 409
7.8.4 Dynamic Effects Caused by Impacts......Page 410
7.8.5 Virtual Mass......Page 412
7.8.7 Optimization Problems for Impact Motion Generation......Page 414
 A Simplified Model of the Humanoid Robot HOAP-2......Page 416
 Performance Index for Stability Margin Evaluation......Page 417
 Optimization of the Posture and Velocity at the Impact......Page 418
 Optimization of the Velocity Before/After the Impact......Page 419
7.8.9 Experimental Verification of the Generated Impact Motion......Page 421
 References......Page 423
8.1 Overview......Page 429
8.2 Robot Simulators......Page 430
8.3 Structure of a Robot Simulator......Page 432
 Using CAD Files......Page 437
 Using the URDF File......Page 442
8.4.2 Generating the Simulink Model......Page 445
8.4.3 Joint Mode Configuration......Page 448
8.4.4 Modeling of Contact Forces......Page 458
8.4.5 Computing the ZMP......Page 466
8.4.6 Motion Design......Page 471
8.4.7 Simulation......Page 473
 References......Page 477
A.2 Model Parameters for a Small-Size Humanoid Robot With 7-DoF Arms......Page 480
 References......Page 486
Index......Page 487
Back Cover......Page 498