Humanoid Robots: Modeling and Control

Cover......Page 1
HUMANOID
ROBOTS:
Modeling and Control
......Page 4
Copyright
......Page 5
Dedication......Page 6
Preface......Page 7
Acknowledgments......Page 9
1.1 Historical Development......Page 10
1.2.1 Human Likeness of a Humanoid Robot......Page 11
1.2.3 Human-Friendly Humanoid Robot Design......Page 12
1.3 Characteristics of Humanoid Robots......Page 13
1.4.2 Constrained Multibody Systems and Contact Modeling......Page 14
 Single-Leg, Multilegged, and Multilimb Robots......Page 15
1.5 Prerequisite and Structure......Page 16
 References......Page 17
2.2 Kinematic Structure......Page 24
2.3 Forward and Inverse Kinematic Problems......Page 27
2.4.1 Twist, Spatial Velocity, and Spatial Transform......Page 28
 Multi-DoF Joint Models......Page 31
 Parametrization of Instantaneous Rotation......Page 33
2.4.3 Inverse Differential Kinematic Relations......Page 34
2.5 Differential Kinematics at Singular Configurations......Page 35
2.7 Kinematic Redundancy......Page 41
2.7.1 Self-Motion......Page 42
2.7.2 General Solution to the Inverse Kinematics Problem......Page 44
2.7.3 Weighted Generalized Inverse......Page 46
 Singularity Avoidance Subtask via the Manipulability Measure......Page 47
2.7.5 Redundancy Resolution via the Extended Jacobian Technique......Page 48
2.8 Inverse Kinematics Solution Under Multiple Task Constraints......Page 49
2.8.1 Motion-Task Constraints......Page 50
 Restricted Generalized Inverse and Task Prioritization......Page 51
 Multiple Tasks With Fixed Priorities......Page 52
 Variable Task Priorities With Smooth Task Transitions......Page 54
2.8.3 Iterative Optimization Methods......Page 55
 Introducing a Hierarchical Structure With Fixed Task Priorities......Page 56
 Introducing Inequality Constraints......Page 57
2.8.4 Summary and Discussion......Page 58
2.9 Motion Constraints Through Contacts......Page 59
2.9.1 Contact Joints......Page 60
2.9.2 Contact Coordinate Frames......Page 61
2.9.3 Kinematic Models of Frictionless Contact Joints......Page 62
2.10 Differential Kinematics of Chains With Closed Loops......Page 63
2.10.1 Instantaneous Motion Analysis of Chains With Closed Loops......Page 64
 Limb Velocities......Page 66
 Velocities Within the Closed Chain......Page 67
2.10.2 Inverse Kinematics Solution......Page 69
2.10.3 Forward Kinematics Solution......Page 70
2.11.1 Quasivelocity, Holonomic and Nonholonomic Contact Constraints......Page 71
2.11.2 First-Order Differential Motion Relations Expressed in Terms of Base Quasivelocity......Page 72
 Constraint-Consistent Joint Velocity......Page 74
 Constraint-Consistent Generalized Velocity......Page 75
2.11.3 Second-Order Differential Motion Constraints and Their Integrability......Page 76
2.11.4 First-Order Differential Motion Relations With Mixed Quasivelocity......Page 79
 Implementation Example......Page 82
 References......Page 84
3.2 Wrench and Spatial Force......Page 92
3.3 Contact Joints: Static Relations......Page 93
3.3.1 Static Models of Frictionless Contact Joints......Page 94
 Point-Contact Model......Page 95
 Soft-Finger Contact Model......Page 96
 Polyhedral Convex Cone Model......Page 97
 Plane-Contact Model: the Contact Wrench Cone......Page 98
3.3.3 Motion/Force Duality Relations Across Contact Joints......Page 99
 Summary and Discussion......Page 101
3.4 Kinetostatic Relations in Independent Closed-Loop Chains......Page 102
3.4.2 Orthogonal Decomposition of the Loop-Closure and Root Link Wrenches......Page 103
3.4.3 Decomposition of the Limb Joint Torque......Page 104
3.5 The Wrench Distribution Problem......Page 105
3.5.1 General Solution to the Wrench Distribution Problem......Page 106
 Internal Forces......Page 107
 Internal Moments......Page 108
 Internal Wrench......Page 109
3.5.4 Which Generalized Inverse?......Page 111
3.5.5 Priorities Among the Joint Torque Components......Page 112
3.6.1 The Composite Rigid Body (CRB) and the CRB Wrench......Page 113
3.6.2 Interdependent Closed Loops......Page 115
3.6.3 Independent Closed Loops......Page 116
3.6.4 Determining the Joint Torques......Page 117
 Double Stance on Flat Floor in 2D (Lateral Plane)......Page 118
 Double Stance on Flat Floor With Friction......Page 120
 Double Stance With Noncoplanar Contacts......Page 121
3.6.6 Summary and Discussion......Page 122
3.7 Static Posture Stability and Optimization......Page 123
3.7.1 Static Posture Stability......Page 124
 An Example......Page 125
 Joint Torque Limit Test......Page 126
3.7.2 Static Posture Optimization......Page 127
3.8 Posture Characterization and Duality Relations......Page 128
 References......Page 130
4.1 Introduction......Page 134
4.2 Underactuated Robot Dynamics......Page 135
4.3.1 The Linear Inverted Pendulum Model......Page 137
 Linearized IP-on-Foot Model......Page 139
 IP-on-Cart Model......Page 140
 LIP-on-Cart Model......Page 141
4.3.3 Linear Reaction Wheel Pendulum Model and Centroidal Moment Pivot......Page 142
4.3.4 Reaction Mass Pendulum Model......Page 145
4.4.1 3D Inverted Pendulum With Variable Length......Page 146
4.4.2 Spherical IP-on-Foot and Sphere-on-Plane Models......Page 148
4.4.3 The 3D Reaction Wheel Pendulum Model......Page 149
4.4.4 The 3D Reaction Mass Pendulum Model......Page 150
4.5.1 Dynamic Model in Joint-Space Coordinates......Page 151
4.5.2 Dynamic Model in Spatial Coordinates......Page 153
 Operational Space Method [60]......Page 154
 Constrained Dynamics in Spatial Coordinates......Page 155
 Complete Dynamic Decoupling via the KD-JSD Method [116]......Page 156
4.5.3 Null-Space Dynamics With Dynamically Decoupled Hierarchical Structure......Page 157
4.6 Spatial Momentum of a Manipulator Floating Freely in Zero Gravity......Page 158
4.6.2 Spatial Momentum......Page 159
4.6.3 Locked Joints: the Composite Rigid Body......Page 160
4.6.4 Joints Unlocked: Multibody Notation......Page 162
4.6.5 Instantaneous Motion of a Free-Floating Manipulator......Page 165
4.7.1 The Momentum Equilibrium Principle......Page 167
 Coupling Spatial Momentum Conservation: the Reaction Null Space......Page 168
4.7.3 Angular Momentum-Based Redundancy Resolution......Page 169
 System Angular Momentum Conservation......Page 170
4.7.4 Motion of a Free-Floating Humanoid Robot in Zero Gravity......Page 171
4.8 Equation of Motion of a Free-Floating Manipulator in Zero Gravity......Page 172
4.8.1 Representation in Terms of Base Quasivelocity......Page 173
 In the Presence of External Forces......Page 174
4.8.2 Representation in Terms of Mixed Quasivelocity......Page 176
4.8.3 Representation in Terms of Centroidal Quasivelocity......Page 177
4.9 Reaction Null Space-Based Inverse Dynamics......Page 179
4.10 Spatial Momentum of a Humanoid Robot......Page 180
4.11 Equation of Motion of a Humanoid Robot......Page 182
4.12 Constraint-Force Elimination Methods......Page 184
4.12.1 Gauss' Principle of Least Constraint......Page 185
4.12.2 Direct Elimination......Page 187
4.12.3 Maggi's Equations (Null-Space Projection Method)......Page 188
4.12.4 Range-Space Projection Method......Page 191
4.12.5 Summary and Conclusions......Page 192
4.13.1 Joint-Space Dynamics-Based Representation......Page 193
4.13.2 Spatial Dynamics-Based Representation (Lagrange-d'Alembert Formulation)......Page 194
 Adjoining the Object Dynamics......Page 195
4.13.3 Equation of Motion in End-Link Spatial Coordinates......Page 196
 System Dynamics Projection Along the Unconstrained Motion Directions......Page 197
 Projection Along the Constrained and Unconstrained Motion Directions......Page 198
4.13.4 Summary and Discussion......Page 199
4.14.1 Based on the Direct Elimination/Gauss/Maggi/Projection Methods......Page 201
4.14.3 Based on the Joint-Space Dynamics Elimination Approach......Page 203
4.14.4 Summary and Conclusions......Page 204
 References......Page 205
5.1 Overview......Page 212
5.2 Dynamic Postural Stability......Page 214
5.3.1 The Extrapolated CoM and the Dynamic Stability Margin......Page 216
5.3.2 Extrapolated CoM Dynamics......Page 218
5.3.3 Discrete States With Transitions......Page 219
5.3.4 Dynamic Stability Region in 2D......Page 220
5.4 ZMP Manipulation-Type Stabilization on Flat Ground......Page 221
5.4.1 The ZMP Manipulation-Type Stabilizer......Page 223
5.4.2 Velocity-Based ZMP Manipulation-Type Stabilization in 3D......Page 224
5.4.3 Regulator-Type ZMP Stabilizer......Page 226
5.4.4 ZMP Stabilization in the Presence of GRF Estimation Time Lag......Page 228
5.4.5 Torso Position Compliance Control (TPCC)......Page 229
5.5.1 Capture Point (CP) and Instantaneous Capture Point (ICP)......Page 231
5.5.2 ICP-Based Stabilization......Page 232
5.5.3 ICP Stabilization in the Presence of GRF Estimation Time Lag......Page 233
5.5.4 ICP Dynamics and Stabilization in 2D......Page 234
5.6.1 Stability Analysis Based on the LRWP Model......Page 235
5.6.2 Stability Analysis in 3D: the Divergent Component of Motion......Page 237
5.6.3 DCM Stabilizer......Page 240
5.6.4 Summary and Conclusions......Page 241
5.7 Maximum Output Admissible Set Based Stabilization......Page 242
5.8.1 Fundamental Functional Dependencies in Balance Control......Page 244
5.8.3 Whole-Body Balance Control With Relative Angular Momentum/Velocity......Page 246
 Relative Angular Momentum/Velocity (RAM/V) Balance Control......Page 248
 Special Cases: Balance Control That Conserves the System or the Coupling Angular Momentum......Page 250
5.8.4 RNS-Based Stabilization of Unstable Postures......Page 251
 Summary and Conclusions......Page 252
5.8.5 An Approach to Contact Stabilization Within the Resolved Momentum Framework......Page 253
5.8.6 Spatial Momentum Rate Stabilization Parametrized by the CMP/VRP......Page 255
5.8.7 CRB Motion Trajectory Tracking With Asymptotic Stability......Page 256
5.9 Task-Space Controller Design for Balance Control......Page 257
5.9.1 Generic Task-Space Controller Structure......Page 258
5.9.2 Optimization Task Formulation and Constraints......Page 259
5.10.1 Pseudoinverse-Based Body-Wrench Distribution......Page 262
5.10.2 The ZMP Distributor......Page 263
5.10.3 Proportional Distribution Approach......Page 264
5.10.4 The DCM Generalized Inverse......Page 265
 Vertical GRF Force Distribution Policy......Page 266
 Friction Policy......Page 267
 CoP Allocation Policy......Page 268
 Final Result......Page 269
 Implementation Example......Page 270
5.10.5 The VRP Generalized Inverse......Page 271
5.10.6 Joint Torque-Based Contact Wrench Optimization......Page 273
5.11.1 Independent Motion Optimization With CRB Wrench-Consistent Input......Page 275
5.11.2 Stabilization With Angular Momentum Damping......Page 276
5.11.3 Motion Optimization With Task-Based Hand Motion Constraints......Page 279
5.12.1 Multicontact Motion/Force Controller Based on the Closed-Chain Model......Page 280
5.12.2 Motion/Force Optimization Based on the Operational-Space Formulation......Page 282
 Example......Page 284
5.13 Reactive Balance Control in Response to Weak External Disturbances......Page 287
5.13.1 Gravity Compensation-Based Whole-Body Compliance With Passivity......Page 288
5.13.2 Whole-Body Compliance With Multiple Contacts and Passivity......Page 289
5.13.3 Multicontact Motion/Force Control With Whole-Body Compliance......Page 292
5.14 Iterative Optimization in Balance Control......Page 293
5.14.1 A Brief Historical Overview......Page 294
5.14.2 SOCP-Based Optimization......Page 295
5.14.3 Iterative Contact Wrench Optimization......Page 296
 Sequential Approach......Page 297
 Nonsequential Approach......Page 298
 Hierarchical Multiobjective Optimization With Hard Constraints......Page 299
 Penalty-Based Multiobjective Optimization With Soft Constraints......Page 300
5.14.6 Mixed Iterative/Noniterative Optimization Approaches......Page 301
 Hierarchical Task Formulation With Decoupling......Page 302
5.14.7 Computational Time Requirements......Page 303
 References......Page 304
6.1 Introduction......Page 312
6.2.1 Grasp Matrix and Hand Jacobian Matrix......Page 313
6.2.3 Constraint Types......Page 316
6.2.4 Form Closure......Page 317
 Case Study......Page 318
 Definition of Force Closure......Page 319
 Case Study......Page 320
6.3.1 Background of Multiarm Object Manipulation......Page 322
6.3.2 Kinematics and Statics of Multiarm Cooperation......Page 323
6.3.3 Force and Moment Applied to the Object......Page 325
 Case Study......Page 326
6.3.5 Control of the External and Internal Wrenches......Page 327
 Virtual Linkage [28] (see also Section 3.5.2)......Page 328
 Virtual Stick [25,27]......Page 331
 Cooperation Among Three Robot Arms......Page 332
 Cooperation Between Two Humanoid Robots......Page 333
 Cooperation Among Four Humanoid Robots......Page 335
6.3.6 Hybrid Position/Force Control......Page 337
 Hybrid Position/Force Controller......Page 338
6.4.1 On-Line Footstep Planning......Page 339
6.4.2 Coordinated Movement of Hands and Feet......Page 340
6.4.4 Leader-Follower-Type Cooperative Object Manipulation......Page 342
 Concept of a Leader-Follower-Type Cooperative Object Manipulation......Page 343
 Experiment of Object Transportation......Page 344
 Simulation of Symmetry-Type Cooperation......Page 345
 Simulation Results......Page 346
6.4.6 Comparison Between Leader-Follower-Type and Symmetry-Type Cooperation......Page 347
6.5.1 Equation of Motion of the Object......Page 349
6.5.2 Controller......Page 350
 References......Page 354
7.1 Overview......Page 356
7.2.1 CP-Based Walking Control......Page 358
7.2.2 CP-Based Gait Generation......Page 359
7.2.3 ICP Controller......Page 362
7.2.4 CP-Based Gait Generation and ZMP Control......Page 363
7.3.1 Landing Position Control for Walking on Sand......Page 364
7.3.2 Experiments of Walking on Sand......Page 365
7.3.3 Summary and Discussion......Page 370
7.4.1 Continuous Double-Support (CDS) Gait Generation......Page 371
7.4.2 Heel-to-Toe (HT) Gait Generation......Page 373
7.4.3 Simulation......Page 374
7.5 Synergy-Based Motion Generation......Page 375
7.5.2 Combinations of Primitive Synergies......Page 377
7.6 Synergy-Based Reactive Balance Control With Planar Models......Page 379
 Lateral Plane......Page 380
7.6.3 Sagittal-Plane Ankle/Hip Synergies......Page 382
7.6.4 Lateral Plane Ankle, Load/Unload and Lift-Leg Synergies......Page 386
7.6.5 Transverse-Plane Twist Synergy......Page 388
7.6.6 Complex Reactive Synergies Obtained by Superposition of Simple Ones......Page 389
7.6.7 Summary and Discussion......Page 390
7.7.1 Reactive Synergies Generated With a Simple Dynamic Torque Controller......Page 391
7.7.2 The Load/Unload and Lift-Leg Strategies Revisited......Page 392
7.7.3 Compliant-Body Response......Page 393
7.7.4 Impact Accommodation With Angular Momentum Damping From the RNS......Page 395
 Anticipatory-Type Impact Accommodation......Page 397
 Nonanticipatory-Type Impact Accommodation......Page 398
7.7.5 Reactive Stepping......Page 399
 Impact Phase......Page 401
 Simulation......Page 402
7.7.6 Accommodating a Large Impact Without Stepping......Page 405
7.8.1 Historical Background......Page 408
7.8.2 Considering the Effects of the Reduction Gear Train......Page 409
7.8.3 Ground Reaction Force and Moment......Page 410
7.8.4 Dynamic Effects Caused by Impacts......Page 411
7.8.5 Virtual Mass......Page 413
7.8.7 Optimization Problems for Impact Motion Generation......Page 415
 A Simplified Model of the Humanoid Robot HOAP-2......Page 417
 Performance Index for Stability Margin Evaluation......Page 418
 Optimization of the Posture and Velocity at the Impact......Page 419
 Optimization of the Velocity Before/After the Impact......Page 420
7.8.9 Experimental Verification of the Generated Impact Motion......Page 422
 References......Page 424
8.1 Overview......Page 430
8.2 Robot Simulators......Page 431
8.3 Structure of a Robot Simulator......Page 433
 Using CAD Files......Page 438
 Using the URDF File......Page 443
8.4.2 Generating the Simulink Model......Page 446
8.4.3 Joint Mode Configuration......Page 449
8.4.4 Modeling of Contact Forces......Page 459
8.4.5 Computing the ZMP......Page 467
8.4.6 Motion Design......Page 472
8.4.7 Simulation......Page 474
 References......Page 478
A.2 Model Parameters for a Small-Size Humanoid Robot With 7-DoF Arms......Page 481
 References......Page 487
Index......Page 488
Back Cover......Page 499