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1 | (18) |
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19 | (50) |
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2.1 Coordinate Transformations |
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19 | (6) |
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19 | (1) |
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2.1.2 Local Coordinates and Homogeneous Transformations |
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20 | (3) |
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2.1.3 Local Coordinate Systems Local to Local Coordinate Systems |
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23 | (2) |
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2.1.4 Homogeneous Transformations and Chain Rules |
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25 | (1) |
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2.2 Characteristics of Rotational Motion |
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25 | (11) |
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2.2.1 Roll, Pitch and Yaw Notation |
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26 | (1) |
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2.2.2 The Meaning of Rotation Matrices |
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27 | (1) |
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2.2.3 Calculating the Inverse of a Rotation Matrix |
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28 | (1) |
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2.2.4 Angular Velocity Vector |
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29 | (3) |
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2.2.5 Differentiation of the Rotation Matrix and Angular Velocity Vectors |
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32 | (2) |
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2.2.6 Integration of the Angular Velocity Vector and Matrix Exponential |
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34 | (1) |
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35 | (1) |
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2.3 Velocity in Three Dimensional Space |
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36 | (4) |
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2.3.1 The Linear and Angular Velocity of a Single Object |
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36 | (2) |
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2.3.2 The Linear and Angular Velocity of Two Objects |
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38 | (2) |
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2.4 Robot Data Structure and Programming |
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40 | (5) |
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40 | (2) |
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2.4.2 Programming with Recursions |
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42 | (3) |
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2.5 Kinematics of a Humanoid Robot |
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45 | (24) |
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45 | (2) |
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2.5.2 Forward Kinematics: Calculating the Position of the Links from Joint Angles |
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47 | (2) |
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2.5.3 Inverse Kinematics: Calculating the Joint Angles from a Link's Position and Attitude |
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49 | (4) |
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2.5.4 Numerical Solution to Inverse Kinematics |
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53 | (4) |
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57 | (2) |
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2.5.6 Jacobian and the Joint Velocity |
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59 | (3) |
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62 | (1) |
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2.5.8 Inverse Kinematics with Singularity Robustness |
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63 | (2) |
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2.5.9 Appendix: Supplementary Functions |
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65 | (4) |
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69 | (36) |
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3.1 ZMP and Ground Reaction Forces |
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69 | (8) |
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69 | (2) |
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71 | (2) |
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73 | (4) |
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77 | (6) |
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77 | (2) |
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79 | (3) |
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3.2.3 ZMP for Both Feet Contact |
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82 | (1) |
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3.3 Dynamics of Humanoid Robots |
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83 | (12) |
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3.3.1 Humanoid Robot Motion and Ground Reaction Force |
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83 | (2) |
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85 | (2) |
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87 | (2) |
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3.3.4 Angular Momentum and Inertia Tensor of Rigid Body |
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89 | (3) |
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3.3.5 Calculation of Robot's Center of Mass |
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92 | (1) |
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3.3.6 Calculation of Link Speed and Angular Velocity |
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93 | (1) |
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3.3.7 Calculation of Robot's Momentum |
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94 | (1) |
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3.3.8 Calculation of Robot's Angular Momentum |
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94 | (1) |
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3.4 Calculation of ZMP from Robot's Motion |
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95 | (3) |
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95 | (2) |
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3.4.2 Calculation of ZMP Using Approximation |
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97 | (1) |
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98 | (4) |
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98 | (1) |
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3.5.2 Does ZMP Exist Outside the Support Polygon due to the Acceleration of the Center of Mass? |
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98 | (3) |
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101 | (1) |
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3.6 Appendix: Convex Set and Convex Hull |
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102 | (3) |
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105 | (54) |
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4.1 How to Realize Biped Walking? |
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105 | (2) |
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4.2 Two Dimensional Walking Pattern Generation |
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107 | (13) |
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4.2.1 Two Dimensional Inverted Pendulum |
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107 | (1) |
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4.2.2 Behavior of Linear Inverted Pendulum |
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108 | (4) |
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112 | (1) |
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4.2.4 Support Leg Exchange |
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113 | (2) |
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4.2.5 Planning a Simple Biped Gait |
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115 | (1) |
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4.2.6 Extension to a Walk on Uneven Terrain |
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116 | (4) |
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4.3 3D Walking Pattern Generation |
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120 | (18) |
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4.3.1 3D Linear Inverted Pendulum |
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120 | (2) |
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4.3.2 Natures of the 3D Linear Inverted Pendulum |
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122 | (4) |
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4.3.3 3D Walking Pattern Generation |
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126 | (7) |
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4.3.4 Introducing Double Support Phase |
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133 | (2) |
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4.3.5 From Linear Inverted Pendulum to Multi-body Model |
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135 | (2) |
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4.3.6 Implementation Example |
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137 | (1) |
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4.4 ZMP Based Walking Pattern Generation |
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138 | (11) |
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138 | (2) |
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4.4.2 Off-Line Walking Pattern Generation |
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140 | (2) |
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4.4.3 On-Line Walking Pattern Generation |
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142 | (5) |
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4.4.4 Dynamics Filter Based on Preview Control |
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147 | (2) |
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4.4.5 Advanced Pattern Generators |
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149 | (1) |
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149 | (6) |
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4.5.1 Principles of Stabilizing Control |
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150 | (4) |
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4.5.2 Stabilizing Control of Honda Humanoid Robot |
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154 | (1) |
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4.5.3 Advanced Stabilizers |
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155 | (1) |
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4.6 Pioneers of Dynamic Biped Walking Technology |
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155 | (1) |
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4.7 Additional Methods for Biped Control |
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156 | (3) |
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4.7.1 Passive Dynamic Walk |
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157 | (1) |
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4.7.2 Nonlinear Oscillator and Central Pattern Generators |
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158 | (1) |
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4.7.3 Learning and Evolutionary Computing |
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158 | (1) |
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5 Generation of Whole Body Motion Patterns |
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159 | (24) |
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5.1 How to Generate Whole Body Motion |
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159 | (1) |
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5.2 Generating Rough Whole Body Motion |
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160 | (5) |
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5.2.1 Using Motion Capture |
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162 | (1) |
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5.2.2 Using a Graphical User Interface |
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163 | (1) |
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5.2.3 Using High Speed Multivariate Search Methods |
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164 | (1) |
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5.3 Converting Whole Body Motion Patterns to Dynamically Stable Motion |
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165 | (4) |
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165 | (1) |
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166 | (1) |
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5.3.3 Strict Trunk Motion Computation Algorithm |
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167 | (2) |
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5.4 Remote Operation of Humanoid Robots with Whole Body Motion Generation |
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169 | (8) |
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5.4.1 Remote Generation of Whole Body Motion Using the Operation Point Switching Method |
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170 | (2) |
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5.4.2 Full Body Motion Generation of Stable Motion Using Split Momentum Control |
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172 | (2) |
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5.4.3 Application and Experiments with the Humanoid Robot HRP-2 |
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174 | (3) |
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5.5 Reducing the Impact of a Humanoid Robot Falling Backwards |
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177 | (3) |
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5.6 Making a Humanoid Robot Get Up Again |
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180 | (3) |
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183 | (28) |
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6.1 Dynamics of Rotating Rigid Body |
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184 | (2) |
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6.1.1 Euler's Equation of Motion |
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184 | (1) |
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6.1.2 Simulation of Rigid Body Rotation |
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185 | (1) |
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186 | (3) |
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6.2.1 Speed of Rigid Body |
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186 | (2) |
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6.2.2 Integration of Spatial Velocity |
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188 | (1) |
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6.3 Dynamics of Rigid Body |
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189 | (7) |
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6.3.1 Newton-Euler Equations |
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189 | (2) |
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6.3.2 Dynamics by Spatial Velocity |
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191 | (1) |
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6.3.3 Rigid Body Simulation Based on Spatial Velocity |
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192 | (1) |
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6.3.4 Simulation of a Spinning Top |
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193 | (3) |
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6.4 Dynamics of Link System |
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196 | (9) |
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6.4.1 Forward Kinematics with Acceleration |
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196 | (1) |
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6.4.2 Inverse Dynamics of Link System |
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197 | (3) |
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6.4.3 Forward Dynamics of Link System |
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200 | (3) |
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6.4.4 Featherstone's Method |
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203 | (2) |
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6.5 Background Material for This Section |
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205 | (1) |
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206 | (5) |
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6.6.1 Treatment of Force and Moment |
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206 | (1) |
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207 | (4) |
References |
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211 | (10) |
Index |
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221 | |