Preface |
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Contents |
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xi | |
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x | |
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1.1 Mathematical Modeling of Robots |
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5 | (2) |
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1.1.1 Symbolic Representation of Robot Manipulators |
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5 | (1) |
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1.1.2 The Configuration Space |
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5 | (1) |
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6 | (1) |
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7 | (1) |
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1.2 Robots as Mechanical Devices |
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7 | (6) |
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1.2.1 Classification of Robotic Manipulators |
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8 | (2) |
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10 | (1) |
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1.2.3 Accuracy and Repeatability |
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10 | (2) |
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1.2.4 Wrists and End Effectors |
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12 | (1) |
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1.3 Common Kinematic Arrangements |
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13 | (5) |
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1.3.1 Articulated Manipulator (RRR) |
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13 | (1) |
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1.3.2 Spherical Manipulator (RRP) |
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14 | (1) |
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1.3.3 SCARA Manipulator (RRP) |
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14 | (1) |
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1.3.4 Cylindrical Manipulator (RPP) |
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15 | (1) |
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1.3.5 Cartesian Manipulator (PPP) |
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15 | (3) |
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1.3.6 Parallel Manipulator |
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18 | (1) |
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18 | (15) |
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18 | (9) |
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1.4.2 Underactuated and Mobile Robots |
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27 | (1) |
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27 | (2) |
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29 | (4) |
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33 | (130) |
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35 | (40) |
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2.1 Representing Positions |
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36 | (2) |
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2.2 Representing Rotations |
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38 | (6) |
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2.2.1 Rotation in the Plane |
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38 | (3) |
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2.2.2 Rotations in Three Dimensions |
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41 | (3) |
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2.3 Rotational Transformations |
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44 | (4) |
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2.4 Composition of Rotations |
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48 | (4) |
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2.4.1 Rotation with Respect to the Current Frame |
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48 | (2) |
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2.4.2 Rotation with Respect to the Fixed Frame |
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50 | (1) |
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2.4.3 Rules for Composition of Rotations |
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51 | (1) |
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2.5 Parameterizations of Rotations |
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52 | (9) |
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53 | (2) |
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2.5.2 Roll, Pitch, Yaw Angles |
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55 | (2) |
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2.5.3 Axis-Angle Representation |
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57 | (2) |
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2.5.4 Exponential Coordinates |
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59 | (2) |
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61 | (4) |
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2.6.1 Homogeneous Transformations |
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62 | (3) |
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2.6.2 Exponential Coordinates for General Rigid Motions |
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65 | (1) |
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65 | (10) |
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67 | (6) |
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73 | (2) |
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75 | (26) |
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75 | (3) |
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3.2 The Denavit-Haxtenberg Convention |
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78 | (9) |
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3.2.1 Existence and Uniqueness |
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80 | (3) |
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3.2.2 Assigning the Coordinate Frames |
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83 | (4) |
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87 | (9) |
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3.3.1 Planar Elbow Manipulator |
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87 | (2) |
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3.3.2 Three-Link Cylindrical Robot |
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89 | (1) |
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3.3.3 The Spherical Wrist |
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90 | (1) |
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3.3.4 Cylindrical Manipulator with Spherical Wrist |
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91 | (2) |
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3.3.5 Stanford Manipulator |
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93 | (2) |
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95 | (1) |
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96 | (5) |
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96 | (3) |
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99 | (2) |
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101 | (40) |
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4.1 Angular Velocity: The Fixed Axis Case |
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102 | (1) |
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4.2 Skew-Symmetric Matrices |
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103 | (4) |
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4.2.1 Properties of Skew-Symmetric Matrices |
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104 | (1) |
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4.2.2 The Derivative of a Rotation Matrix |
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105 | (2) |
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4.3 Angular Velocity: The General Case |
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107 | (1) |
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4.4 Addition of Angular Velocities |
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108 | (2) |
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4.5 Linear Velocity of a Point Attached to a Moving Frame |
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110 | (1) |
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4.6 Derivation of the Jacobian |
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111 | (8) |
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112 | (1) |
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113 | (2) |
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4.6.3 Combining the Linear and Angular Velocity Jacobians |
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115 | (4) |
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119 | (2) |
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4.8 The Analytical Jacobian |
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121 | (1) |
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122 | (7) |
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4.9.1 Decoupling of Singularities |
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123 | (2) |
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4.9.2 Wrist Singularities |
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125 | (1) |
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125 | (4) |
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4.10 Static Force/Torque Relationships |
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129 | (2) |
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4.11 Inverse Velocity and Acceleration |
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131 | (2) |
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133 | (3) |
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136 | (5) |
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138 | (2) |
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140 | (1) |
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141 | (22) |
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5.1 The General Inverse Kinematics Problem |
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141 | (2) |
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143 | (2) |
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5.3 Inverse Position: A Geometric Approach |
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145 | (6) |
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5.3.1 Spherical Configuration |
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146 | (2) |
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5.3.2 Articulated Configuration |
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148 | (3) |
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151 | (5) |
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5.5 Numerical Inverse Kinematics |
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156 | (2) |
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158 | (5) |
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160 | (2) |
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162 | (1) |
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II DYNAMICS AND MOTION PLANNING |
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163 | (106) |
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165 | (50) |
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6.1 The Euler---Lagrange Equations |
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166 | (11) |
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166 | (4) |
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6.1.2 Holonomic Constraints and Virtual Work |
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170 | (4) |
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6.1.3 D'Alembert's Principle |
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174 | (3) |
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6.2 Kinetic and Potential Energy |
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177 | (4) |
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178 | (2) |
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6.2.2 Kinetic Energy for an n-Link Robot |
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180 | (1) |
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6.2.3 Potential Energy for an n-Link Robot |
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181 | (1) |
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181 | (3) |
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6.4 Some Common Configurations |
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184 | (10) |
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6.5 Properties of Robot Dynamic Equations |
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194 | (4) |
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6.5.1 Skew Symmetry and Passivity |
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194 | (2) |
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6.5.2 Bounds on the Inertia Matrix |
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196 | (1) |
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6.5.3 Linearity in the Parameters |
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196 | (2) |
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6.6 Newton-Euler Formulation |
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198 | (11) |
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6.6.1 Planar Elbow Manipulator Revisited |
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206 | (3) |
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209 | (6) |
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211 | (3) |
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214 | (1) |
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7 Path and Trajectory Planning |
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215 | (54) |
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7.1 The Configuration Space |
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216 | (6) |
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7.1.1 Representing the Configuration Space |
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217 | (1) |
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7.1.2 Configuration Space Obstacles |
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218 | (3) |
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7.1.3 Paths in the Configuration Space |
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221 | (1) |
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7.2 Path Planning for Q = R2 |
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222 | (7) |
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7.2.1 The Visibility Graph |
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224 | (2) |
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7.2.2 The Generalized Voronoi Diagram |
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226 | (1) |
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7.2.3 Trapezoidal Decompositions |
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226 | (3) |
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7.3 Artificial Potential Fields |
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229 | (16) |
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7.3.1 Artificial Potential Fields for Q = Rn |
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230 | (5) |
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7.3.2 Potential Fields for Q ≠ Rn |
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235 | (10) |
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7.4 Sampling-Based Methods |
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245 | (7) |
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7.4.1 Probabilistic Roadmaps (PRM) |
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246 | (4) |
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7.4.2 Rapidly-Exploring Random Trees (RRTs) |
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250 | (2) |
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252 | (11) |
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7.5.1 Trajectories for Point-to-Point Motion |
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253 | (8) |
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7.5.2 Trajectories for Paths Specified by Via Points |
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261 | (2) |
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263 | (6) |
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265 | (2) |
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267 | (2) |
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III CONTROL OF MANIPULATORS |
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269 | (168) |
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8 Independent Joint Control |
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271 | (40) |
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271 | (2) |
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273 | (3) |
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276 | (2) |
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8.4 Independent Joint Model |
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278 | (3) |
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281 | (7) |
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288 | (4) |
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8.6.1 Trajectory Tracking |
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289 | (2) |
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8.6.2 The Method of Computed Torque |
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291 | (1) |
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292 | (5) |
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297 | (7) |
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8.8.1 State Feedback Control |
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299 | (2) |
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301 | (3) |
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304 | (7) |
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307 | (2) |
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309 | (2) |
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9 Nonlinear and Multivariable Control |
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311 | (34) |
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311 | (2) |
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313 | (4) |
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317 | (12) |
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9.3.1 Joint Space Inverse Dynamics |
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317 | (3) |
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9.3.2 Task Space Inverse Dynamics |
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320 | (2) |
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9.3.3 Robust Inverse Dynamics |
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322 | (5) |
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9.3.4 Adaptive Inverse Dynamics |
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327 | (2) |
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9.4 Passivity-Based Control |
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329 | (4) |
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9.4.1 Passivity-Based Robust Control |
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331 | (1) |
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9.4.2 Passivity-Based Adaptive Control |
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332 | (1) |
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333 | (4) |
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337 | (8) |
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341 | (2) |
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343 | (2) |
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345 | (20) |
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10.1 Coordinate Frames and Constraints |
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347 | (4) |
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347 | (2) |
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10.1.2 Natural and Artificial Constraints |
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349 | (2) |
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10.2 Network Models and Impedance |
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351 | (4) |
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10.2.1 Impedance Operators |
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353 | (1) |
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10.2.2 Classification of Impedance Operators |
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354 | (1) |
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10.2.3 Thevenin and Norton Equivalents |
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355 | (1) |
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10.3 Task Space Dynamics and Control |
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355 | (6) |
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356 | (2) |
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10.3.2 Hybrid Impedance Control |
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358 | (3) |
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361 | (4) |
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362 | (2) |
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364 | (1) |
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365 | (44) |
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11.1 Design Considerations |
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366 | (2) |
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11.1.1 Camera Configuration |
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366 | (1) |
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11.1.2 Image-Based vs. Position-Based Approaches |
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367 | (1) |
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11.2 Computer Vision for Vision-Based Control |
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368 | (10) |
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11.2.1 The Geometry of Image Formation |
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369 | (4) |
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373 | (5) |
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11.3 Camera Motion and the Interaction Matrix |
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378 | (1) |
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11.4 The Interaction Matrix for Point Features |
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379 | (7) |
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11.4.1 Velocity Relative to a Moving Frame |
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380 | (1) |
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11.4.2 Constructing the Interaction Matrix |
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381 | (3) |
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11.4.3 Properties of the Interaction Matrix for Points |
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384 | (1) |
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11.4.4 The Interaction Matrix for Multiple Points |
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385 | (1) |
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11.5 Image-Based Control Laws |
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386 | (7) |
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11.5.1 Computing Camera Motion |
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387 | (2) |
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11.5.2 Proportional Control Schemes |
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389 | (1) |
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11.5.3 Performance of Image-Based Control Systems |
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390 | (3) |
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11.6 End Effector and Camera Motions |
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393 | (1) |
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11.7 Partitioned Approaches |
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394 | (3) |
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11.8 Motion Perceptibility |
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397 | (2) |
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399 | (10) |
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401 | (4) |
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405 | (4) |
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12 Feedback Linearization |
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409 | (28) |
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410 | (7) |
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12.1.1 Manifolds, Vector Fields, and Distributions |
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410 | (4) |
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12.1.2 The Frobenius Theorem |
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414 | (3) |
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12.2 Feedback Linearization |
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417 | (2) |
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12.3 Single-Input Systems |
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419 | (10) |
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429 | (4) |
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433 | (4) |
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433 | (2) |
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435 | (2) |
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IV CONTROL OF UNDERACTUATED SYSTEMS |
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437 | (86) |
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439 | (40) |
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439 | (1) |
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440 | (3) |
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13.3 Examples of Underactuated Robots |
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443 | (5) |
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13.3.1 The Cart-Pole System |
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443 | (2) |
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445 | (1) |
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446 | (1) |
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13.3.4 The Reaction-Wheel Pendulum |
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447 | (1) |
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13.4 Equilibria and Linear Controllability |
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448 | (8) |
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13.4.1 Linear Controllability |
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450 | (6) |
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13.5 Partial Feedback Linearization |
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456 | (5) |
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13.5.1 Collocated Partial Feedback Linearization |
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457 | (2) |
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13.5.2 Noncollocated Partial Feedback Linearization |
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459 | (2) |
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13.6 Output Feedback Linearization |
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461 | (5) |
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13.6.1 Computation of the Zero Dynamics |
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463 | (3) |
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13.6.2 Virtual Holonomic Constraints |
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466 | (1) |
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13.7 Passivity-Based Control |
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466 | (8) |
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13.7.1 The Simple Pendulum |
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467 | (4) |
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13.7.2 The Reaction-Wheel Pendulum |
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471 | (2) |
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13.7.3 Swingup and Balance of The Acrobot |
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473 | (1) |
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474 | (5) |
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476 | (1) |
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477 | (2) |
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479 | (44) |
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14.1 Nonholonomic Constraints |
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480 | (4) |
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14.2 Involutivity and Holonomy |
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484 | (3) |
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14.3 Examples of Nonholonomic Systems |
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487 | (6) |
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493 | (2) |
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14.5 Controllability of Driftless Systems |
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495 | (4) |
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499 | (10) |
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14.6.1 Conversion to Chained Forms |
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499 | (7) |
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14.6.2 Differential Flatness |
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506 | (3) |
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14.7 Feedback Control of Driftless Systems |
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509 | (10) |
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509 | (2) |
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511 | (2) |
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14.7.3 Trajectory Tracking |
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513 | (2) |
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14.7.4 Feedback Linearization |
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515 | (4) |
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519 | (4) |
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520 | (1) |
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521 | (2) |
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523 | (2) |
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A.1 The Two-Argument Arctangent Function |
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523 | (1) |
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A.2 Useful Trigonometric Formulas |
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523 | (2) |
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525 | (14) |
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525 | (1) |
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526 | (2) |
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528 | (2) |
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B.4 Eigenvalues and Eigenvectors |
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530 | (3) |
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B.5 Differentiation of Vectors |
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533 | (1) |
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B.6 The Matrix Exponential |
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534 | (1) |
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B.7 Lie Groups and Lie Algebras |
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534 | (2) |
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536 | (1) |
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536 | (1) |
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B.10 Singular Value Decomposition (SVD) |
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537 | (2) |
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539 | (12) |
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C.1 Continuity and Differentiability |
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539 | (2) |
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C.2 Vector Fields and Equilibria |
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541 | (4) |
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545 | (1) |
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545 | (1) |
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C.5 Global and Exponential Stability |
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546 | (1) |
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C.6 Stability of Linear Systems |
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547 | (1) |
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548 | (1) |
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549 | (2) |
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551 | (4) |
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D.1 Unconstrained Optimization |
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551 | (1) |
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D.2 Constrained Optimization |
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552 | (3) |
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555 | (6) |
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E.1 The Image Plane and the Sensor Array |
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555 | (1) |
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E.2 Extrinsic Camera Parameters |
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556 | (1) |
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E.3 Intrinsic Camera Parameters |
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557 | (1) |
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E.4 Determining the Camera Parameters |
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557 | (4) |
Bibliography |
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561 | (15) |
Index |
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576 | |