| Introduction |
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xvii | |
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Terminology and general definitions |
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1 | (12) |
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1 | (1) |
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Mechanical components of a robot |
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2 | (2) |
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4 | (3) |
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4 | (1) |
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4 | (1) |
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5 | (1) |
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5 | (1) |
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5 | (1) |
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6 | (1) |
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6 | (1) |
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Choosing the number of degrees of freedom of a robot |
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7 | (1) |
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Architectures of robot manipulators |
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7 | (4) |
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Characteristics of a robot |
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11 | (1) |
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12 | (1) |
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Transformation matrix between vectors, frames and screws |
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13 | (22) |
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13 | (1) |
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14 | (1) |
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Representation of a point |
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14 | (1) |
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Representation of a direction |
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14 | (1) |
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Representation of a plane |
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15 | (1) |
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Homogeneous transformations |
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15 | (12) |
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15 | (1) |
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Transformation of vectors |
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16 | (1) |
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17 | (1) |
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Transformation matrix of a pure translation |
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17 | (1) |
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Transformation matrices of a rotation about the principle axes |
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18 | (1) |
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Transformation matrix of a rotation about the x axis by an angle θ |
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18 | (1) |
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Transformation matrix of a rotation about the y axis by an angle θ |
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19 | (1) |
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Transformation matrix of a rotation θ about the z axis by an angle θ |
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19 | (1) |
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Properties of homogeneous transformation matrices |
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20 | (3) |
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Transformation matrix of a rotation about a general vector located at the origin |
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23 | (2) |
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Equivalent angle and axis of a general rotation |
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25 | (2) |
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27 | (2) |
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27 | (1) |
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Representation of velocity (kinematic screw) |
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28 | (1) |
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28 | (1) |
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Differential translation and rotation of frames |
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29 | (3) |
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Representation of forces (wrench) |
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32 | (1) |
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33 | (2) |
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Direct geometric model of serial robots |
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35 | (22) |
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35 | (1) |
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Description of the geometry of serial robots |
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36 | (6) |
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42 | (3) |
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Optimization of the computation of the direct geometric model |
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45 | (2) |
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Transformation matrix of the end-effector in the world frame |
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47 | (1) |
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Specification of the orientation |
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48 | (7) |
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49 | (2) |
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51 | (2) |
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53 | (2) |
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55 | (2) |
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Inverse geometric model of serial robots |
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57 | (28) |
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57 | (1) |
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Mathematical statement of the problem |
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58 | (1) |
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Inverse geometric model of robots with simple geometry |
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59 | (12) |
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59 | (2) |
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Special case: robots with a spherical wrist |
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61 | (1) |
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62 | (1) |
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62 | (5) |
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Inverse geometric model of robots with more than six degrees of freedom |
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67 | (1) |
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Inverse geometric model of robots with less than six degrees of freedom |
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68 | (3) |
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Inverse geometric model of decoupled six degree-of-freedom robots |
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71 | (9) |
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71 | (1) |
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Inverse geometric model of six degree-of-freedom robots having a spherical joint |
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72 | (1) |
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General solution of the position equation |
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72 | (6) |
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General solution of the orientation equation |
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78 | (1) |
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Inverse geometric model of robots with three prismatic joints |
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79 | (1) |
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Solution of the orientation equation |
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79 | (1) |
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Solution of the position equation |
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79 | (1) |
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Inverse geometric model of general robots |
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80 | (3) |
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83 | (2) |
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Direct kinematic model of serial robots |
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85 | (32) |
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85 | (1) |
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Computation of the Jacobian matrix from the direct geometric model |
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86 | (1) |
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87 | (5) |
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Computation of the basic Jacobian matrix |
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88 | (2) |
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Computation of the matrix iJn |
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90 | (2) |
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Decomposition of the Jacobian matrix into three matrices |
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92 | (2) |
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Efficient computation of the end-effector velocity |
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94 | (1) |
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Dimension of the task space of a robot |
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95 | (1) |
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Analysis of the robot workspace |
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96 | (7) |
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96 | (1) |
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97 | (1) |
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98 | (1) |
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99 | (2) |
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101 | (2) |
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Velocity transmission between joint space and task space |
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103 | (4) |
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Singular value decomposition |
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103 | (2) |
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Velocity ellipsoid: velocity transmission performance |
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105 | (2) |
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107 | (3) |
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Representation of a wrench |
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107 | (1) |
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Mapping of an external wrench into joint torques |
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107 | (1) |
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108 | (2) |
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Second order kinematic model |
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110 | (1) |
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Kinematic model associated with the task coordinate representation |
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111 | (4) |
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112 | (1) |
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113 | (1) |
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114 | (1) |
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114 | (1) |
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115 | (2) |
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Inverse kinematic model of serial robots |
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117 | (28) |
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117 | (1) |
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General form of the kinematic model |
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117 | (1) |
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Inverse kinematic model for a regular case |
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118 | (3) |
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119 | (1) |
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119 | (2) |
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Solution in the neighborhood of singularities |
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121 | (5) |
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122 | (1) |
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Use of the damped pseudoinverse |
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123 | (2) |
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Other approaches for controlling motion near singularities |
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125 | (1) |
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Inverse kinematic model of redundant robots |
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126 | (7) |
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126 | (2) |
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128 | (1) |
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128 | (1) |
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Jacobian pseudoinverse with an optimization term |
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129 | (1) |
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129 | (1) |
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Increasing the manipulability |
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130 | (1) |
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131 | (2) |
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Numerical calculation of the inverse geometric problem |
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133 | (1) |
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Minimum description of tasks |
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134 | (10) |
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Principle of the description |
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135 | (2) |
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Differential models associated with the minimum description of tasks |
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137 | (1) |
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Point contact (point on plane) |
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138 | (1) |
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Line contact (line on plane) |
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139 | (1) |
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Planar contact (plane on plane) |
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140 | (1) |
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Cylindrical groove joint (point on line) |
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140 | (1) |
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Cylindrical joint (line on line) |
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141 | (1) |
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Spherical joint (point on point) |
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142 | (1) |
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Revolute joint (line-point on line-point) |
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142 | (1) |
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Prismatic joint (plane-plane on plane-plane) |
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142 | (2) |
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144 | (1) |
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Geometric and kinematic models of complex chain robots |
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145 | (26) |
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145 | (1) |
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Description of tree structured robots |
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145 | (3) |
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Description of robots with closed chains |
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148 | (5) |
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Direct geometric model of tree structured robots |
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153 | (1) |
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Direct geometric model of robots with closed chains |
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154 | (1) |
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Inverse geometric model of closed chain robots |
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155 | (1) |
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Resolution of the geometric constraint equations of a simple loop |
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155 | (7) |
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155 | (1) |
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156 | (4) |
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Particular case of a parallelogram loop |
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160 | (2) |
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Kinematic model of complex chain robots |
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162 | (5) |
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Numerical calculation of qp and qc in terms of qa |
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167 | (1) |
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Number of degrees of freedom of robots with closed chains |
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168 | (1) |
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Classification of singular positions |
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169 | (1) |
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169 | (2) |
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Introduction to geometric and kinematic modeling of parallel robots |
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171 | (20) |
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171 | (1) |
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Parallel robot definition |
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171 | (1) |
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Comparing performance of serial and parallel robots |
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172 | (2) |
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Number of degrees of freedom |
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174 | (1) |
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Parallel robot architectures |
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175 | (6) |
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175 | (1) |
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176 | (1) |
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Three degree-of-freedom spatial robots |
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177 | (1) |
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Six degree-of-freedom spatial robots |
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177 | (2) |
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The Delta robot and its family |
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179 | (2) |
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Modeling the six degree-of-freedom parallel robots |
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181 | (8) |
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181 | (2) |
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183 | (1) |
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184 | (1) |
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185 | (1) |
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185 | (3) |
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188 | (1) |
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189 | (1) |
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190 | (1) |
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Dynamic modeling of serial robots |
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191 | (44) |
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191 | (1) |
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192 | (1) |
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193 | (12) |
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193 | (1) |
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General form of the dynamic equations |
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194 | (1) |
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Computation of the elements of A, C and Q |
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195 | (1) |
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Computation of the kinetic energy |
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195 | (3) |
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Computation of the potential energy |
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198 | (1) |
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198 | (1) |
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199 | (2) |
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Considering the rotor inertia of actuators |
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201 | (1) |
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Considering the forces and moments exerted by the end-effector on the environment |
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201 | (1) |
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Relation between joint torques and actuator torques |
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201 | (1) |
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Modeling of robots with elastic joints |
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202 | (3) |
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Determination of the base inertial parameters |
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205 | (14) |
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Computation of the base parameters using the dynamic model |
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205 | (2) |
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Determination of the base parameters using the energy model |
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207 | (1) |
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Determination of the parameters having no effect on the dynamic model |
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208 | (2) |
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General grouping relations |
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210 | (2) |
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Particular grouped parameters |
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212 | (1) |
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Practical determination of the base parameters |
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213 | (1) |
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Considering the inertia of rotors |
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214 | (5) |
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219 | (3) |
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219 | (1) |
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Newton-Euler inverse dynamics linear in the inertial parameters |
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219 | (2) |
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Practical form of the Newton-Euler algorithm |
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221 | (1) |
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Real time computation of the inverse dynamic model |
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222 | (6) |
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222 | (3) |
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Customization of the Newton-Euler formulation |
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225 | (2) |
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Utilization of the base inertial parameters |
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227 | (1) |
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228 | (5) |
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Using the inverse dynamic model to solve the direct dynamic problem |
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228 | (2) |
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Recursive computation of the direct dynamic model |
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230 | (3) |
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233 | (2) |
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Dynamics of robots with complex structure |
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235 | (22) |
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235 | (1) |
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Dynamic modeling of tree structured robots |
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235 | (7) |
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235 | (1) |
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236 | (1) |
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Direct dynamic model of tree structured robots |
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236 | (1) |
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Determination of the base inertial parameters |
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237 | (1) |
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General grouping equations |
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238 | (2) |
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Particular grouped parameters |
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240 | (2) |
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Dynamic model of robots with closed kinematic chains |
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242 | (14) |
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Description of the system |
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242 | (1) |
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Computation of the inverse dynamic model |
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243 | (2) |
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Computation of the direct dynamic model |
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245 | (3) |
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Base inertial parameters of closed chain robots |
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248 | (1) |
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Base inertial parameters of parallelogram loops |
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249 | (1) |
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Practical computation of the base inertial parameters |
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250 | (6) |
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256 | (1) |
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Geometric calibration of robots |
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257 | (34) |
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257 | (1) |
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258 | (3) |
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258 | (1) |
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Parameters of the base frame |
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259 | (1) |
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260 | (1) |
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Generalized differential model of a robot |
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261 | (2) |
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Principle of geometric calibration |
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263 | (7) |
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General calibration model |
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263 | (2) |
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Identifiability of the geometric parameters |
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265 | (1) |
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Determination of the identifiable parameters |
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266 | (1) |
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Optimum calibration configurations |
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267 | (1) |
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Solution of the identification equation |
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268 | (2) |
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270 | (9) |
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Calibration using the end-effector coordinates |
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270 | (2) |
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Calibration using distance measurement |
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272 | (1) |
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Calibration using location constraint and position constraint |
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273 | (1) |
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Calibration methods using plane constraint |
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274 | (1) |
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Calibration using plane equation |
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274 | (2) |
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Calibration using normal coordinates to the plane |
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276 | (3) |
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Correction and compensation of errors |
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279 | (3) |
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Calibration of parallel robots |
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282 | (3) |
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283 | (2) |
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285 | (1) |
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Measurement techniques for robot calibration |
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285 | (3) |
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286 | (1) |
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286 | (1) |
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287 | (1) |
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287 | (1) |
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288 | (3) |
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Identification of the dynamic parameters |
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291 | (22) |
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291 | (1) |
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Estimation of inertial parameters |
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292 | (1) |
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Principle of the identification procedure |
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292 | (8) |
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Resolution of the identification equations |
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293 | (2) |
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Identifiability of the dynamic parameters |
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295 | (1) |
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Estimation of the friction parameters |
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295 | (1) |
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296 | (1) |
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296 | (2) |
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Sequential identification |
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298 | (1) |
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Calculation of the joint velocities and accelerations |
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298 | (1) |
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Calculation of joint torques |
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299 | (1) |
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Dynamic identification model |
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300 | (1) |
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Other approaches to the dynamic identification model |
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301 | (5) |
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Sequential formulation of the dynamic model |
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301 | (1) |
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Filtered dynamic model (reduced order dynamic model) |
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302 | (4) |
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Energy (or integral) identification model |
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306 | (3) |
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Principle of the energy model |
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306 | (2) |
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308 | (1) |
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Recommendations for experimental application |
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309 | (1) |
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310 | (3) |
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313 | (34) |
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313 | (1) |
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Trajectory generation and control loops |
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314 | (1) |
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Point-to-point trajectory in the joint space |
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315 | (14) |
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316 | (1) |
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316 | (1) |
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316 | (1) |
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317 | (2) |
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Computation of the minimum traveling time |
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319 | (1) |
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Bang-bang acceleration profile |
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320 | (1) |
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321 | (5) |
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Continuous acceleration profile with constant velocity phase |
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326 | (3) |
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Point-to-point trajectory in the task space |
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329 | (2) |
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Trajectory generation with via points |
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331 | (13) |
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Linear interpolations with continuous acceleration blends |
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331 | (1) |
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331 | (4) |
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335 | (2) |
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Trajectory generation with cubic spline functions |
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337 | (1) |
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337 | (3) |
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Calculation of the minimum traveling time on each segment |
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340 | (2) |
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Trajectory generation on a continuous path in the task space |
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342 | (2) |
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344 | (3) |
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347 | (30) |
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347 | (1) |
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347 | (1) |
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348 | (5) |
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PID control in the joint space |
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348 | (2) |
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350 | (2) |
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PID control in the task space |
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352 | (1) |
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Linearizing and decoupling control |
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353 | (7) |
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353 | (1) |
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Computed torque control in the joint space |
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354 | (1) |
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354 | (1) |
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355 | (1) |
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356 | (1) |
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Predictive dynamic control |
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357 | (1) |
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Practical computation of the computed torque control laws |
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357 | (1) |
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Computed torque control in the task space |
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358 | (2) |
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360 | (8) |
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360 | (1) |
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Hamiltonian formulation of the robot dynamics |
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360 | (2) |
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Passivity-based position control |
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362 | (1) |
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Passivity-based tracking control |
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363 | (5) |
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368 | (1) |
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368 | (8) |
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368 | (1) |
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Adaptive feedback linearizing control |
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369 | (2) |
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Adaptive passivity-based control |
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371 | (5) |
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376 | (1) |
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377 | (70) |
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377 | (1) |
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Description of a compliant motion |
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378 | (1) |
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Passive stiffness control |
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378 | (1) |
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379 | (2) |
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381 | (4) |
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Hybrid position/force control |
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385 | (8) |
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Parallel hybrid position/force control |
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386 | (5) |
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External hybrid control scheme |
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391 | (2) |
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393 | (2) |
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Solution of the inverse geometric model equations (Table 4.1) |
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395 | (6) |
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395 | (1) |
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396 | (1) |
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397 | (1) |
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397 | (1) |
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398 | (1) |
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398 | (1) |
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399 | (2) |
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401 | (2) |
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403 | (2) |
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Solution of systems of linear equations |
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405 | (12) |
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405 | (1) |
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Resolution based on the generalized inverse |
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406 | (1) |
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406 | (1) |
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Computation of a generalized inverse |
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406 | (1) |
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Resolution based on the pseudoinverse |
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407 | (1) |
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407 | (1) |
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Pseudoinverse computation methods |
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408 | (1) |
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Method requiring explicit computation of the rank |
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408 | (1) |
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408 | (2) |
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Method based on the singular value decomposition of W |
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410 | (3) |
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Resolution based on the QR decomposition |
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413 | (1) |
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413 | (1) |
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414 | (3) |
|
Numerical computation of the base parameters |
|
|
417 | (4) |
|
|
|
417 | (1) |
|
Base inertial parameters of serial and tree structured robots |
|
|
418 | (2) |
|
Base inertial parameters of closed loop robots |
|
|
420 | (1) |
|
Generality of the numerical method |
|
|
420 | (1) |
|
Recursive equations between the energy functions |
|
|
421 | (6) |
|
Recursive equation between the kinetic energy functions of serial robots |
|
|
421 | (2) |
|
Recursive equation between the potential energy functions of serial robots |
|
|
423 | (1) |
|
Recursive equation between the total energy functions of serial robots |
|
|
424 | (1) |
|
Expression of a(j)λj in the case of the tree structured robot |
|
|
424 | (3) |
|
Dynamic model of the Staubli RX-90 robot |
|
|
427 | (4) |
|
Computation of the inertia matrix of tree structured robots |
|
|
431 | (4) |
|
Inertial parameters of a composite link |
|
|
431 | (2) |
|
Computation of the inertia matrix |
|
|
433 | (2) |
|
Stability analysis using Lyapunov theory |
|
|
435 | (4) |
|
|
|
435 | (1) |
|
|
|
435 | (1) |
|
Positive definite and positive semi-definite functions |
|
|
436 | (1) |
|
Lyapunov direct theorem (sufficient conditions) |
|
|
436 | (1) |
|
La Salle theorem and invariant set principle |
|
|
437 | (1) |
|
|
|
437 | (1) |
|
|
|
437 | (1) |
|
|
|
437 | (2) |
|
Computation of the dynamic control law in the task space |
|
|
439 | (4) |
|
Calculation of the location error ex |
|
|
439 | (1) |
|
Calculation of the velocity of the terminal link X |
|
|
440 | (1) |
|
|
|
441 | (1) |
|
|
|
442 | (1) |
|
|
|
442 | (1) |
|
Stability of passive systems |
|
|
443 | (4) |
|
|
|
443 | (1) |
|
Stability analysis of closed-loop positive feedback |
|
|
444 | (1) |
|
Stability properties of passive systems |
|
|
445 | (2) |
| References |
|
447 | (28) |
| Index |
|
475 | |
Lisainfo e-raamatute kohta