by Joseph Chun-kong Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 117-124). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgments --- p.iv / List of Figures --- p.xi / List of Tables --- p.xii / List of Algorithms --- p.xiii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Related Work --- p.5 / Chapter 1.3 --- Contributions --- p.7 / Chapter 1.4 --- Organization of the Thesis --- p.9 / Chapter 2 --- Contact Modeling: Kinematics --- p.11 / Chapter 2.1 --- Introduction --- p.11 / Chapter 2.2 --- Contact Kinematics between Two Rigid Bodies --- p.14 / Chapter 2.2.1 --- Contact Modes --- p.14 / Chapter 2.2.2 --- Montana's Contact Equations --- p.15 / Chapter 2.3 --- Finger Kinematics --- p.18 / Chapter 2.3.1 --- Finger Forward Kinematics --- p.19 / Chapter 2.3.2 --- Finger Jacobian --- p.21 / Chapter 2.4 --- Grasp Kinematics between a Finger and an Object --- p.21 / Chapter 2.4.1 --- Velocity Transformation between Different Coordinate Frames --- p.22 / Chapter 2.4.2 --- Grasp Kinematics for the zth Contact --- p.23 / Chapter 2.4.3 --- Different Fingertip Models and Different Contact Modes --- p.25 / Chapter 2.5 --- Velocity Constraints of the Entire System --- p.28 / Chapter 2.6 --- Summary --- p.29 / Chapter 3 --- Contact Modeling: Dynamics --- p.31 / Chapter 3.1 --- Introduction --- p.31 / Chapter 3.2 --- Multi-fingered Robot Hand Dynamics --- p.33 / Chapter 3.3 --- Object Dynamics --- p.35 / Chapter 3.4 --- Constrained System Dynamics --- p.37 / Chapter 3.5 --- Summary --- p.39 / Chapter 4 --- Collision Modeling --- p.40 / Chapter 4.1 --- Introduction --- p.40 / Chapter 4.2 --- Assumptions of Collision --- p.42 / Chapter 4.3 --- Collision Point Velocities --- p.43 / Chapter 4.3.1 --- Collision Point Velocity of the ith. Finger --- p.43 / Chapter 4.3.2 --- Collision Point Velocity of the Object --- p.46 / Chapter 4.3.3 --- Relative Collision Point Velocity --- p.47 / Chapter 4.4 --- Equations of Collision --- p.47 / Chapter 4.4.1 --- Sliding Mode Collision --- p.48 / Chapter 4.4.2 --- Sticking Mode Collision --- p.49 / Chapter 4.5 --- Summary --- p.51 / Chapter 5 --- Dynamic Simulation --- p.53 / Chapter 5.1 --- Introduction --- p.53 / Chapter 5.2 --- Architecture of the Dynamic Simulation System --- p.54 / Chapter 5.2.1 --- Input Devices --- p.54 / Chapter 5.2.2 --- Dynamic Simulator --- p.58 / Chapter 5.2.3 --- Virtual Environment --- p.60 / Chapter 5.3 --- Methodologies and Program Flow of the Dynamic Simulator --- p.60 / Chapter 5.3.1 --- Interference Detection --- p.61 / Chapter 5.3.2 --- Constraint-based Simulation --- p.63 / Chapter 5.3.3 --- Impulse-based Simulation --- p.66 / Chapter 5.4 --- Summary --- p.69 / Chapter 6 --- Simulation Results --- p.71 / Chapter 6.1 --- Introduction --- p.71 / Chapter 6.2 --- Change of Grasping Configurations --- p.71 / Chapter 6.3 --- Rolling Contact --- p.76 / Chapter 6.4 --- Sliding Contact --- p.76 / Chapter 6.5 --- Collisions --- p.85 / Chapter 6.6 --- Dextrous Manipulation Motions --- p.93 / Chapter 6.7 --- Summary --- p.94 / Chapter 7 --- Conclusions --- p.99 / Chapter 7.1 --- Summary of Contributions --- p.99 / Chapter 7.2 --- Future Work --- p.100 / Chapter 7.2.1 --- Improvement of Current System --- p.100 / Chapter 7.2.2 --- Applications --- p.101 / Chapter A --- Montana's Contact Equations for Finger-object Contact --- p.103 / Chapter A.1 --- Local Coordinates Charts --- p.103 / Chapter A.2 --- "Curvature, Torsion and Metric Tensors" --- p.104 / Chapter A.3 --- Montana's Contact Equations --- p.106 / Chapter B --- Finger Dynamics --- p.108 / Chapter B.1 --- Forward Kinematics of a Robot Finger --- p.108 / Chapter B.1.1 --- Link-coordinate Transformation --- p.109 / Chapter B.1.2 --- Forward Kinematics --- p.109 / Chapter B.2 --- Dynamic Equation of a Robot Finger --- p.110 / Chapter B.2.1 --- Kinetic and Potential Energy --- p.110 / Chapter B.2.2 --- Lagrange's Equation --- p.111 / Chapter C --- Simulation Configurations --- p.113 / Chapter C.1 --- Geometric models --- p.113 / Chapter C.2 --- Physical Parameters --- p.113 / Chapter C.3 --- Simulation Parameters --- p.116 / Bibliography --- p.124

A complete solution to the inverse kinematics problem for a large class of practical manipulators, which includes manipulators with no closed form inverse kinematics equations, is presented in this thesis. A complete solution to the inverse kinematics problem of a manipulator is defined as a method for obtaining the required joint variable values to establish the desired endpoint position, endpoint orientation, and manipulator configuration; the only requirement being that the desired solution exists. For all manipulator geometries that satisfy a set of conditions (THEOREM I), an algorithm is presented that is theoretically guaranteed to always converge to the desired solution (if it exists). The algorithm is extensively tested on two complex 6 degree of freedom manipulators which have no known closed form inverse kinematics equations. It is shown that the algorithm can be used in real time manipulator control. Applications of the method to other 6 DOF manipulator geometries and to redundant manipulators are discussed. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Tang Wai Sum. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 68-70). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Redundant Manipulators --- p.1 / Chapter 1.2 --- Inverse Kinematics of Robotic Manipulators --- p.2 / Chapter 1.3 --- Inverse Dynamics of Robotic Manipulators --- p.4 / Chapter 1.4 --- Redundancy Resolutions of Manipulators --- p.5 / Chapter 1.5 --- Motivation of Using Neural Networks for these Applications --- p.9 / Chapter 1.6 --- Previous Work for Redundant Manipulator Inverse Kinematics and Inverse Dynamics Computation by Neural Networks --- p.9 / Chapter 1.7 --- Advantages of the Proposed Recurrent Neural Networks --- p.11 / Chapter 1.8 --- Contribution of this work --- p.11 / Chapter 1.9 --- Organization of this thesis --- p.12 / Chapter 2 --- Problem Formulations --- p.14 / Chapter 2.1 --- Constrained Optimization Problems for Inverse Kinematics Com- putation of Redundant Manipulators --- p.14 / Chapter 2.1.1 --- Primal and Dual Quadratic Programs for Bounded Joint Velocity Minimization --- p.14 / Chapter 2.1.2 --- Primal and Dual Linear Programs for Infinity-norm Joint Velocity Minimization --- p.15 / Chapter 2.2 --- Constrained Optimization Problems for Inverse Dynamics Com- putation of Redundant Manipulators --- p.17 / Chapter 2.2.1 --- Quadratic Program for Unbounded Joint Torque Mini- mization --- p.17 / Chapter 2.2.2 --- Primal and Dual Quadratic Programs for Bounded Joint Torque Minimization --- p.18 / Chapter 2.2.3 --- Primal and Dual Linear Programs for Infinity-norm Joint Torque Minimization --- p.19 / Chapter 3 --- Proposed Recurrent Neural Networks --- p.20 / Chapter 3.1 --- The Lagrangian Network --- p.21 / Chapter 3.1.1 --- Optimality Conditions for Unbounded Joint Torque Min- imization --- p.21 / Chapter 3.1.2 --- Dynamical Equations and Architecture --- p.22 / Chapter 3.2 --- The Primal-Dual Network 1 --- p.24 / Chapter 3.2.1 --- Optimality Conditions for Bounded Joint Velocity Min- imization --- p.24 / Chapter 3.2.2 --- Dynamical Equations and Architecture for Bounded Joint Velocity Minimization --- p.26 / Chapter 3.2.3 --- Optimality Conditions for Bounded Joint Torque Mini- mization --- p.27 / Chapter 3.2.4 --- Dynamical Equations and Architecture for Bounded Joint Torque Minimization --- p.28 / Chapter 3.3 --- The Primal-Dual Network 2 --- p.29 / Chapter 3.3.1 --- Energy Function for Infinity-norm Joint Velocity Mini- mization Problem --- p.29 / Chapter 3.3.2 --- Dynamical Equations for Infinity-norm Joint Velocity Minimization --- p.30 / Chapter 3.3.3 --- Energy Functions for Infinity-norm Joint Torque Mini- mization Problem --- p.32 / Chapter 3.3.4 --- Dynamical Equations for Infinity-norm Joint Torque Min- imization --- p.32 / Chapter 3.4 --- Selection of the Positive Scaling Constant --- p.33 / Chapter 4 --- Stability Analysis of Neural Networks --- p.36 / Chapter 4.1 --- The Lagrangian Network --- p.36 / Chapter 4.2 --- The Primal-Dual Network 1 --- p.38 / Chapter 4.3 --- The Primal-Dual Network 2 --- p.41 / Chapter 5 --- Simulation Results and Network Complexity --- p.45 / Chapter 5.1 --- Simulation Results of Inverse Kinematics Computation in Re- dundant Manipulators --- p.45 / Chapter 5.1.1 --- Bounded Least Squares Joint Velocities Computation Using the Primal-Dual Network 1 --- p.46 / Chapter 5.1.2 --- Minimum Infinity-norm Joint Velocities Computation Us- ing the Primal-Dual Network 2 --- p.49 / Chapter 5.2 --- Simulation Results of Inverse Dynamics Computation in Redun- dant Manipulators --- p.51 / Chapter 5.2.1 --- Minimum Unbounded Joint Torques Computation Using the Lagrangian Network --- p.54 / Chapter 5.2.2 --- Minimum Bounded Joint Torques Computation Using the Primal-Dual Network 1 --- p.57 / Chapter 5.2.3 --- Minimum Infinity-norm Joint Torques Computation Us- ing the Primal-Dual Network 2 --- p.59 / Chapter 5.3 --- Network Complexity Analysis --- p.60 / Chapter 6 --- Concluding Remarks and Future Work --- p.64 / Publications Resulted from the Study --- p.66 / Bibliography --- p.68