The thesis investigates extensively several key problems in the kinematic control of redundant robotic manipulators. The main results of this thesis are as follows: First, a three-degree-of-freedom planar arm, as a specific case of kinematically redundant manipulators, is studied thoroughly. Workspace is analyzed for general planar arms, then an omission, in a frequently quoted paper, on the working range of a planar manipulator is identified and improved. Primary applications of the gradient projection method are exemplified, among which are joint limit avoidance, collision avoidance, joint kinetic energy minimization, and singularity escaping. Effects of singular joint configurations on Cartesian task execution are examined and ways to avoid them are discussed. An improvement of the gradient projection scheme and relevant algorithm are proposed, such that a secondary performance index is optimized dynamically according to the manipulator's distance away from singularity, and joint velocities are expected to change more smoothly. Repeatability of kinematic control of redundant robots is illustrated with an example. Second, based on studies on kinematic singularity, the contradiction between singularity escaping and performance optimization is resolved. The damped pseudoinverse solution is deduced in the sense of damped least squares, then a new damped pseudoinverse controller is presented. By implementation of this controller damping can be applied automatically according to actual joint situations, thus high joint speed near singularity is restrained and tracking error of end-effect or path is minimized for regular joint configurations. The extended damped pseudoinverse control scheme is an integrated solution, whose theoretical advantage is automatic switching between dynamic damping and dynamic optimization of secondary performance criterion. A computationaUy efficient parallel algorithm strengthens the scheme in that it is expected to be implemented in real-time robotic systems. Simulations show the advantages of the scheme to conventional relative ones. Seeing the shortcomings of unrepeatable pseudoinverse control methods for manipulators with redundant joints, and the characteristics of several available repeatable ones, a general framework for repeatable control of redundant mechanisms is provided and redundancy is resolved in the framework. By taking algorithmic singularity into consideration, the scheme is improved in such a way that tracking error for primary task is minimized and repeatability is guaranteed if no singularity is encountered. Via our choice of dynamic damping, joint speed is expected to change smoothly and tracking error of secondary goals is also hoped for to be minimized. The whole scheme can be applied readily to the case of non-redundant manipulators, to ensure the execution of the most important tasks to the maximum extent. Further discussions on algorithm enhancement an
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