Optimal kinematic control of constrained and redundant manipulators

The inverse kinematics of over-constrained and redundant robot manipulators is considered. In each case, an optimization problem is formulated to obtain the optimal inverse kinematic solution for the manipulator. The necessary and sufficient conditions for the existence and uniqueness of the solutions are also derived. A series of recursive control algorithms, which utilize joint position feedback, is then proposed to generate the optimal joint velocity commands. The stability of the control algorithms and the convergence of the resulting joint space trajectories to the optimal trajectories are rigorously analyzed. A simulation example of a redundant planar robot is presented to illustrate the theoretical results