12 Manipulability-Maximizing SMP Scheme

Studies on and applications of a redundant robot manipulator are the topical research issues in the robotic community. In particular, the inverse-kinematics problem, which finds the joint motion for a given manipulator’s end-effector task is one of the important and challenging issues in operating the redundant manipulators. Note that there are an infinite number of joint configurations of a manipulator with respect to a specific task, due to the redundancy; and redundancy resolution is to make a suitable selection from the configurations. This kind of selection is usually used to accomplish some secondary tasks for robot manipulators or generate an optimal solution to achieve some performance criteria, besides finishing the main end-effector path-tracking task. The redundancy-resolution problem can be readily solved by optimization techniques, especially QP. Note that the quadratic program (QP) can be converted to a linear variational inequality (LVI), and the resultant LVI is equivalent to a piecewise-linear equation (PLE) that can be solved by many algorithms and techniques efficiently, such as numerical algorithm E47 and numerical algorithm 94LVI presented in previous chapters as well as recurrent neural networks.