LOCAL OPTIMALITY, STABILITY AND REPEATABILITY IN REDUNDANCY RESOLUTION FOR ROBOTIC MANIPULATORS

Abstract

Local optimal redundant manipulation is resolved as a Lagrangian problem of optimal control. Although the problem is highly nonlinear, the analytical results provided in this treatment are in surprisingly simple and elegant form which gives new insight into the inherent relations between local and global optimality in redundancy resolution of robotic manipulators. The symbolic results of the weighted projection operator of Jacobian matrix are derived and greatly facilitate the numerical as well as the analytical treatments encountered in the local optimal redundant manipulations. The effects of the weight matrix on both local and global redundancy resolution are analyzed in terms of the Singular Value Decomposition of the Jacobian matrix. In particular, it is shown that the three variables for algorithmic singularities, which are: v;., the null space vectors of the Jacobian matrix; z, an arbitrary vector determined by optimization criteria and W, a weight matrix for redundancy resolution, play very important roles in avoiding numerical instability. They provide a theoretical basis for avoiding instability in redundant manipulation. Sufficient conditions on the weight matrix W are developed in this thesis that will ensure stability in redundant manipulators. Finally, an optimal closed-form solution for the kinematically redundant manipulators that is repeatable is presented .