Motion planning of redundant robot manipulators using constrained optimization: a parallel approach

A redundant manipulator can achieve a principal task and additional tasks by utilizing the degrees of redundancy. In the present paper, the redundancy resolution problem is formulated as a local equality constrained optimization problem. A motion planning solution corresponding to a design objective is then obtained using a new approach, called the perturbation method. In contrast to conventional approaches, the inverse of the Jacobian matrix is not required in the method proposed. Tracking errors can be bounded by a permissible zone, which is a function of normal tracking error and a safety factor. Positioning of the end effector within the permissible zone is satisfactory for the completion of any given step and signals the beginning of the next step. The position angle change of each joint is also bounded in each sampling interval as a function of robot maximum speed. Computer simulations written in the parallel processing language occam and computed on a transputer-based computation network are used to study the behaviour of the method proposed. Results validate the approach.