Optimum path planning of robot arms

The optimum control of an industrial robot can be achieved by splitting the problem into two tasks: off-line programming of an optimum path, followed by an on-line path tracking. The aim of this paper is to address the numerical solution of the optimum path planning problem. Because of its mixed nature, it can be expressed either in terms of Cartesian coordinates or at joint level. Whatever the approach adopted, the optimum path planning problem can be formulated as the problem of minimizing the overall time (taken as objective function) subject to behavior and side constraints arising from physical limitations and deviation error bounds. The paper proposes a very general optimization algorithm to solve this problem, which is based on the concept of mixed approximation. A numerical application is presented which demonstrates the computational efficiency of the proposed algorithm.