In this research, a numerical approach is proposed to solve the minimum time trajectory planning problem of kinematically redundant manipulators for a given path. The first step is to transform the trajectory planning problem into an optimal control problem. Then a procedure to find the minimum time solution is proposed. The minimum time control of the manipulator can be devided into two case: first case has object function and second case has no object function. To get the minimum time solution, the following topic is discussed. Firstly, phase plane shooting algorithm used in the non-redundant manipulator cant be adapted to the redundant manipulator. Secondly, the algorithm to get the minimum time control for a general case using dynamic programming(DP) is proposed. In order to obtain a general trajectory planning algorithm which could account for various constraints and performance indices, the technique of dynamic programming is adopted and the dimension of the state space is reduced from two times the number of joints to the number of degree of redundancy.
As numerical examples, the trajectory planning method is simulated for a planar three-link robotic manipulator for several paths.
