Optimal Trajectory Generation for Robotic Manipulators Using Dynamic Programming

Abstract

The problem of optimal control of robotic manipulators is dealt with in two stages: (1) optimal trajectory planning, which is performed off-line and results in the prescription of the position and velocity of each link as a function of time along a “given” path and (2) on-line trajectory tracking, during which the manipulator is guided along the planned trajectory using a feedback control algorithm. 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. It is shown that for a given path, this problem is reduced to a search over the velocity of one moving manipulator link. The design of the algorithm for optimal trajectory planning and the relevant computational issues are discussed. Simulations are performed to test the effectiveness of this method. The use of this algorithm in conjunction with an on-line controller is also presented.