An Algorithm of Near-Optimum Trajectory Planning for Manipulators

Although many algorithms of optimum trajectory planning for manipulators have been proposed, the efficient ones which treat the general cost problem have not necessarily been obtained yet. This paper treats this general trajectory planning problem which includes the optimization of a spatial path. The proposed method is divided into two stages. One is the optimization of time trajectory with a given spatial path. For this part some efficient algorithms have already been proposed. Therefore, we use one of these algorithms in our method. The other is the optimization of the spatial path itself. To consider this problem, we represent the manipulator dynamics using a path parameter ‘s’, and we solve this differential equation as a two-point boundary value problem. In this procedure, the gradient method is used to calculate the improved input torques. The advantages of the proposed method are the following. (1) It is easy to satisfy the given boundary condition because the dynamics is represented by the path parameter ‘s’ which is not directly related to time. (2) The algorithm takes the form of a feasible method, thus we may stop the calculation when we get the desired accuracy of a solution. Finally the proposed method is applied to a manipulator with two links. Numerical results of the example show the effectiveness of this method.