A New Solution of Two-Point Boundary Value Variational Problem with B-Spline and Its Application to Trajectory Planning of a Manipulator

Abstract

In this paper, a solution for the two-point boundary value variational problem, whose basic algorithm was published earlier by us, is formalized completely and universally. The optimum solution of the variational problem is obtained as a uniform B-spline curve by parallel and iterative computation. The degree of the B-spline used can be selected to correspond to the specified problem, and the solution is derived as a set of the control points of the B-spline. The algorithm is very simple and easily applicable to various engineering problems. As an application, trajectory planning of a manipulator with redundant degrees of freedom and a specified end effector path is selected, and the objective function which takes account of both the smoothness of the trajectories and the accuracy of the end effector path is constructed using the relative weighting coefficients. The effectiveness of the algorithm is well confirmed by the numerical examples.