Trajectory Planning of Manipulator Using Optimization of Uniform B-Spline

A basic optimization algorithm is presented in this paper, in order to obtain the optimum solution of a two-point boundary value variational problem without constraints. The solution is given by a parallel and iterative computation and described as a set of control points of a uniform B-spline. This algorithm can also be applied to solving problems with some constraints, if we introduce an additional component, namely the potential function, corresponding to constraints in the original objective function. 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 is considered under the conditions that the end effector path, the smoothness of movement, and the constraints of the control or the state variables are specified. The validity of the algorithm is well confirmed by numerical examples.