Optimal B-spline joint trajectory generation for collision-free movements of a manipulator under dynamic constraints

A method is proposed which describes the joint trajectories of a manipulator with B-spline curves, and which optimizes the values of these control points using the complex method under collision-free, full dynamic and kinematic constraints. This method utilizes the B-spline curve's uniqueness, continuity, and local controllability to the control points, and incorporates the complex method which does not require evaluation of the gradient in the optimization. This method has the following advantages: (1) It is applicable to manipulators with arbitrary degrees of freedom; (2) It achieves the generation of the trajectory which takes the priority of specified constraints into consideration; (3) Weighting factors of the performance indices corresponding to the constraints are automatically computed. The method has been applied to the collision-free trajectory generation problems of a manipulator with three degrees of freedom and the results show its effectiveness