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