Energy optimal control of serial manipulators avoiding collisions

A non-linear programming approach to energy optimal control of serial manipulators is introduced that prevents collision of manipulator and spatial obstacles. Attention is given to the description of spatial obstacles and the definition of a distance measure thereupon. The generalized coordinates of the manipulator model are approximated by suitable ansatz functions. Thus the optimal control problem, a boundary value problem, is transformed to a constrained algebraic non-linear programming problem in terms of the ansatz function parameters. The constraints arise from the collision detection. The approach is applicable to redundant and non-redundant manipulators and can be extended to parallel manipulators.