Optimal rate allocation in kinematically-redundant manipulators-the dual projection method

A coordination algorithm for optimal solution of the rate allocation problem in kinematically redundant manipulators is presented. This solution follows from exploring the projection properties of orthogonal surfaces characterized by the velocity kinematics of the redundant system. It is shown that, using the dual projection theorems between the row and the null spaces to be derived, a commonly used, general solution can be reformulated into a computationally efficient form. This method, known as the dual projection method, offers an equivalent but more efficient alternative to the conventional pseudo-inverse based, gradient projection technique, and is applicable to any linear systems with redundancy. To demonstrate its effectiveness, an analytic example using a spatial manipulator with one degree of redundancy is presented. Discussions of computational efficiency based on numbers of arithmetic operations are included