A study of rate coordination algorithm in serial chain redundant manipulators

Presents a general algorithm which results in an efficient solution for the rate coordination problem in redundant manipulators. An alternative formulation of minimum norm solution is first introduced based on a geometric interpretation that vectors orthogonal to constraint space should pass through the origin of the solution space. It is shown that for any spacial manipulator with 1 or 2 degrees of redundancy, the minimum norm rate solution can be derived analytically. The properties of orthogonal vectors are then utilized in formulating the general solution to incorporate any performance criterion. The method offers an equivalent but much more efficient alternative to using the pseudoinverse in redundancy resolution and, in fact, is applicable to any underdetermined linear system. Analytical as well as numerical examples are presented to demonstrate the effectiveness of the method.<>