Recursive Model Reference Adaptive Control of Open and Closed Kinematic Chains

An algorithm for the adaptive control of a manipulator arm consisting of either open or closed kinematic chains is presented. The algorithm for closed chains differs from procedures presented by other investigators in three ways. First, the recursive algorithm exactly produces the control law. Secondly, pains have been taken to make the procedures resemble the original Newton-Euler algorithm. Finally, for the case of closed kinematic chains the method of determining the closure reactions is unique compared to other recursive algorithms developed for such manipulators. Regardless of the number of closed mechanical loops, even zero, the inverse dynamic calculation requires a single forward pass and a single backward pass.