Kalman filtering, smoothing, and recursive robot arm forward and inverse dynamics

Abstract

The inverse and forward dynamics problems for multilink serial manipulators are solved by using recursive techniques from linear filtering and smoothing theory. The pivotal step is to cast the system dynamics and kinematics as a two-point boundary-value problem. Solution of this problem leads to filtering and smoothing techniques similar to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The solutions prescribe an inward filtering recursion to compute a sequence of constraint moments and forces followed by an outward recursion to determine a corresponding sequence of angular and linear accelerations. An inward recursion refers to a sequential technique that starts at the tip of the terminal link and proceeds inwardly through all of the links until it reaches the base. Similarly, an outward recursion starts at the base and propagates out toward the tip. The recursive solutions are O(N), in the sense that the number of required computations only grows linearly with the number of links. A technique is provided to compute the relative angular accelerations at all of the joints from the applied external joint moments (and vice versa). It also provides an approach to evaluate recursively the composite multilink system inertia matrix and its inverse. The main contribution is to establish the equivalence between the filtering and smoothing techniques arising in state estimation theory and the methods of recursive robot dynamics. The filtering and smoothing architecture is very easy to understand and implement. This provides for a better understanding of robot dynamics. While the focus is not on exploring computational efficiency, some initial results in that direction are obtained. This is done by comparing performance with other recursive methods for a planar chain example. The analytical foundation is laid for the potential use of filtering and smoothing techniques in robot dynamics and control.