Nonlinear Adaptive Control of Mechanical Linkage Systems with Application to Robotics

This paper considers the problem of adaptively controlling the nonlinear dynamics associated with connected mechanical links such as those which form robotic manipulators. By first considering a single link, linear and nonlinear adaptive control methodologies are compared. It is shown by simulation that for certain geometries and loading the proposed nonlinear adaptive scheme can produce considerable improvement in performance over the linear scheme proposed in earlier investigations. The case of a two degree of freedom, two link, planar arm is then considered in detail. A discrete time model matching adaptive controller is then derived using a specific descretization of the continuous time nonlinear dynamics. Conditions which guarantee global stability of the control scheme are derived for the case of controlling the descretized model, and simulations are presented for the case of controlling the actual continuous time dynamics.