Adaptive Control of Mechanical Manipulators

What is believed to be the first golbally convergent, rigorous proof of the stability of such a scheme in its non-linear setting, as well as its asymptotic properties and conditions for parameter convergence are presented.

Abstract

When an accurate dynamic model of a mechanical manipu lator is available, it may be used in a nonlinear, model-based scheme to control the manipulator. Such a control formula tion yields a controller that suppresses disturbances and tracks desired trajectories uniformly in all configurations of the manipulator. Use of a poor dynamic model with this kind of model-based decoupling and linearizing scheme, however, may result in performance that is inferior to a much simpler, fixed-gain scheme. In this paper, we develop a parameter-adaptive control scheme in a set of adaptive laws that can be added to the nonlinear, model-based controller. The scheme is unique be cause it is designed specifically for the nonlinear, model- based controller and has been proven stable in a full, nonlin ear setting. After adaptation, the error dynamics of the joints are decoupled with uniform disturbance rejection in all ma nipulator configurations. The issues of sufficient excitation and the effect of disturbances are also discussed. The theory is demonstrated with simulation results and also with data from an implementation for an industrial robot, the Adept One.