A dynamic prediction error based adaptive multiple-model control scheme for robotic manipulators

This paper first proposes a new dynamic prediction error based adaptive controller for robotic manipulators with uncertain parameters. Unlike most prediction errors used in the robotics literature, a dynamic prediction error is generated from an adaptive predictor of a parametrized and dynamic manipulator model. A multiple-model adaptive control scheme is then developed using multiple prediction errors and multiple controllers, incorporated with multiple parameter estimators and a control switching mechanism. The use of an adaptive dynamic predictor for parameter estimation leads to a new, effective and simple control structure. Multiple controllers are constructed with different parameter estimators, and a most appropriate control signal is selected by the control switching mechanism which is designed to find the model that best approximates the manipulator dynamics. Closed-loop system stability and output tracking are proved and the detailed analysis is given. Simulation results demonstrate the desired control system performance.

I. Introduction

Since the number of robotic manipulators used in industrial fields is increasing significantly these years, the control problem of manipulators has spurred interest of many researchers. When dealing with the trajectory tracking problems in unknown environments, adaptive control lends itself a powerful tool [3]–[8], [10]–[18]. However, the convergence theorems in previous research are based on asymptotic arguments, and very little is said about the transient behavior of the resulting system [3]. This situation motivated us to do research in this field. When large load variations happen, the transient tracking errors can be large and oscillatory, leading to poor transient behavior. Multiple-model control, with strength in improving overall system performance, may be one of the solutions to this situation [1]–[3], [7]–[9]. When rigid robotic manipulators are executing tasks with uncertainty, such as grabbing or carrying different objects with unknown masses, dimension, or gripping points, multiple-model and switching will allow us not only to identify the different environments, but also to control them rapidly, avoiding slowness of the adaptation process and large transient errors [7]. In 1994, Ciliz and Narendra combined multiple-model and switching with robotic manipulators, and showed the positive effect of this method in improving system performance [1], [3]. They utilized an indirect adaptive control scheme, which eliminates the need of acceleration signals by a first-order filter (proposed by Middleton and Goodwin in 1988 [6]), as the baseline controller structure for multiple-model control. Such an adaptive controller, using a static prediction error for adaptive law design, ensures system stability and output tracking, under the assumption that the time-derivative of the inverse of the estimate of the manipulator inertia matrix is well-defined and bounded.