Adaptive Control of Robot Manipulator Using Fuzzy

Abstract

This paper presents two kinds of adaptive control schemes for robot manipulator which has the parametric uncer- tainties. In order to compensate these uncertainties, we use the FLS (fuzzy logic system) that has the capability to approximate any nonlinear function over the compact input space. In the proposed control schemes, we need not derive the linear formulation of robot dynamic equation and tune the parameters. We also suggest the ro- bust adaptive control laws in all proposed schemes for decreasing the effect of approximation error. To reduce the number of fuzzy rules of the FLS, we consider the properties of robot dynamics and the decomposition of the uncertainty function. The proposed con- trollers are robust not only to the structured uncertainty such as payload parameter, but also to the unstructured one such as fric- tion model and disturbance. The validity of the control scheme is shown by computer simulations of a two-link planar robot manip- ulator. not accomplished. The structure of neural network and the adap- tive laws have to be found by the trial-and-error method. To overcome these difficulties, in this paper we propose the adap- tive control schemes which utilize an FLS as a compensator for any uncertainty. The proposed control algorithm need not derive the regressive matrix and tune the parameters. Many applications of universal approximation theorem (25) that an FLS is capable of uniformly approximating any nonlinear function over compact input space were presented in (25)-(36). In these publications, their authors attempt to resolve some drawbacks of conventional control theory, difficulties of modeling and analysis for the complicated system, and fuzzy control theory, difficulties of mathematical analysis. Wang (28) proposed an adaptive fuzzy control algorithm based on error dynamics and (29)-(34) presented applications of the FLS. References (35) and (36) proposed the fuzzy sliding-mode control scheme and proved the stability of the control system mathematically, where Ham utilized the FLS's as approximators of unknown nonlinear functions and in . But the control scheme is applicable to SISO-nonlinear system. In this paper we extend a MISO (multi-input single-output)-FLS to a MIMO (multi-input multi-output)-FLS and utilize it to compensate the uncertainties of robot manipulator. The function of structured and unstruc- tured uncertainty of a robot is replaced by a MIMO-FLS('s) in each scheme. To reduce the error between the real uncertainty function and the compensator, we design simple and robust adaptive laws based on Lyapunov stability theory. In the proposed control schemes, the fuzzy compensator has to use too many fuzzy rules because uncertainties depend on all state variables. To overcome this problem, therefore, we introduce the control schemes in which the number of fuzzy rules of the fuzzy compensator can be reduced by using the properties of robot dynamics and uncertainties. We also propose the method to reduce the number of total fuzzy rules through the decompo- sition of uncertainty function. By computer simulations, it is verified that the FLS is capable to compensate the uncertainties of robot manipulator. This paper is organized as follows. Section II presents MIMO-FLS. In Section III, several properties of robot dy- namics are introduced. In Section IV, the first adaptive control scheme is proposed, where the FLS is utilized to compensate the uncertainties of the robot manipulator. The robust adaptive law is also designed. The algorithms that reduce the number of fuzzy rules are proposed based on the properties of robot dynamics and uncertainties in Section V. The decomposition algorithm of uncertainty function and results of computer simulations for the first control scheme are also drawn. In