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AESTRACT In this paper we investigate the the motion control of robotic manipulators using the recently developed stable factorization approach to tracking and disturbance rejection. Given a nominal model of the manipulator dynamics, the control scheme consists of an approximate feedback linearizing control followed by a linear compensator design based on the stable factorization approach to achieve optimal tracking and disturbance rejection.Using a multiloop version of the small gain theorem [ 171, the applicability of the linear design techniques and the stability of the closed loop system are rigorously demonstrated. I. INTRODUCTIOKPractical implementation of nonlinear control for robot manipulators requires consideration of the issues of robustness to parameter uncertainty, external disturbances, sensor noise and computational complexity. I t is well known that the state space equations of motion of an n -link rigid robot can be globally linearized and decoupled by appropriate nonlinear feedback. Called inverse dynamics or compued torque[lI, the method is very attractive from a control viewpoint since the complex highly coupled nonlinear dynamics of the manipulator are replaced by a simple set of second order linear differential equations[3]. It is not surprising that the complexity of the feedback law that performs the external linearization is of the order of the complexity of the manipulator dynamics themselves and requires an accurate model and high sampling rate for successful implementation. It is highly advantageous therefore to consider nonlinear feedback based upon simplified models and to quantify the performance of such controllers.Recently several algorithms have been proposed which explicitly account for model uncertainty and simplification [4,9,10,11,15]. In each case the overall control scheme is nonlinear and consists of an approximate "computed torque" based upon a simplified or available model together with additional state feedback compensation to guarantee robustness to parameter uncertainty and external disturbances. Slotine and Sastry [9] choose the additional state feedback based on sliding mode theory. Samson [15] uses high gain nonlinear state feedback to achieve boundedness of the tracking error. Spong, Thorp, and Kleinwaks[ 1 11 design a saturating nonlinear state feedback controller via the second method of Liapunov and, in addition, treat sensor noise and actuator saturation. In this paper, we consider dynamic linear com-Waterloo, Ontario, Canada, N2L 3G1pensation to achieve optimal tracking and disturbance rejection for the motion control of robot manipulators. Our scheme allows the use of simplified and/or uncertain models, and is thus practical for on-line implementation. The overall control is nonlinear and consists of a "nominal inverse dynamics" followed by a linear compensation scheme based on the recently developed method of stable factorizations. The main advantages of the overall control scheme can be summarized as follows:1) The closed loop performance of the system i...

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Abstruct-In tbis paper, weformulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude, but is otherwise arbitrary. The objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance. Mathematically, this corresponds to requiring uniformly good disturbance rejection over all time. Since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used (see [7, sect. 5.6]), the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose L2-norm is small, as is the case with the currently popular H E theory. The present theory is a natural counterpart to the existing theory of optimal disturbance rejection (the so-called HE theory) which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square-integrable and has unit energy. It is shown that the problem studied here has quite different features from its predecessor. Complete solutions to the problem are given in several important cases, including those where the plant is minimum phase or when it has only a single unstable zero. In other cases, procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers.