A decentralised variable structure model following controller for robot manipulators

A new algorithm for the trajectory control of robot manipulators by decentralised feedback is proposed, by dealing with the manipulator and joint actuator dynamic models in a model following framework. A variable structure control law is used with or without force measurement. The controller is simple, computationally easy, and robust to parametric uncertainties and payload variations. INTRODUCTION A well-known approach for the control of interconnected systems is to consider the interactions as disturbances, and to reject them by disturbance rejection methodsl. In this paper we develop a new control algorithm for stabilisation of interconnected systems by decentralised feedback, based on the above approach, and apply it to the trajectory control of robot manipulators. We treat the stable (or locally stabilised) isolated subsystem as a 'model' for the interconnected subsystem, so that the stabilisation of the latter becomes a problem of model following. Incorporation of the model following behaviour requires an adaptive control mechanism, and we make use of the variable structure control (VSC) approach for tis purpose. Controller design is proposer! for cases with and without force/torque measurement. The proposed controller is simple, computationally easy, and robust to parametric changes and external disturbances. It compares favourably with some of the recently proposed control methods based on model following and/or variable structure control approaches. CONTROL OF ROBOT MANIPULATORS The complexity of the robot control problem arises due to the nonlinear dependence of system parameters on variables such as displacement and velocity, on the geometry and inertia of the links, uncertainties associated with gravity, Coriolis and centrifugal forces, variations in payload handled by the manipulator, and environmental influences. Non-adaptive control techniques such as optimal control and computed torque methods have serious drawbacks, namely complex controller structure, excessive on-line computation, and sensitivity to non-linearities and uncertainties in the system . These difficulties are compounded further by their being centralised approaches. Adaptive control methods tackle the robot control problem quite effectively^, but this comes about at the cost of complexity of the controller. In much of the works on adaptive control of manipulators, the justification for this added complexity is not addressed. Formulating the variable structure control problem in a decentralised model following framework will help overcome many of the difficulties encountered in controlling manipulators by the above methods. The VSC approach4-6 js non-adaptive, but exhibits the model following capabilities of model reference adaptive techniques, with its gains being discontinuous across a specified switching plane. Once the system is in the sliding mode, it is insensitive to parametric variations and disturbances. THE PROPOSED CONTROLLER The above decentralised control problem is simplified, if we deal with the dynamic models of the joint actuators along with that of the manipulator^. Let the dynamics of the actuator associated with i-th link in an N-link manipulator be given by the linear,timeinvariant system : x. = A. x. + b. u. + d. f. (1) 1 1 1 1 1 1 1 where x. is an n.-vector, and u. is a scalar control. Neglecting the actuator friction torque, f. is the driving torque acting on the actuator and is given by the nonlinear, uncertain dynamics of the manipulator: f. = H.(q,d) q + h.(q,q,d) (2) where q = (q , q , ..., q )' is the N-vector of joint angles or displacements and d is an Jt-vector of parameters such as link masses and inertias. H. is the N-vector of inertia and h. represents Coriolis, centrifugal and gravity forces. In each x., two coordinates coincide with q. and q.. In trajectory tracking applications, the control task is to make the system track the desired or nominal trajectories (q (t), q 2(t),..., q N(t)) over te [0,T]. The nominal