Control and Control Theory for Flexible Robots

Abstract

As the requirements for robot performance increase, the dynamics of the manipulator become more dominated by flexibility. These flexible effects generate model uncertainty which reduces the end-point positioning accuracy of the manipulator. Residual vibration or tip deflection due to uncertain payloads may contribute to the error in tip position. This paper addresses several control strategies currently used by researchers to account for flexibility in robots and their ability to perform tasks despite the flexibility. The demands for increased robot accuracy coupled with high speed and large workspace requirements necessitate the evaluation of robot flexibility. The influence of flexibilityon modelling and controller design must be better understood to achieve these requirements. This paper presents a review of current research in the control .of flexible robots and reports on algorithms with specific experimental and theoretical results. Other researchers have conducted such surveys regarding modelling, design and control of flexible robot arms. Desoyer, Kopacek, Lugner and Troch (24) compare various modelling methods for I ightweight robots and discuss the effects of flexibi lity on possible control strategies. They examine the kinetostatic method, the vibrational mode approach and the finite element method as a means of modelling flexible systems. Troch and Kopacek (60) discuss control strategies for flexible robots, designs based on model simplification and the effects of actuator dynamics. Peng and Liou (43) survey experimental studies involving flexible mechanisms from a designer's point of view. They examine the identification of damping and mode shapes, vibration reduction and various means of measuring flexible mechanism responses. Book (11) describes the modelling of flexibility, the large motion equations used and the design of flexible arms. He also presents trajectory planning and trajectory tracking strategies for the control of flexible robot arms. . This paper begins with a short discussion of modelling the behavior of a flexible beam. The mathematical expression forthe beam deflection is given as a function of mode shapes and generalized coordinates. The difficulty in choosing appropriate mode shapes and representing the correct boundary conditions is then presented. Once an expression for t~e beam deflection is established, it can be incorporated into a recursive Lagrangian approach for modelling the dynamics of a serial chain of flexible links. The dependence of several control algorithms on model information is then investigated. The control methods surveyed involve end-point tracking, trajectory planning, modal damping and vibration suppression. Several model identification algorithms are also presented to demonstrate adaptive control for flexible systems with_variable payload.