A Survey on Control of Parallel Manipulator

Based on extensive study on literatures of control of parallel manipulators and serial manipulators, control strategies such as computed torque control, PD+ control, PD with feedforward compensation, nonlinear adaptive control are classified into two categories: model-based control and performance-based control. Besides, as advanced control strategies, robust control and passivity-based control for the parallel manipulators are also introduced. Comparative study in view of computation burden and tracking performance are performed. It turned out that the physical structure properties of parallel manipulators’ dynamics are similar with that of serial ones, and this constitutes a common foundation for the two kinds of manipulators to develop together that control design of parallel manipulators can start with ever established control methods of serial manipulators. Introduction Traditionally, the most widely-used robots have been serial manipulators which have a sequence of links connected in a series through revolute or/and prismatic joints. This type of manipulators usually has larger workspace and greater dexterity than parallel manipulators. Parallel manipulators differ from serial manipulators by virtue of their kinematical structure. They are composed of multiple closed kinematical loops. Typically, these kinematical loops are formed by two or more kinematical chains that connect a moving platform to a base, where one joint in the chain is active and the others are passive. A typical parallel manipulator called Stewart platform, is shown in Fig.1. Fig.1 A Stewart Platform Originally it was designed by Stewart (1965) as a flight simulator. In 1978, Hunt suggested using Stewart platform as robot manipulators and mentioned that such parallel manipulators deserved detailed study in the context of robotic applications in view of their higher rigidity, higher positioning precision and higher load capacity over serial manipulators [1]. In the past decades, parallel manipulators have received much attention from many researchers. The study of parallel manipulators covers diverse areas such as kinematics, singularity, calibration, dynamics and control. And parallel manipulators have their way to various application areas such as motion simulator, precise machine tools, micro mechanisms, haptic devices, and so on. The literatures on control of serial manipulators are vast. An excellent treatment, covering many of different approaches to robot control, was given by Spong [2]. However, literatures on control of parallel manipulators are relatively few. Ghorbel [3, 4] derived the motion equations of constrained Key Engineering Materials Vol. 339 (2007) pp 307-313 online at http://www.scientific.net © (2007) Trans Tech Publications, Switzerland Online available since 2007/May/15 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.34-16/04/08,14:27:55) rigid bodies including closed-chain mechanisms. Ghorbel suggested that the control law methodologies available for serial manipulators were applicable to closed-chain mechanisms. In this paper, in order to lay out a common foundation on which serial and parallel manipulators can develop together, a survey on control of parallel manipulators will be presented. Although this paper focuses mainly on the control of parallel manipulators, the control of serial manipulators is also involved in adequate places. Physical Structure Property of Parallel Manipulator The key process in the stability validation for a robot manipulator control strategy is to construct appropriate Lyapunov function. It is commonly not easy for a certain nonlinear systems. But if making use of the physical structure property of parallel manipulator, it is usually not so difficult to find out the Lyapunov function. And if appropriate output signals are defined, this function may become the storage function which will guarantee the system dissipative [5]. Reduced model of constrained rigid body, like parallel manipulator, was derived by [3]: : Σ τ = + + ) ( ) , ( ) ( q G q q q C q q M (1) Where τ ——applied generalized force vector —— generalized coordinates q —— inertia matrix ) (q M —— centrifugal and coriolis term ) , ( q q C —— gravity vector ) (q G Though the concrete structures and parameters of the Lagrangian equation may differ, the following four properties may hold [5~8]: (1) M is symmetric and positive definite for n R q∈ ∀ M λ (2) There exist positive constant and such that m λ I q M I M m λ λ ≤ ≤ < ) ( 0 , (2) n R q∈ ∀ (3) is skew symmetric. For any ) , ( 2 ) ( q q C q M − x , 0 )) , ( 2 ) ( ( = − x q q C q M x (3) (4) The coefficient matrices M , andG depend linearly on unknown parameters such as payload, frictional coefficient, etc. Then, if let C θ represent unknown parameters vector, and by adequately selecting the matrix , the following equation holds ) , , ( q q q Φ θ ) , , ( ) ( ) , ( ) ( q q q q G q q q C q q M Φ = + + (4) From properties listed above, the structure of the motion equations of closed-chain manipulators is similar to that of serial ones. This similarity motivates the application of existing controllers designed for serial manipulators to closed-chain manipulators, e.g. PD control, augmented PD control, computed torque control and adaptive control. Model-based Control Computed Torque Control (CTC). The concept of computed torque control was proposed in 1972 by Paul [9] with the term ‘computed torque’. Computed torque control is a special application of feedback linearization, which controls a nonlinear system along a desired trajectory. 308 Progress of Precision Engineering and Nano Technology