Roberto Horowitz Graduate Student. 1 Masayoshi Tomizuka Associate Professor. Mem.ASME Department of Mechanical Engineering, University of California, Berkeley, CA 94720 An Adaptive Control Scheme for Mechanical Manipulators- Compensation of Nonlinearity and Decoupling Control This paper presents a new adaptive control scheme for mechanical manipulators. Making use of the fundamental properties of the manipulator equations, an adap- tive algorithm is developed for compensating a nonlinear term in the dynamic equa- tions and for decoupling the dynamic interaction among the joints. A computer simulation study is conducted to evaluate the performance of a manipulator control system composed of the manipulator, adaptive nonlinear compensator/decoupling controller and state feedback controller with integral action. Simulation results show that the manipulator control system with adaptive controller is insensitive to variations of manipulator configurations and payload. I Introduction A mechanical manipulator can be defined as a multidegree of freedom open loop chain of mechanical linkages and joints. These mechanisms driven by actuators are capable of moving an object in space from initial to final locations or along prescribed trajectories. The dynamic equations of a mechanical manipulator are highly nonlinear and complex. The inertia characteristics of the manipulator depend on the payload also. To overcome these difficulties, a number of techniques for dynamic control of mechanical manipulators have been proposed. In the com- puted torque drive method [1, 2, 3], the torques required to move the manipulator along a prescribed trajectory are numerically computed using the dynamic equations. A disad- vantage of this method is that a considerable amount of com- putational effort is required to solve the equations, making its use difficult in real time control. The resulting control, if used without closed loop feedback, is subject to problems inherent in open loop control. To increase the computational speed, table look-up control methods have been proposed where data pertaining to manipulator characteristics are stored and are retrieved as needed [4]. Combinations of the torque drive methods and the table look-up methods are also possible [5]. The dynamic equations are often linearized about nominal tra- jectories, and linear feedback and/or optimal control laws are obtained analytically [6, 7]. The use of nonlinear feedback compensation has been proposed for making the equations of motion linear in simple locomotion systems [8]. The nonlinear compensation is either computed in real time or retrieved from memory storage. In general, a detailed description of the model and informa- tion on load characteristics are required in the methods Presently Assistant Professor. Contributed by the Dynamic Systems and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS and presented at the Winter Annual Meeting, Chicago, 111., November 16-21, 1980. Manuscript received at ASME Headquarters, February 6, 1986. Paper No. 80-WA/DSC-6. described above. To relax these requirements, a considerable amount of effort has been devoted to the development of new techniques. Recently proposed techniques include the use of the theory of the variable structure systems [9, 10] and a model reference adaptive control approach [11]. This paper presents a new adaptive scheme, different from the one in [11], for dynamic control of mechanical manipulators. After discussing the kinematics and dynamics of mechanical manipulators, the fundamental properties of the manipulator equations are stated in Section II. Making use of the fundamental properties, a simple adaptive algorithm for compensation of a nonlinear term in the manipulator equations and decoupling control is derived in Section III. Section IV presents the simulation results of a manipulator control system composed of the manipulator, adaptive nonlinear compensator/decoupling controller and state feed- back controller with an integral action. A discussion of future research items is also given. II Mathematical Model of Mechanical Manipulators 2.1 Kinematics. In order to define the location (position and orientation) of a rigid body in space, it is necessary to specify six independent coordinates. Although an adaptive control scheme in the next section is for positioning of a three degree of freedom manipulator, the mathematical modelling is discussed for a general mechanical manipulator composed of linkages connected by cylindrical, revolute or prismatic joints. Most existing manipulators are built with only revolute or prismatic joints. A cylindrical joint permits the two connected links to slide and rotate along its axis. A revolute joint can be treated as a cylindrical joint which does not permit sliding while a prismatic joint can be treated as a cylindical joint which does not permit rotation along its axis. A six degree of freedom manipulator is sketched in Fig. 1. Symbols in the figure are defined as follows: Journal of Dynamic Systems, Measurement, and Control JUNE 1986, Vol. 108/127 Copyright © 1986 by ASME Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/09/2015 Terms of Use: http://asme.org/terms