Expert Systems With Applications, Vol. 4, pp. 305-313, 1992 0957-4174/92 $5.00 + .00 Printed in the USA. © 1992 Pergamon Press Ltd. Two-Dimensional ing-Control Theory for Robotic Manipulators A. ZILOUCHIAN AND A. GAUTAM Departmentof Electrical Engineering, FloridaAtlantic University, BocaRaton, FL 33431, USA Abstract--In this paper a two-dimensional ( 2-D ) learning control scheme for robot manipulators is proposed. The scheme is based on an iterative structure that utilizes available data from previous operation of a specified trajectory. It is shown that the fast convergence of the actual trajectory to the desired one is guaranteed upon proper selection of a weighting matrix. The proposed learning-control technique is applied to a trajectory-tracking problem for a two-link, as well as a Microbot, manipulator. Convergence of the scheme for various weighting matrices is shown. 1. INTRODUCTION CLASSICAL SERVOMECHANISM Control Theory is the primary methodology of motion control currently uti- lized for industrial and commercial robots. This con- ventional method is usually adequate for small excur- sion tasks at low bandwidths. However, due to system complexities, such as unknown perturbations and load variation, more sophisticated control schemes are needed for accurate robot performance under various conditions. During the last decade, many advanced control schemes have been proposed for robot manip- ulators. These include nonlinear-cancellation method, adaptive control, resolved motion and acceleration control, time-optimal control, and learning control. Although adaptive control techniques such as (Du- bowsll and DesForges, 1979; Slotine, and Li, 1987) do not require a precise description of the mathematical model of the system and can face parameter variation, they still require a complicated structure for the reg- ulator due to the complexity of the adaptive mecha- nism. On the other hand, the design and implemen- tation of learning-control schemes for robot manipu- lators has been proposed by different researchers (Arimoto, Kawamura, & Miyazaki, 1984a; Zilouchian & Gautam, 1990). The preliminary results in both theoretical and implementation phases appear prom- ising. In general, human beings have the ability to learn from experience. People with experience can complete a given task in a better way, since the experience acts as a sort of feedback of information that is used to modify the control action (Arimoto et al., 1984a; 1984b). Although humans and mechanical robots can perform similar tasks, there are sharp distinctions be- Requests for reprints should be sent to A. Zilouchian, Del~rtment of Electrical Engineering, Florida Atlantic University, Boca Raton, FL 33431. tween the robots and human control strategy. For ex- ample, human control is largely acquired through learning, whereas the operation of a robot is specified by a pre~written algorithm. However, the fundamental principle of self-learning of a human being through repeated operation can be implemented for motion control of a robot manipulator. In a way similar to a human being learning a desired motion pattern through repeated trial, the robot is able to acquire dynamically real-time data of the system during each trial, and makes changes according to its control-input signal for each successive repetitive operation. One of the im- l)ortant features of a learning-control scheme is that it has the capability of modifying the unsatisfactory con- trol-input signal automatically, based on the knowled~_=e of previous operations of the same task with a form of intelligence. The goal of a well-designed learning-con- trol technique is to generate a control input that causes the output trajectory to be close enough to the desired trajectory, after a finite number of learning iterations. The implementation of learning-control techniques for robot manipulators has attracted considerable at- tention in the last several years. Arimoto et al. ( 1984a, 1984b, 1985, Arimoto, Kawamura, Miyazall, & Ta- moll; 1985) were among the first who proposed an iterative learning algorithm. Kawamura, Miyazaki, and Arimoto ( 1985, 1988) investigated learning control of robots based on repeatibility of robot motion and linear approximation. The repeatability of robot motion was also required to design learning filters in (Craig 1984), (Dawson, Qu, Lewis, & Dorsey, 1989), and (Dawson et al., in press). Gu and Loh (1987) presented a multi- step learning-control scheme with input signals chosen as the weighted summation of the errors of previous operations. On the other hand, Bondi, Casalino and Gambardella (1988) and Casalino and Gambardella (1986) studied the learning-control problem using a "high gain" position, velocity, and acceleration feed- back control. Recently, learning control using neural 305