IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 9, NO. 4, JULY 1998 581 Robust Neural-Network Control of Rigid-Link Electrically Driven Robots Chiman Kwan, Member, IEEE, Frank L. Lewis, Fellow, IEEE, and Darren M. Dawson, Senior Member, IEEE Abstract— A robust neural-network (NN) controller is pro- posed for the motion control of rigid-link electrically driven (RLED) robots. Two-layer NN’s are used to approximate two very complicated nonlinear functions. The main advantage of our approach is that the NN weights are tuned on-line, with no off-line learning phase required. Most importantly, we can guarantee the uniformly ultimately bounded (UUB) stability of tracking errors and NN weights. When compared with standard adaptive robot controllers, we do not require lengthy and tedious preliminary analysis to determine a regression matrix. The controller can be regarded as a universal reusable controller because the same controller can be applied to any type of RLED robots without any modifications. Index Terms— Neural network, nonlinearity, robust control, robot, stability. I. INTRODUCTION I N THE PAST decade, there has been much research on the applications of nonlinear control theory to the motion control of robots. Many useful properties of robot dynamics such as the skew-symmetry property were discovered. As a result, many robust and adaptive control schemes were developed with the aim of explicitly counteracting parametric uncertainties in the robot system and hence improving the accuracy of motion as well as force tracking. Most of these controllers were based on a second-order nonlinear robot model and can be found in survey papers by Abdallah et al. [1] and Ortega and Spong [18]. One major drawback of these approaches is that the actuator dynamics have been neglected. As pointed out by Eppinger and Seering [9] and Tarn et al. [26], neglecting actuator dynamics may affect the performance of motion and/or force tracking controllers. An intuitive reasoning suggests that, with the inclusion of actuator dynamics, we should be able to improve the robot performance. The robot-plus-actuator system is also termed as rigid-link electrically driven (RLED) robot system by Taylor [27]. To explicitly counteract the actuator dynamics, several ap- proaches have been taken. Tarn et al. [26] applied nonlinear feedback linearization theory to this problem. Link accelera- Manuscript received March 1, 1995; revised March 19, 1996 and March 14, 1998. This work was supported by the NSF under Grant IRI-9216545. C. Kwan is with Intelligent Automation Incorporated, Rockville, MD 20850 USA. F. L. Lewis is with the Automation and Robotics Research Institute, The University of Texas at Arlington, Fort Worth, TX 76118 USA. D. M. Dawson is with the Department of Electrical and Computer Engi- neering, Center for Advanced Manufacturing, Clemson University, Clemson, SC 29634 USA. Publisher Item Identifier S 1045-9227(98)04458-0. tion measurement is needed for implementation. Taylor et al. [27] formulated the RLED robot as a singular perturbation system. By using a time-scale separation, a controller was designed based on a “slow” reduced-order model of the original RLED system. Dawson et al. [7] derived a robust controller based on the general framework of [12] which achieves global uniform ultimate bounded stability. For control engineers, the approximation capability of NN is usually used for system identification [3], [10], or identification-based [2], [15], [17], [19]. However there is very little about the use of neural networks (NN’s) in direct closed-loop controllers that yield guaranteed performance. Problems that remain to be addressed in NN research in- clude ad hoc controller structures and the inability to guarantee satisfactory performance of the system in terms of small tracking errors and bounded NN weights. Uncertainty on how to initialize the NN weights leads to the necessity for “preliminary off-line tuning” [2], [4]. In fact, many existing NN methods in robot control (e.g., [11] and [19]) do not offer closed-loop stability proofs. Here we use two-layer NN’s in our controller and closed-loop stability is rigorously proven. In this paper, we propose a new robust control scheme for RLED robot using the theory of NN. Our approach can be considered as consisting of three steps. We first treat certain signals in the robot as fictitious control signals to the rigid robot subsystem. An NN controller is designed to achieve good tracking and stability results. Then in the second step, our control objective is to make the error between the actual signal and the fictitious signal as small as possible so that the objective of the first step can be achieved. The final step is the overall stability analysis. The above design procedure is also known as backstepping control [12]. It should be noted that the purpose of NN in our design is to approximate certain complicated nonlinear functions. An immediate advantage is that the NN structure is the same irrespective of the kind of robot under control. Hence no preliminary dynamical analysis to determine a regression matrix is needed. In backstepping design procedures, this is especially important, for typically two regression matrices must be found, and one of these must be differentiated in order to get the other one. The procedure will become very tedious if we are dealing with a robot with multiple degrees of freedom. Compared with other NN approaches, the NN weights here are tuned on-line, with no off-line learning phase required. Most importantly, we can guarantee the uniformly ultimately bounded (UUB) stability of tracking errors and NN weight updates. When compared with standard adaptive robot controllers, we do not require persistent excitation conditions. 1045–9227/98$10.00  1998 IEEE