N. G. Chalhoub Assistant Professor, Department of Mechanical Engineering, University of Nevada-Reno, Reno, Nevada 89557-0030 Assoc. Mem. ASME A. G. Ulsoy Associate Professor, Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, Mich. 48109-2125 Mem. ASME Control of a Flexible Robot Arm: Experimental and Theoretical Results The operation of high precision robots is severely limited by. their manipulator dynamic deflection, which persists for a period of time after a move is completed. These unwanted vibrations deteriorate the end effector positional accuracy and reduce significantly the robot arm production rate. A "rigid and flexible motion controller" is derived to introduce additional damping into the flexible motion. This is done by using additional sensors to measure the compliant link vibrations and feed them back to the controller. The existing actuators at the robot joints are used (i.e., no additional actuators are introduced). The performance of the controller is tested on a dynamic model, developed in previous work, for a spherical coordinate robot arm whose last link only is considered to be flexible. The simulation results show a significant reduction in the vibratory motion. The important issue of control and observation spillover is examined and found to present no significant practical problems. Partial evaluation of this approach is performed experimentally by testing two controllers, a "rigid body controller" and a "rigid and flexible motion con- troller, " on a single joint of a spherical coordinate, laboratory robot arm. The ex- perimental results show a significant reduction in the end effector dynamic deflec- tion; thus partially validating the results of the digital simulation studies. 1 Introduction The operation of high precision robots is severely limited by their manipulator dynamic deflection, which persists for a period of time after a move is completed. The settling time re- quired for this residual vibration delays subsequent opera- tions, thus conflicting with the demand for increased produc- tivity. These conflicting requirements between high speed and high accuracy have rendered the robotic assembly task a challenging research problem. The automation of assembly tasks will be greatly enhanced if robots can operate at higher speeds with greater positioning accuracy. These goals cannot be achieved with the existing massive robot designs, which make them slow and heavy. Many robot arms are made to be massive for increased rigidi- ty. For higher operating speeds, mechanisms should be made lightweight to reduce the driving torque requirements and to enable the robot arm to respond faster. Lightweight robot structures are also desirable for space applications. However, lighter members are more likely to elastically deform, thus making it a necessity to take into consideration the dynamic effects of the distributed link flexibility. This is because high speed operation leads to high inertial forces which in turn cause vibration and deteriorate accuracy. To obtain an accurate dynamic model for a very flexible structure, all the coupling terms between the flexible and the Contributed by the Dynamic Systems and Control Division and presented at the Winter Annual Meeting, Boston, Mass., December 14-17, 1987 of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. Manuscript received at ASME Headquarters May 21, 1987. Paper No. 87-WA/DSC-3. rigid body motions need to be retained. This is done by using coupled reference position and elastic deformation models. The resulting equations, which represent the combined rigid and flexible motions, are coupled and very complex. They reveal the nonlinear and nonstationary characteristics inherent in robotic manipulators. The implementation of conventional linear control tech- niques have led to poor performance because of both the in- herent geometric nonlinearities of these systems, and the dependence of the system dynamics on the characteristic of the manipulated objects. Therefore, a sophisticated controller design is needed to ensure the desired performance of the robot. In the control of rigid robots, adaptive, nonlinear, and op- timal control techniques have been investigated. Adaptive control theory (Dubowsky and Desforges, 1979, Horowitz and Tomizuka, 1980, Landau, 1979, Balestrino et al., 1983, Lee and Lee, 1984, Donalson and Leondes, 1963) has been pro- posed as a promising solution to the nonlinearity and nonsta- tionarity problems. The main task is to adjust the feedback gains of the arm controller so that its closed loop performance characteristics closely match the desired ones. However, the large required computation time has restricted the application of adaptive control strategies to simulation studies. Nonlinear control, or the "computed torque" method (Gilbert and Ha, 1984), has led to better performance over conventional control techniques in computer simulations. The controller is based on an idealized model of the manipulator. This is a severe drawback because when the "idealized" con- Journal of Dynamic Systems, Measurement, and Control DECEMBER 1987, Vol. 109 / 299 Copyright © 1987 by ASME Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 11/17/2014 Terms of Use: http://asme.org/terms