Control of Flexible Robot Arm

T h i s work is a computer simulation of the control of flexi ble robot arm. The dynamic equations for a single-link flexible robot arm have been derived rigorously. Th is arm has two degrees of freedom in rotation and one in translation so that the workspdce i s three-dimensional. The payload is simulated by attaching additional mass to the arm at a specified location. The governing equations of the plant and the measurements are nonlinear. The process of control i s divided into two stages: coarse control and fine control. Based on the pole-placement method, a linear observer is constructed for fine control. The numerical results of several cases are presented here. The effects of damp ing and sampling rate are also discussed. LNTRODUCTION Most of today’s industrial robots can lift only about one twentieth of their own weight. Compare that to the human arm which can li f t about ten times i ts own weight. The top slew velocity of a robot arm is typically around one meter per second while the top slew velocity that can be achieved by the human arm during a task such as throwing a baseball i s around 48 meters per second. Although these comparisons may not be fair, the point stands that there is vast room for the improvements in the performance of robotic manipulators. O n e of the most elementary problem in robotics is that of accuracy. The repeata bility of most of today’s robots is on the order of 1 mm over the working space, the accuracy of absolute positioning (for the end effector to reach the commanded point) may be off as much as 1 cm. The present solution to the problem of accuracy is to make robot smctures very s t i f f and rigid. Another problem in robotics i s control. Nowadays, in order to position the end effector to the commanded location the angles that each of the robot’s joint must assume are computed and then the joints are driven simul* Also, a graduate research assistant at Department of Mechanical Engineering, Robotics Laboratory, University of Maryland. taneously to said angles. After the joint angles assume those computed values, the robot i s presumed st i f f enough so that the end effector will thus (by dead reckoning) be in the intended location. Therefore. not only the robots arc built to be. massive and unwieldy, the analysis and the controls in robotics are based on the assumption that the robot arm is just a collection of rigid bodies. I t is desirable to build a lightweight robot arm which has a long reach and the capability to carry heavy payload and to move rapidly. In order to meet these requirements, the robot arm has to be flexible. In other words, even the static deflection of the robot arm has to be taken into account for positioning accuracy; more importantly, the high moving speed of the arm implies the inertia forces acting on the arm are very large and the stability of the robot arm becomes a critical problem which requires the engineers to design a more sophisticated control system. In the area of control of flexible robot arm, Cannon and Schmitz [l]published the pioneer work in 1984 . In that work the mathematical modeling and the initial expreriments have been carried out to address the control of a flexible member (one link of a robot system) where the position of the end effector (tip) is controlled by measuring that position and using the measurement as a basis for applying control torque to the other end of the flexible member (joint). Also, i t is worthwhile to mention the works of Harashima and Ueshiba [2], Wang and Vidyasagar [3, 41, Sangveraphunsiri [5], Book et al [6]. In all those abovementioned works, there are two things in common: the one-link robot arm, with i ts hub rotating about z-axis, sweeps the horizontal x-y plane; the flexible arm i s modeled as a beam whose deflection is represented by a series in terms of eigenfunctions (normal modes). In this work, the computer simulation of the control of a single-link flexible robot arm is presented. The hub of the arm can rotate about z-axis, specif ied by the joint angle 9(r) , and y’axis, specified by the joint angle +(r) . Also, the arm can slide along i ts own longitudinal axis. So that the working region of the