Techniques for controlling a two-link flexible arm

摘要

The long length and relatively small cross sectional area of the robotic arms envisioned for use inside of the underground nuclear waste storage tanks will require the control of flexible structures. This will become an important problem in the characterization and remediation of these tanks. We are developing control strategies to actively damp residual vibrations in flexible robotic arms caused by high speed motion and abrupt external forces. A planar, two-link flexible arm is currently being used to test these control strategies. In this paper, two methods of control are discussed. The first is a minimum-time control approach which utilizes a finite element model and and optimization program. These tools plan the motor torque profiles necessary for the tip of the arm to move along a straight line, in minimum time, within the motors' torque constraints, and end in a quiescent state. To account for modeling errors in the finite element model, errors in joint angles, velocities, and link curvatures are added to the optimal torque trajectory. Linear quadratic Gaussian (LQG) regulatory design theory is used to determine the feedback gains. The second method of control is a teleoperated joystick controller which uses an input shaping technique to alter the commands of the joystick so as to reduce the residual vibration of the fundamental modes. Approximating the system as linear, the natural frequency and damping ratio are estimated on-line for the complete system, which includes the structure plus a lower level proportional derivative controller. An input shaping filter is determined from the estimated natural frequency, estimated damping ratio, and the desired transfer function of the system. 11 reps., 9 figs.