Dynamic Control Modification Techniques in Teleoperation of a Flexible Manipulator

by David P. Magee

Advisor: Wayne J. Book

The objective of this research is to reduce the end-point vibration of a large, teleoperated manipulator while preserving the usefulness of the system motion. A master arm is designed to measure desired joint angles as the user specifies a desired tip motion. The desired joint angles from the master arm are the inputs to an adaptive P.D. control algorithm that positions the end-point of the manipulator. As the user moves the tip of the master, the robot will vibrate at its natural frequencies which makes it difficult to position the end-point. To eliminate the tip vibration during teleoperated motions, an input shaping method developed by Singer and Seering from MIT is presented.

The input shaping method transforms each sample of the desired input into a new set of impulses that do not excite the system resonances. The method is explained using the equation of motion for a simple, second-order system. The impulse response of such a system is derived and the constraint equations for vibrationless motion are presented. To evaluate the robustness of the method, a different residual vibration equation from Singer's is derived that more accurately represents the input shaping technique. The input shaping method will be shown to actually increase the residual vibration in certain situations when the system parameters are not accurately specified. Finally, the implementation of the input shaping method to a system with varying parameters is shown to induce a vibration into the system. To eliminate this vibration, a modified command shaping technique is developed. The ability of the modified command shaping method to reduce vibration at the system resonances is tested by varying input perturbations to trajectories in a range of possible user inputs. By comparing the frequency responses of the transverse acceleration at the end-point of the manipulator, the modified method is compared to the original P.D. routine. The control scheme that produces the smaller magnitude of resonant vibration at the first natural frequency is considered the more effective control method.


David P. Magee
dpm@euler.marc.gatech.edu
Last Revised: August 23, 1995