Ph.D. Thesis Defense by Klaus Obergfell
Tuesday, August 18, 1998

(Dr. Wayne Book, advisor)

"End-Point Position Sensing and Control of Flexible Multi-Link Manipulators"

Abstract

This research developed sensing and control methods for end-point positioning of long0reach, multi-link, flexible manipulators and implemented and tested these methods on RALF (Robotic Arm Large and Flexible), a two-link flexible manipulator testbed at Georgia Tech, for a variety of operating conditions.

Two end-point position sensors were evaluated.  The first consisted of a computer vision based landmark tracking system (LTS) that directly measured end-point position in a subspace.  The second system, a manipulator based system, estimated tip position from link deflection and joint angle measurements.  However, the link deflection sensors were useful in improving closed-loop performance through link deflection feedback.

A mathematical model of the dynamics of a two-link flexible manipulator was derived using Lagrange's equations and the assumed modes methods.  Although the natural frequencies of this model matched literature cases well, the frequency response plots of the model did not match experimental frequency response plots.  As experiments showed that the velocity output of the hydraulic actuators was approximately proportional to the voltage input, two methods for including actuator dynamics in the model were considered.  The first transformed the equations of motions in order to accept a velocity input.  The second simulated the operation of the hydraulic servo valves with velocity feedback.  The latter method matched the frequency response better than the former and essentially captured RALF's dynamics including the non-minimum phase characteristic.  However, discrepancies remained between model and experiment as a result of parameter errors in the structural model and limitations of the actuator model.

Previous work by Wang and Vidyasagar showed that a modified output allowed for a simpler endpoint for single link flexible manipulators.  Their controller is identical to PD joint control with positive link deflection feedback.  By applying link deflection to all links of RALF, structural vibrations were reduced by 44-86% for a variety of tip speeds and payloads.  Although positive link deflection feedback improved the dynamic response of the manipulator, an end-point error remained due to static link deflection, kinematical error, and payload uncertainty.  An end-point position feedback loop utilizing the inverse manipulator Jacobian and integral compensation was added to eliminate these errors.  This feedback loop reduced the average tip position error by 48-85%.