MODELING AND CONTROL OF TRANSVERSE AND TORSIONAL VIBRATIONS IN A SPHERICAL ROBOTIC MANIPULATOR - THEORETICAL AND EXPERIMENTAL RESULTS

The present work addresses modeling and control issues pertaining to t he positioning and orientating of rigid body payloads as they are bein g manipulated by flexible spherical robotic manipulators. A general ap proach, to systematically derive the equations of motion of the roboti c manipulator, is used herein. The objective of the controller is to y ield a desired rigid body response of the arm while damping out the tr ansverse and torsional vibrations of the compliant link. Note that the control objective has to be achieved by solely relying on the existin g joint actuators whose bandwidths are far below the natural frequenci es of the torsional modes. The current work demonstrates that, in spit e of the physical limitations of the system, the controller can active ly damp out the torsional vibrations by relying on the coupling terms between the torsional vibrations and the remaining degrees of freedom of the arm. Moreover, a gain scheduling procedure is introduced to con tinuously tune the controller to the natural frequencies of the flexib le link whose length is varied by the prismatic joint. The digital sim ulation results demonstrate the capability of the ''rigid and flexible motion controller (RFMC)'' in drastically attenuating the transverse and torsional vibrations during point-to-point (PTP) maneuvers of the arm. Further more, the gain scheduling procedure is shown to significa ntly reduce the degradations in the RFMC performance that are brought about by having the flexible link connected to a prismatic joint. A li mited experimental work has also been conducted to demonstrate the via bility of the proposed approach.