| Increased demands for higher productivity and the need to extend the scope of applications of robot arms to precise assembly tasks have been the major driving forces for addressing the control problem of flexible robotic manipulators. An essential step towards achieving this goal is the development of an accurate model for the robot arm. Such a model should be capable of predicting the positioning and orientation of the manipulated objects.;In this work, a spherical robotic manipulator is considered. The equations, describing its rigid and flexible motions, are derived by exploiting the serial characteristic of kinematic chains through the use of 4 x 4 homogeneous D-H and structural flexibility transformation matrices. The derivation takes into consideration the geometric nonlinearity in the von Karman sense, the axial geometric shortening and the stiffening effect induced by the centripetal acceleration. The structural flexibility expressions include torsional, in-plane and out-of-plane transverse deformations. The structural damping and the viscous damping at the joints are considered in the derivation by implementing the Rayleigh's dissipation function. Furthermore, the dynamics of the joint actuators along with their indirect drives are included in the dynamic model.;To simulate actual tasks, the formulation is derived so that it can address situations whereby the manipulated objects are being handled by their extremities. Therefore, the payload is treated as a rigid body with finite geometric dimensions.;An LQI with gain scheduling is used to control the robot arm over its entire work envelope. The controller has demonstrated its capability in directly compensating, through the joint actuators, for the rigid body motion and the transverse vibrations of the arm. In addition, the relationships, with which the rigid body motion and the transverse vibrations of the arm would interact with the torsional vibrations, have enabled the controller to indirectly compensate for the undesired torsional vibrations at the end-effector.;The experimental results illustrate the feasibility of designing a controller that is capable of attenuating the torsional and transverse vibrations at the end-effector. They serve to partially validate the theoretical results. |
