| There is growing interest in robotic manipulation of flexible materials due to its potential applications in industries. This thesis addresses the problem of controlling a two-manipulator system handling flexible objects. A particular case of handling a flexible beam is first concerned, where the vibration dynamics of the beam is approximated by m assumed modes. Three approaches focusing on the position control and trajectory tracking are presented. The first approach shows that a PD position feedback plus an I-type force feedback is able to stabilize the beam to a desired position and orientation while suppressing its vibration, and simultaneously control the internal forces between the beam and manipulators. The second approach is to develop a hybrid impedance control scheme that combines impedance control and an I-type force feedback into one scheme by designing a proper response of the interaction including external and internal forces. Compared to the PD feedback, the impedance control is robost to external disturbances and displays a higher rate of convergence. The proposed controllers use no feedback of the flexible coordinates but the measurable information. The asymptotic stability of the system is investigated by LaSalle theorem. To achieve position and force tracking, a tracking scheme is developed in the third approach by utilizing the saturation functions to compensate the flexible effect so that no information about the vibration is used. Under this controller, the errors of position and force as well as the vibrations are under an upper bound determined by control parameters. It must be noted that the proofs in the three approaches are not limited to any specific number m of vibration modes. The simulation results illustrate the validities of the three approaches. We further consider the case of handling a general flexible object handled by two manipulators with six revolute joints. It is shown that under a PD position feedback, the position/orientation of the object is able to approach the desired one and at the same time the vibration of each contact is suppressed. The investigation is based on such a boundary condition that one contact is fixed and the other one free so that the flexible object is decomposed into two components representing the rigid body and the deformation by using the finite element method. |
