Modelling and control of rigid-flexible multibody systems is studied in this paper. As a specified application, a space robotic system with flexible appendages during a cooperative object manipulation task is considered. This robotic system necessitates delicate force exertion by several end-effectors to move an object along a desired path. During such maneuvers, flexible appendages like solar panels may get stimulated and vibrate. This vibrating motion will cause some oscillatory disturbing forces on the spacecraft, which in turn produces error in the motion of the end-effectors of the cooperative manipulating arms. In addition, vibration control of these flexible members to protect them from fracture is another challenging problem in an object manipulation task for the stated systems. Therefore, the multiple impedance control algorithm is extended to perform an object manipulation task by such complicated rigid-flexible multibody systems. This extension in the control algorithm considers the modification term which compensates the disturbing forces due to vibrating motion of flexible appendages. Finally, a space free-flying robotic system which contains two 2-DOF planar cooperative manipulators, appended with two highly flexible solar panels, is simulated. Obtained results reveal the merits of the developed model-based controller which will be discussed. 1. Introduction Robotic manipulators are widely used in unsafe, costly, and repetitive boring tasks. Most available robotic manipulators are designed such that they can provide essential stiffness for end-effector to reach its desired position without flexible deformations [1]. This stiffness is usually attained by massive links. Consequently, design and use of weighty rigid manipulators may be deficient in energy consumption and the speed of operation. In particular, for space and on-orbit applications minimum weight design does not allow using such stiff manipulators. On the other hand, even assuming rigid manipulators, existence of flexible components on space robotic systems such as solar panels, necessitates considering their effect. The required settling time for vibration of such parts may delay the operation and so conflicts with increasing time efficiency of the system. This conflict of high speed and high accuracy during any operation makes these robots a disputative research problem [2–5]. Robotic systems with flexible components include continuous dynamic systems that are simplified by using a finite number of rigid degrees of freedom and a limited number of modes. This leads to a set of
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