Control of two robotic manipulators moving a constrained object

We address the problem of two robots manipulating a rigid object which moves along a constraint surface. The dynamic model of such a system is usually very complicated. However, because of the constrained motion, some degrees of freedom are lost or irrelevant to the required task. The work space is divided into two subspaces which describe the linear motion and the angular motion. Based on the fact that the two manipulators, the object, and the constraint surface form a closed chain, the dynamic couplings as well as the kinematic couplings among the system elements are exploited to get a reduced order dynamic model. Next, the control problem is addressed. When manipulating a constrained object using multiple robot manipulators, it is necessary to control the position of the object, the internal force exerted on the object by the manipulators, and the constraint force. Using the reduced order model, a controller consisting of a nonlinear feedback and servo compensators is proposed. Under a certain condition, this controller decouples the object position, the internal force and the constraint force. This controller also guarantees the asymptotic convergence of the position, the internal force, and the constraint force to their desired values. To validate our results, simulations for two three-link planar manipulators moving a constrained object are carried out. The simulation results show that the proposed controller achieves the desired asymptotic tracking