Independent force and position control for cooperating manipulators handling an unknown object interacting with an unknown environment

In this paper, we consider two manipulators grasping a rigid object in contact with a deformable working surface, whose real physical parameters are unknown. Dynamics of the closed chain mechanism is expressed based on the objects center of mass, and different robust controllers are designed for position and force control subspace. The position controller is composed of a sliding mode control term, and involves the position and velocity feedback of end-effector, while the force control is developed based on the highest derivative in feedback methodology. The force controller does not need any derivation of the force signal as well as the internal force controller induced in the system, and it appears to be very practical. Using a Lyapunov stability approach, the controller is proven to be robust in the face of varying systems dynamics. The position/orientation and the force errors are also shown to asymptotically converge to zero under such conditions. Simulation results for two three joint arms moving a rigid object are presented to validate the theoretical results.