An Approach to Simultaneous Control of Trajectory and Interaction Forces in Dual Arm Configurations

Abstract

When two robot arms are used to grasp an object for cooperative manipulation, the two arms with the grasped object form a closed kinematic chain. This induces kinematic and dynamic constraints and the resulting equations of motion are extremely nonlinear and coupled. Further, the number of actuators exceeds the mobility of the chain in a typical case, which results in an under-determined system. In this paper, an approach to control such a constrained dynamic system is described which utilizes the surplus inputs to control the constraint or interaction forces between the two arms. A dynamic control model is derived for the closed chain, that is suitable for designing a controller, in which the position of the object as well as the interaction forces between the manipulators are explicitly controlled. Nonlinear feedback techniques derived from differential geometry are then applied to linearize and decouple the nonlinear model. This general method can be employed for the control of any mechanical system with redundantly actuated closed kinematic chains and is therefore applicable to walking robots, multifingered grippers and in general, to all parallel manipulation systems.