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

Multiple arm systems, multifingered grippers, and walking vehicles all have two common features. In each case, more than one actively coordinated articulation interacts with a passive object, thus forming one or more closed chains. For example, when two arms grasp an object simultaneously, the arms together with the object and the ground (base) form a closed chain. This induces kinematic and dynamic constraints and the resulting equations of motion are extremely nonlinear and coupled. Furthermore, the number of actuators exceeds the kinematic mobility of the chain in a typical case, which results in an underdetermined system of equations. An approach to control such constrained dynamic systems is described in this short paper. The basic philosophy is to utilize a minimal set of inputs to control the trajectory and the surplus inputs to control the constraint or interaction forces and moments in the closed chain. A dynamic control model is derived for the closed chain that is suitable for designing a controller, in which the trajectory as well as the interaction forces and moments are explicitly controlled. Nonlinear feedback techniques derived from differential geometry are then applied to linearize and decouple the nonlinear model. In this paper, these ideas are illustrated through a planar example in which two arms are used for cooperative manipulation. Results from a simulation are used to illustrate the efficacy of the method