Internal and external force-based impedance control for cooperative manipulation

An asymptotically stable cascaded control algorithm is proposed for cooperative manipulation of a common object. This algorithm controls motion and internal forces of the object, as well as the contact forces between the object and environment. The motion of each manipulator is controlled using an inverse dynamics type of controller. Only knowledge of the kinematics of the manipulated object is required, since the interaction forces and moments between the object and manipulators are measured. The internal stresses in the object are controlled based on enforced impedance relationships between the object and each manipulator. The internal forces and moments are computed using the object kinematics. Contact with the environment is controlled with an enforced impedance relationship between the object and the environment. For both internal and external forces, reference trajectories can be specified. Asymptotic stability of each controller is proven using Lyapunov stability theory and LaSalle´s invariance principle. Guidelines are suggested to compute control parameters of the internal impedance parameters. Merits of the control algorithm are demonstrated in simulations.