Dynamics and control of multiple cooperating manipulators with rolling contacts

Abstract

In this article, we investigate the control of multiple cooperating mechanisms manipulating a common object, with rolling contact between the end-effectors and the object. We derive new kinematic and dynamic formulations for the system, in which the rolling degrees of freedom between the end-effector and the object are modeled as one or more unactuated joints of the manipulator. Differential geometric concepts are used to interpret the curvature and torsion forms used in contact kinematic equations derived by Montana. The augmentation of the rolling contacts imparts each manipulator with additional degrees of freedom and could also make it kinematically redundant. This can be exploited for the satisfaction of a secondary subtask criterion such as collision avoidance, which is demonstrated in the examples. In addition, a control law can be specified that enables simultaneous control of the object trajectory, the internal forces in the object, and the trajectories of the contact points on the object or the end-effectors.