Kinematics and control of redundantly actuated closed chains

The instantaneous kinematics are discussed of a hybrid manipulation system that combines the traditional serial chain geometry with parallelism in actuation. Such a system is characterized by closed chains in the structure and redundancy in actuation. This redundancy is shown to be dual to the kinematic redundancy in serial chain robot manipulators. The presence of redundancy in the system allows the specification of force set-points that will ensure an optimal load distribution for force control or hybrid control schemes. In addition, the singularities in the inverse kinematics and statics equations, which are typical of robotic systems with closed chains, are analyzed. Coordination algorithms for the computation of optimal force distribution that minimize joint torques while avoiding singularities with reasonable computation efficiency are the authors´ main focus. In particular, a planar dual-arm manipulation system is used as an example and is analyzed in some detail