Object impedance control using a closed-chain task definition

Humanoid robots are intended to interact with unstructured environments and to perform diverse applications. Often, such work involves manipulating an object cooperatively with multiple hands or fingers. This work presents an impedance based control framework for such cases with multi-priority tasking. The primary task governs the impedance response of the object and a secondary task governs the impedance response of the joints. Using a novel transformation, the primary task may specify a subset of the object degrees of freedom (DOFs), allocating the remaining DOFs to the secondary task. This results in an integrated null space that includes not only the redundant DOFs of each manipulator independantly, but also the free DOFs of the object shared across the manipulators.