Adaptive Admittance Control for Cooperative Manipulation using Dual Quaternion Representation and Logarithmic Mapping

This paper addresses the problem of admittance control for bimanual and cooperative manipulators. First, a novel admittance controller is devised to be consistent with the geometry of the cooperative task space and exploits the dual quaternion logarithmic mapping of wrenches and corresponding elastic displacements. By describing the coupled motion exploiting the geometric features of dual quaternions, the desired compliant behaviour is enforced on the whole dual-arm system and not on the single manipulator separately. The solution is thereafter extended by means of an adaptive modulation of the impedance gains along the logarithmic space of the dual quaternion algebra for cooperative dual task-space variables. The overall scheme consists of a stiffness adapter, cooperative admittance controller, and wrench adapter complete with an inner motion controller along with the cooperative system. Stability proofs and conditions for the stiffness and damping adaptation of the cooperative variables is provided. Finally, we present a use case depicting a cooperative variable stiffness adaptation policy with respect to the relative elastic behaviour between arms to reduce internal stress whilst satisfying grasp feasibility under shear forces and varying load conditions. Our formulation is validated by thorough simulation studies on two Franka Emika Panda robots carrying a shared object under varying loading conditions. The experimental investigations reinforce our claim of robust performance when compared with fixed stiffness and standard width-adaptation solutions.