Dual quaternion-based bimodal global control for robust rigid body pose kinematic stabilization

A hybrid bimodal controller for rigid body pose stabilization within the group of unit norm dual-quaternions is proposed in this paper. Using two binary logic state variables, this hysteresis-based controller represents a middle term solution between the memoryless discontinuous controller and the fixed-width hysteretic one. The proposed strategy is novel within the dual-quaternions framework and addresses three common difficulties that appears in the literature of pose and attitude stabilization: global stability, robustness against chattering and against unwinding. The efficacy and performance of the proposed controller are illustrated with numerical examples.