Centrally Synergistic Hybrid Feedback for Global Pose Tracking Using Dual Quaternions

Abstract

This article is concerned about global pose tracking problem, namely, attitude-plus-position, for the rigid body systems. First, we propose the synergistic potential functions (SPFs) on the unit dual quaternion group, denoted $\mathbb {D} \mathbb {Q}_{u}$, with the central synergism property—each potential function in the SPF is positive definite with respect to the identity pose. Second, two synergistic hybrid controllers, mainly consisting of the state feedback associated with the SPF and a hybrid switching mechanism, are proposed for pose tracking in different measurement contexts: full-state measurements, which include pose and twist, and twist-free measurements. Both the controllers ensure global asymptotic stability and maintain consistency with respect to the unit dual quaternion representation of rigid-body pose. To the best of our knowledge, this is the first centrally synergistic hybrid feedback that is designed on $\mathbb {D} \mathbb {Q}_{u}$ for pose tracking. Finally, simulation results are presented to demonstrate the performance of the proposed hybrid controllers.