Hybrid Kinematic Control for Rigid Body Pose Stabilization using Dual Quaternions

In this paper, we address the rigid body pose stabilization problem using dual quaternion formalism. We propose a hybrid control strategy to design a switching control law with hysteresis in such a way that the global asymptotic stability of the closed-loop system is guaranteed and such that the global attractivity of the stabilization pose does not exhibit chattering, a problem that is present in all discontinuous-based feedback controllers. Using numerical simulations, we illustrate the problems that arise from existing results in the literature—as unwinding and chattering—and verify the effectiveness of the proposed controller to solve the robust global pose stability problem.