# Hybrid Kinematic Control for Rigid Body Pose Stabilization using Dual Quaternions

## TL;DR

This paper introduces a hybrid control method using dual quaternions for rigid body pose stabilization, ensuring global stability without chattering, and demonstrates its effectiveness through simulations.

## Contribution

It presents a novel hybrid control strategy with hysteresis for pose stabilization that guarantees global asymptotic stability and avoids chattering.

## Key findings

- The proposed controller achieves robust global pose stability.
- Numerical simulations confirm the elimination of unwinding and chattering.
- The method outperforms existing discontinuous feedback controllers.

## Abstract

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.