Asymptotic and finite-time almost global attitude tracking: representations free approach

TL;DR

This paper develops control protocols for attitude tracking on SO(3) that achieve almost global convergence asymptotically and in finite time without requiring a fixed reference frame, using only relative state information.

Contribution

It introduces new control protocols that overcome topological restrictions, achieving almost global tracking with finite-time convergence using a representations free approach.

Findings

Protocols achieve almost global asymptotic tracking

Finite-time tracking is achieved with non-smooth analysis techniques

Simulations verify the effectiveness of the proposed methods

Abstract

In this paper, the attitude tracking problem is considered using the rotation matrices. Due to the inherent topological restriction, it is impossible to achieve global attractivity with any continuous attitude control system on $SO(3)$. Hence in this work, we propose some control protocols achieve almost global tracking asymptotically and in finite time, respectively. In these protocols, no world frame is needed and only relative state informations are requested. For finite-time tracking case, Filippov solutions and non-smooth analysis techniques are adopted to handle the discontinuities. Simulation examples are provided to verify the performances of the control protocols designed in this paper.