Geometric Tracking on $\mathcal{S}^{3}$ Based on Sliding Mode Control

TL;DR

This paper develops a sliding mode control approach for attitude tracking on the 3-sphere, utilizing Lie group properties to ensure stability and improve performance over Euclidean space methods.

Contribution

It introduces a novel sliding mode controller on the Lie group for attitude tracking, demonstrating almost global stability with intrinsic error metrics.

Findings

Controller achieves almost global asymptotic stability.

Numerical simulations show improved performance over Euclidean space methods.

The approach leverages Lie group structure for intrinsic error definition.

Abstract

Attitude tracking on the unit sphere of dimension $3$ based on sliding mode is considered in this paper. The tangent bundle of Lagrangian dynamics that describes the rotational motion of a rigid body is first shown to be a Lie group, and then a sliding surface that emerged on it is defined. Next, a sliding-mode controller is designed for attitude tracking that relies on an intrinsic error defined on the Lie group. Almost global asymptotic stability of the closed loop is demonstrated using the Lyapunov analysis. Numerical simulations are included to compare the performance of the sliding mode controller designed on the Lie group with that designed in the embedding Euclidean space.