# Sliding Motions on SO(3), Sliding Subgroups

## TL;DR

This paper introduces a sliding surface on SO(3) for attitude control of rigid bodies, ensuring robustness and stability without unwinding, by leveraging Lie subgroup properties.

## Contribution

It presents a novel sliding surface on SO(3) that is a Lie subgroup, enabling robust sliding-mode control for rigid body attitude without unwinding.

## Key findings

- Reduced-order dynamics are almost globally asymptotically stable.
- The control system is robust against matched disturbances.
- Unwinding phenomenon is eliminated in the proposed approach.

## Abstract

We propose a sliding surface for systems on the Lie group $SO(3)\times \mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable equilibrium. The sliding surface is used to design a sliding-mode controller for the attitude control of rigid bodies. The closed-loop system is robust against matched disturbances and does not exhibit the undesired unwinding phenomenon.