Geometric Adaptive Control of Attitude Dynamics on SO(3) with State Inequality Constraints

TL;DR

This paper introduces a geometric adaptive control method for rigid body attitude dynamics on SO(3) that enforces state inequality constraints and handles unknown disturbances, avoiding singularities and ambiguities.

Contribution

A novel geometric adaptive control approach on SO(3) that incorporates state inequality constraints and disturbance adaptation, avoiding issues of traditional attitude parameterizations.

Findings

Successfully stabilizes desired attitude while avoiding constrained regions.

Demonstrates robustness against unknown disturbances.

Validated through simulations and experiments.

Abstract

This paper presents a new geometric adaptive control system with state inequality constraints for the attitude dynamics of a rigid body. The control system is designed such that the desired attitude is asymptotically stabilized, while the controlled attitude trajectory avoids undesired regions defined by an inequality constraint. In addition, we develop an adaptive update law that enables attitude stabilization in the presence of unknown disturbances. The attitude dynamics and the proposed control systems are developed on the special orthogonal group such that singularities and ambiguities of other attitude parameterizations, such as Euler angles and quaternions are completely avoided. The effectiveness of the proposed control system is demonstrated through numerical simulations and experimental results.