# Attitude and angular velocity tracking for a rigid body using geometric methods on the two-sphere

## TL;DR

This paper develops a geometric control method on the two-sphere for rigid body attitude and angular velocity tracking, addressing limitations of existing controllers by handling large initial errors and avoiding singularities.

## Contribution

A novel global geometric controller on the two-sphere for simultaneous attitude and angular velocity tracking, overcoming issues like unwinding and singularities present in prior methods.

## Key findings

- Improved tracking performance for large initial errors
- Smooth transitions between desired angular velocities
- Effective negotiation of bounded modeling inaccuracies

## Abstract

The control task of tracking a reference pointing direction (the attitude about the pointing direction is irrelevant) while obtaining a desired angular velocity (PDAV) around the pointing direction using geometric techniques is addressed here. Existing geometric controllers developed on the two-sphere only address the tracking of a reference pointing direction while driving the angular velocity about the pointing direction to zero. In this paper a tracking controller on the two-sphere, able to address the PDAV control task, is developed globally in a geometric frame work, to avoid problems related to other attitude representations such as unwinding (quaternions) or singularities (Euler angles). An attitude error function is constructed resulting in a control system with desired tracking performance for rotational maneuvers with large initial attitude/angular velocity errors and the ability to negotiate bounded modeling inaccuracies. The tracking ability of the developed control system is evaluated by comparing its performance with an existing geometric controller on the two-sphere and by numerical simulations, showing improved performance for large initial attitude errors, smooth transitions between desired angular velocities and the ability to negotiate bounded modeling inaccuracies.