# Geometric Surface-Based Tracking Control of a Quadrotor UAV

## TL;DR

This paper introduces geometric surface-based control algorithms for quadrotor UAVs that operate directly on the nonlinear configuration space, providing almost global stability and robustness in aggressive maneuvers.

## Contribution

It develops and rigorously proves the stability of a novel geometric surface-based control approach directly on SE(3), including the first analysis of a position-error-independent region of attraction.

## Key findings

- Controllers demonstrate almost global stability.
- Effective in aggressive maneuvers with disturbances.
- Region of attraction independent of position error.

## Abstract

New quadrotor UAV control algorithms are developed, based on nonlinear surfaces composed of tracking errors that evolve directly on the nonlinear configuration manifold, thus inherently including in the control design the nonlinear characteristics of the SE(3) configuration space. In particular, geometric surface-based controllers are developed and are shown, through rigorous stability proofs, to have desirable almost global closed loop properties. For the first time in regards to the geometric literature, a region of attraction independent of the position error is identified and its effects are analyzed. The effectiveness of the proposed "surface based" controllers are illustrated by simulations of aggressive maneuvers in the presence of disturbances and motor saturation.