Robust Global Exponential Stabilization on the $n$-Dimensional Sphere with Applications to Trajectory Tracking for Quadrotors

TL;DR

This paper introduces a hybrid control method for globally exponentially stabilizing systems on the n-dimensional sphere, with applications to precise trajectory tracking in quadrotors, using potential functions aligned with geodesic flows.

Contribution

It presents a novel hybrid controller based on synergistic potential functions that achieve global exponential stabilization on the sphere, optimized for minimal path convergence.

Findings

Successfully stabilizes systems on the sphere exponentially

Enables precise trajectory tracking for quadrotors

Uses geodesic-aligned potential functions for efficiency

Abstract

In this paper, we design a hybrid controller that globally exponentially stabilizes a system evolving on the n-dimensional sphere, denoted by Sn. This hybrid controller is induced by a synergistic collection of potential functions on Sn. We propose a particular construction of this class of functions that generates flows along geodesics of the sphere, providing convergence to the desired reference with minimal path length. We show that the proposed strategy is suitable to the exponential stabilization of a quadrotor vehicle.