Exploiting Different Symmetries for Trajectory Tracking Control with Application to Quadrotors

TL;DR

This paper introduces a novel control design methodology for quadrotors that exploits different system symmetries to improve trajectory tracking performance, especially under large disturbances.

Contribution

It proposes the Equivariant Regulator design, leveraging various symmetries of quadrotors to enhance control accuracy and robustness.

Findings

Extended pose and pose-velocity symmetries outperform direct product symmetry in simulations.

Symmetry-based linearisation reduces control errors under disturbances.

Different symmetries can be used to define global errors for quadrotor control.

Abstract

High performance trajectory tracking control of quadrotor vehicles is an important challenge in aerial robotics. Symmetry is a fundamental property of physical systems and offers the potential to provide a tool to design high-performance control algorithms. We propose a design methodology that takes any given symmetry, linearises the associated error in a single set of coordinates, and uses LQR design to obtain a high performance control; an approach we term Equivariant Regulator design. We show that quadrotor vehicles admit several different symmetries: the direct product symmetry, the extended pose symmetry and the pose and velocity symmetry, and show that each symmetry can be used to define a global error. We compare the linearised systems via simulation and find that the extended pose and pose and velocity symmetries outperform the direct product symmetry in the presence of large disturbances. This suggests that choices of equivariant and group affine symmetries have improved linearisation error.