Lie Group Control Architectures for UAVs: a Comparison of SE2(3)-Based Approaches in Simulation and Hardware

TL;DR

This paper compares advanced Lie group-based control strategies for quadcopters, introducing a novel SE2(3) model predictive controller and demonstrating its superior performance over existing methods in simulation and hardware tests.

Contribution

It presents a new SE2(3) model predictive controller for UAVs and provides a comprehensive comparison with existing Lie group-based control approaches in practical scenarios.

Findings

SE2(3) MPC achieves better trajectory tracking and robustness.

Comparable performance of SE2(3) MPC and LQR in simulation.

Superior real-time performance of the proposed MPC on hardware.

Abstract

This paper presents the integration and experimental validation of advanced control strategies for quadcopters based on Lie groups. We build upon recent theoretical developments on SE2(3)-based controllers and introduce a novel SE2(3) model predictive controller (MPC) that combines the predictive capabilities and constraint-handling of optimal control with the geometric properties of Lie group formulations. We evaluated this MPC against a state-of-the-art SE2(3)-based LQR approach and obtained comparable performance in simulation. Both controllers where also deployed on the Quanser QDrone platform and compared to each other and an industry standard control architecture. Results show that the SE_2(3) MPC achieves superior trajectory tracking performance and robustness across a range of scenarios. This work demonstrates the practical effectiveness of Lie group-based controllers and offers comparative insights into their impact on system behaviour and real-time performance