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

2025-11-19

AI Summary

To address the demand for high-precision and robust trajectory tracking in quadrotor UAVs, this paper proposes a nonlinear Model Predictive Controller (MPC) formulated on the SE(2,3) Lie group manifold. Unlike conventional Euclidean-space modeling, the approach unifies pose and velocity representation on SE(2,3), explicitly preserving the system’s geometric structure while incorporating optimal control objectives and kinematic constraints. Extensive simulation and real-time hardware experiments are conducted on the Quanser QDrone platform. Results demonstrate that the proposed SE(2,3) MPC achieves significantly improved tracking accuracy—reducing average tracking error by 37%—and enhanced disturbance rejection compared to classical LQR and industrial-grade PID controllers, all while satisfying real-time requirements (≤5 ms per optimization step). The key contribution is the first systematic implementation and experimental validation of an SE(2,3)-geometric MPC on a physical quadrotor platform, thereby confirming the feasibility and superiority of Lie group–based control in resource-constrained embedded systems.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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

Problem

• Developing Lie group control architectures for UAV quadcopter systems
• Comparing SE2(3)-based MPC and LQR controllers in simulation and hardware
• Evaluating trajectory tracking performance and robustness of geometric controllers

Innovation

• Novel SE2(3) MPC combining geometric properties with optimal control
• SE2(3) MPC achieves superior trajectory tracking and robustness
• Experimental validation on Quanser QDrone platform demonstrates practical effectiveness