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

Dimitria Silveria, Kleber Cabral, Peter Jardine, Sidney Givigi

TL;DR

This work advances Lie group-based UAV control by developing a novel SE$_2$(3) MPC that extends prior SE$_2$(3) LQR methods. It provides a unified framework for modeling quadrotor dynamics on SE$_2$(3), implementing left-invariant error dynamics, and solving a constrained quadratic program over a moving horizon. Through extensive simulation and hardware experiments on the Quanser QDrone, the SE$_2$(3) MPC demonstrates superior trajectory tracking and robustness, particularly in altitude control, compared to both SE$_2$(3) LQR and the industry-standard controller. The results underscore the practical viability of Lie group-based controllers for real-time UAV operation and offer a detailed comparison of control architectures in both synthetic and real-world settings.

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

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

TL;DR

This work advances Lie group-based UAV control by developing a novel SE(3) MPC that extends prior SE(3) LQR methods. It provides a unified framework for modeling quadrotor dynamics on SE(3), implementing left-invariant error dynamics, and solving a constrained quadratic program over a moving horizon. Through extensive simulation and hardware experiments on the Quanser QDrone, the SE(3) MPC demonstrates superior trajectory tracking and robustness, particularly in altitude control, compared to both SE(3) LQR and the industry-standard controller. The results underscore the practical viability of Lie group-based controllers for real-time UAV operation and offer a detailed comparison of control architectures in both synthetic and real-world settings.

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

Paper Structure

This paper contains 17 sections, 27 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Lie Groups
  4. Nomenclature
  5. Dynamics of the Quadcopter
  6. Controller in the Special Euclidean Group
  7. Model Predictive Control
  8. System-Level Architecture
  9. Experiments
  10. Simulation Setup and Parameters
  11. Real Experiment Parameters
  12. Results
  13. Simulation
  14. Real-world Experimental Validation
  15. From Simulation to Real World Analysis
  16. ...and 2 more sections

Figures (8)

  • Figure 1: Block diagram containing the control system used in this work to control a real quadcopter
  • Figure 2: Test area used for all the experiments in the real UAV in this work, and the quadcopter used for the experiments
  • Figure 3: (a) Simulated behavior of the baseline SE$_2$(3) LQR vs. (b) simulated behavior of the proposed SE$_2$(3) MPC.
  • Figure 4: QDrone 3D trajectory controlled by (a) Default QDrone Controller, (b) baseline SE$_2$(3) LQR, and (c) SE$_2$(3) MPC.
  • Figure 5: $X$, $Y$, and $Z$ trajectories over time, executed by Qdrone when controlled by the Default QDrone Controller.
  • ...and 3 more figures