Observer-based control of 3DOF hover evolving on Lie group: design, optimization, and real-time implementation

This research presents an innovative methodology for designing, optimizing, and implementing observer-based control systems for 3DOF hover Unmanned Aerial Vehicles (UAVs) using Lie group modeling. When addressing the challenges of nonlinear dynamics and system uncertainties, the study leverages the inherent geometric structure of Lie groups, allowing rotation and translation to be modeled naturally on SO(3) and SE(3) manifolds. This ensures geometric consistency and avoids the singularities and drift associated with conventional approaches. The proposed framework integrates a geometric observer, operating directly on the Lie group manifold with a family of controllers including PID, LQR, and Back-stepping whose parameters are systematically tuned using Multiobjective Particle Swarm Optimization (MPSO). Extensive simulations and real-time experiments on a Quanser 3-DOF Hover platform demonstrate that the proposed approach delivers substantial improvements over traditional Euclidean observer-controller schemes, achieving up to 48% reduction in estimation error, 51% faster convergence, and 16% lower energy consumption. The system also exhibits superior trajectory tracking and disturbance rejection under varied operational conditions. These results validate not only the practical feasibility but also the significant advantages of Lie group-based observer-controller design, offering a robust and energy-efficient solution for advanced UAV applications requiring high precision, resilience, and reliability.