Lie Group Control Architectures for UAVs: A Comparison of SE <sub>2</sub> (3)-Based Approaches in Simulation and Hardware
Bibliographic record
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 SE<inf>2</inf>(3)-based controllers and introduce a novel SE<inf>2</inf>(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 SE<inf>2</inf>(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<inf>2</inf>(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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".