Skip to main content
Have a personal or library account? Click to login
Observer-based control of 3DOF hover evolving on Lie group: design, optimization, and real-time implementation Cover

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

Open Access
|Oct 2026
Read online

References

  1. Ayanian, N. and Kumar, V. (2011) Synthesis of feedback controllers for aerial robots. IEEE Transactions on Robotics, 27, 5, 855–866.
  2. Barrau, A. and Bonnabel, S. (2017) The invariant extended Kalman filter as a stable observer. IEEE Transactions on Automatic Control, 62, 11, 2911–2926.
  3. Brockett, R. W. (1972) System Theory on Group Manifolds and Coset Spaces. Academic Press.
  4. Bullo, F. and Lewis, A. D. (2004) Geometric Control of Mechanical Systems. New York: Springer-Verlag.
  5. Campos, E., Chemori, A., Creuze, V., Torres, J. and Lozano, R. (2017) Saturation based nonlinear depth and yaw control of underwater vehicles with stability analysis and real-time experiments. Mechatronics, 45, 49–59.
  6. Dong, X., Yu, B., Shi, Z. and Zhong, Y. (2015) Nonlinear tracking control of unmanned aerial vehicles with model uncertainties and disturbances via adaptive backstepping. IEEE Transactions on Aerospace and Electronic Systems, 51, 3, 2126–2137.
  7. Dong, X., Yu, B. and Ren, Z. (2025) SE(3)-based backstepping control for quadrotor UAVs under actuator failure with global convergence guarantees. IEEE/CAA Journal of Automatica Sinica, 12, 1, 89–104.
  8. Goffin, N., Condomines, J.-P. and Salaun, E. (2024) Iterated invariant extended Kalman filter: Convergence analysis and applications to UAV state estimation. IEEE Transactions on Aerospace and Electronic Systems, 60, 3, 2245–2258.
  9. Goodarzi, F., Lee, D. and Lee, T. (2013) Geometric nonlinear pid control of a quadrotor uav on se (3). In: 2013 European control conference (ECC), 3845–3850, IEEE.
  10. Hall, B. C. (2015) Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, 2nd ed. Springer.
  11. Hashim, M., Al-Zahrani, A. and Khan, I. (2023) Observer-based robust control of quadrotor UAVs with disturbance estimation. Control Engineering Practice, 138, 105603.
  12. Hsiang, W.-Y. (2017) Lectures on Lie Groups. World Scientific.
  13. Hsiang-Sheng, W. et al. (2017) Lectures on Lie Groups and Lie Algebras. American Mathematical Society.
  14. Huang, L., Wang, S. and Chen, M. (2025) Geometric control on Lie groups: Theory and applications to robotics. Foundations and Trends in Robotics and Control, 15, 1, 1–98.
  15. Instruments, T. (2026) Real-time control implementation: Principles, practices, and performance analysis. Application Note SPRA765.
  16. Kadri, K., Boudjema, F., Bouzid, Y., Ghazali, M. and Sahouli, H. (2023a) Active disturbance rejection control of unconventional quadrotor based on grey wolf optimization algorithm. In: 2023 International Conference on Advances in Electronics, Control and Communication Systems (ICAECCS), 1–7, IEEE.
  17. Kadri, K., Boudjema, F., Bouzid, Y., Ouahab, B. and Draris, H. I. (2023b) A linear active disturbance rejection control based pso to control twin rotor mimo system with experimental validation. In: 2023 International Conference on Electrical Engineering and Advanced Technology (ICEEAT), 1, 1–7, IEEE.
  18. Kadri, K., Boudjema, F., Nail, B. and Tibermacine, I. E. (2025) Optimal blockmode assignment and relocation in matrix polynomials for observerbased static and dynamic multivariable feedback compensators. Control & Cybernetics, 54, 3.
  19. Kadri, K., Boudjema, F., Tibermacine, I. E., Bouzid, Y., Nail, B., Napoli, C. and Rabehi, A. (2026) ADRC parameters tuning using traditional and AI-based methods: A survey. IEEE Access, 14, 5152–5179.
  20. Kadri, K., Bouzid, Y., Derrouaoui, S. H., Tibermacine, I. E., et al. (2026) Adrcbackstepping with sliding mode observer for reconfigurable quadrotor: Design and optimization. Journal of Vibration Testing and System Dynamics, 10, 01, 13–33.
  21. Kennedy, J. and Eberhart, R. (1995) Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Networks, 4, 1942–1948.
  22. Krstić, M., Kanellakopoulos, I. and Kokotović, P. (1995) Nonlinear and adaptive control design. In: Proceedings of the 34th IEEE Conference on Decision and Control, 761–767.
  23. Kumar, E. V. and Jerome, J. (2013) Robust lqr controller design for stabilizing and trajectory tracking of inverted pendulum. Procedia Engineering, 64, 169–178.
  24. Lee, T., Leok, M. and McClamroch, N. H. (2010) Geometric tracking control of a quadrotor uav on se (3). In: 49th IEEE Conference on Decision and Control (CDC), 5420–5425, IEEE.
  25. Lee, T. (2011) Robust adaptive geometric tracking controls on so (3) with an application to the attitude dynamics of a quadrotor uav. arXiv preprint arXiv:1108.6031
  26. Li, Q., Wei, Q. and Liu, D. (2022) Disturbance observer-based control with energy awareness for unmanned aerial vehicles. IEEE Transactions on Industrial Electronics, 69, 10, 10545–10555.
  27. Li, J., Ren, C. and Zhang, L (2024) UniQuad: Geometric control implementation on embedded systems for autonomous quadrotors. IEEE Robotics and Automation Letters, 9, 4, 3125–3132.
  28. Li, S., Chen, X. and Zhao, H. (2025) Navigation variable-based multi-objective particle swarm optimization for UAV path planning with kinematic constraints. IEEE Transactions on Evolutionary Computation, 29, 2, 567–582.
  29. Li, Z., Peng, Y. and Wu, L. (2025) Persistent exploration particle swarm optimization: Entropy-guided parameter adaptation for dynamic optimization. Swarm and Evolutionary Computation, 64, 101145.
  30. Li, M., Zhang, W. and Huang, S. (2025) Adaptive invariant observer framework for nonlinear systems on Lie groups with time-varying uncertainty. Automatica, 162, 111428.
  31. Liu, C., Maithripala, D. and Jayasuriya, S. (2025) Global stability of observerbased control systems on Lie groups with application to SE(3) dynamics. SIAM Journal on Control and Optimization, 63, 2, 891–918.
  32. Mahony, R., Kumar, V. and Corke, P. (2012) Multirotor aerial vehicles: Modeling, estimation, and control of quadrotor. IEEE Robotics and Automation Magazine, 19, 3, 20–32.
  33. Maithripala, D. H. S., Berg, J. M. and Dayawansa, W. P. (2014) An intrinsic observer-based stabilization of a class of nonlinear systems. IEEE Transactions on Automatic Control, 54, 9, 2133–2146.
  34. Maithripala, D. S. and Berg, J. M. (2015) An intrinsic pid controller for mechanical systems on lie groups. Automatica, 54, 189–200.
  35. Park, J., Kim, S., Lee, et al., H. (2025) Nonlinear control of quadrotor UAVs under Rotor Failure: Fault-Tolerant geometric control on SE(3). Nature Machine Intelligence, 7, 1, 45–58.
  36. Rashad, R., Califano, F. and Stramigioli, S. (2019) Port-Hamiltonian passivity based control on se (3) of a fully actuated uav for aerial physical interaction near-hovering. IEEE Robotics and Automation Letters, 4, 4, 4378–4385.
  37. Sun, Y., Xue, B., Zhang, M. and Yen, G. G. (2018) A particle swarm optimization-based flexible convolutional autoencoder for image classification. IEEE Transactions on Neural Networks and Learning Systems, 30, 8, 2295–2309.
  38. Valencia-Rodrıguez, D. C. and Coello Coello, C. A. (2020) A study of swarm topologies and their influence on the performance of multi-objective particle swarm optimizers. In: International Conference on Parallel Problem Solving from Nature, 285–298, Springer.
  39. Wang, X., Chen, Y. and Liu, Z. (2025) Disturbance observer-based geometric tracking control on SE(3) for quadrotor UAVs. Advances in Control Theory and Application, 25, 1, 45–67.
  40. Xu, H., Zhang, X. and Liu, L. (2020) Multiobjective particle swarm optimization for PID parameter tuning of quadrotor UAVs. IEEE Access, 8, 76895–76908.
  41. Xin, B., Lu, S., He, Y., Wang, Q. and Deng, F. (2023) Automatic design of dynamic collaboration strategies for machines and automated guided vehicles via multiobjective genetic programming. Unmanned Systems 13 (1), 233–246. doi:10.1142/S2301385025500153.
  42. Zhang, Y., Zhang, X. and Liu, Z. (2022) Quadcopter control with extended state observer and backstepping under nonlinear dynamics. IEEE Transactions on Control Systems Technology, 30, 5, 2171–2183.
  43. Zhang, T., Tan, Y., Chen, X. and Gu, G. (2024) Visual observer-based statefeedback autonomous motion control on se (3). Unmanned Systems, 12, 02, 375–390.
  44. Zhang, Y., Wang, Q. and Liu, J. (2025) Robust sliding mode observer design on SO(3) for attitude estimation under external perturbations. Journal of Guidance, Control, and Dynamics, 48, 2, 312–325.
DOI: https://doi.org/10.2478/candc-2026-0007 | Journal eISSN: 1314-4081 | Journal ISSN: 1311-9702 (formerly 1314-4081)
Language: English
Page range: 139 - 229
Submitted on: Sep 1, 2025
Accepted on: Apr 1, 2026
Published online: Oct 31, 2026
Published in print: Jun 1, 2026
Published by: Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
In partnership with: Paradigm Publishing Services

© 2026 Kamel Kadri, Bachir Nail, Farès Boudjema, Mohamed Tadjine, Imad Eddine Tibermacine, Salah Eddine Hellal, published by Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.