Skip to main content
Log in

PSO Based Optimal Gain Scheduling Backstepping Flight Controller Design for a Transformable Quadrotor

  • Regular Paper
  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

Transformable Unmanned Aerial Systems (UASs) are increasingly attracting attention in recent years due to their maneuverability, agility and morphological capacities. They have overcame many limitations such as, multi-tasks problem, structural adaptation in flight, energy consumption, fault tolerant control, and maneuverability. Nevertheless, their variable geometries as well as the great number of actuators make them highly nonlinear and over-actuated systems, which are characterized by a slow transformation mechanism, variable mathematical models, and complex design and control architectures. In this article, we propose a simple and lightweight design of a transformable quadrotor, which allows to increase the geometric adaptability in flight, maneuverability, and speed of the transformation process by exploiting fast and performant servomotors. Since the Center of Gravity (CoG) of the quadrotor varies according to the desired shape, it results in a variation of the inertia and the control matrix instantly. These parameters play a crucial role in the system control and its stability, which is substantially a key difference compared to the classic quadrotor. Thus, a new generic model will be developed, which takes into account all these variations together and the asymmetry of the configurations. To validate the developed model, ensure the stability of our quadrotor, and improve the performance of the linear control strategies applied to these new drones, an optimal gain scheduling backstepping controller based on Particle Swarm Optimization (PSO) algorithm will be designed and tested. The realized prototype will be presented at the end of this work.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Puri, A.: A survey of unmanned aerial vehicles (uav) for traffic surveillance. Department of computer science and engineering, University of South Florida, pp. 1–29 (2005)

  2. Floreano, D., Wood, R.J.: Science, technology and the future of small autonomous drones. Nature 521(7553), 460–466 (2015)

    Article  Google Scholar 

  3. Mintchev, S., Floreano, D.: Adaptive morphology: A design principle for multimodal and multifunctional robots. IEEE Robot. Autom. Mag. 23(3), 42–54 (2016)

    Article  Google Scholar 

  4. Yilmaz, E., Zaki, H., Unel, M.: Nonlinear adaptive control of an aerial manipulation system. In: 2019 18th European Control Conference (ECC), pp. 3916–3921. IEEE (2019)

  5. Derrouaoui, S.H., Bouzid, Y., Guiatni, M., Dib, I.: A comprehensive review on reconfigurable drones: Classification, characteristics, design and control technologies. Unmanned Syst., 1–27 (2021)

  6. Fasel, U., Keidel, D., Baumann, L., Cavolina, G., Eichenhofer, M., Ermanni, P.: Composite additive manufacturing of morphing aerospace structures. Manuf. Lett. 23, 85–88 (2020)

    Article  Google Scholar 

  7. Jimenez-Cano, A.E., Martin, J., Heredia, G., Ollero, A., Cano, R.: Control of an aerial robot with multi-link arm for assembly tasks. In: 2013 IEEE International Conference on Robotics and Automation, pp. 4916–4921. IEEE (2013)

  8. Suarez, A., Real, F., Vega, V.M., Heredia, G., Rodriguez-Casta no, A, Ollero, A.: Compliant bimanual aerial manipulation: Standard and long reach configurations. IEEE Access 8, 88844–88865 (2020)

    Article  Google Scholar 

  9. Derrouaoui, S.H., Guiatni, M., Bouzid, Y., Dib, I., Moudjari, N.: Dynamic modeling of a transformable quadrotor. In: 2020 International Conference on Unmanned Aircraft Systems (ICUAS), pp. 1714–1719. IEEE (2020)

  10. Derrouaoui, S.H., Bouzid, Y., Guiatni, M., Dib, I., Moudjari, N.: Design and modeling of unconventional quadrotors. In: 2020 28th Mediterranean Conference on Control and Automation (MED), pp. 721–726. IEEE (2020)

  11. Bucki, N., Mueller, M.W.: Design and control of a passively morphing quadcopter. In: 2019 International Conference on Robotics and Automation (ICRA), pp. 9116–9122. IEEE (2019)

  12. Lee, S., Giri, D.K., Son, H.: Modeling and control of quadrotor uav subject to variations in center of gravity and mass. In: 2017 14th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), pp. 85–90. IEEE (2017)

  13. Xiong, H., Hu, J., Diao, X.: Optimize energy efficiency of quadrotors via arm rotation. J. Dyn. Syst. Meas. Control. 141(9) (2019)

  14. Tang, P., Zhang, F., Ye, J., Lin, D.: An integral tsmc-based adaptive fault-tolerant control for quadrotor with external disturbances and parametric uncertainties. Aerosp. Sci. Technol. 109, 106415 (2021)

    Article  Google Scholar 

  15. Papadimitriou, A., Mansouri, S.S., Kanellakis, C., Nikolakopoulos, G.: Geometry aware nmpc scheme for morphing quadrotor navigation in restricted entrances. arXiv:2101.02965 (2021)

  16. Riviere, V., Manecy, A., Viollet, S.: Agile robotic fliers: A morphing-based approach. Soft Robot. 5(5), 541–553 (2018)

    Article  Google Scholar 

  17. Wang, B., Shen, Y., Zhang, Y.: Active fault-tolerant control for a quadrotor helicopter against actuator faults and model uncertainties. Aerosp. Sci. Technol. 99, 105745 (2020)

    Article  Google Scholar 

  18. Li, Z., Ma, X., Li, Y.: Robust trajectory tracking control for a quadrotor subject to disturbances and model uncertainties. Int. J. Syst. Sci. 51(5), 839–851 (2020)

    Article  MathSciNet  Google Scholar 

  19. Wang, B., Yu, X., Mu, L., Zhang, Y.: A dual adaptive fault-tolerant control for a quadrotor helicopter against actuator faults and model uncertainties without overestimation. Aerosp. Sci. Technol. 99, 105744 (2020)

    Article  Google Scholar 

  20. Shen, Z., Li, F., Cao, X., Guo, C.: Prescribed performance dynamic surface control for trajectory tracking of quadrotor uav with uncertainties and input constraints. Int. J. Control., 1–11 (2020)

  21. Labbadi, M., Cherkaoui, M.: Adaptive fractional-order nonsingular fast terminal sliding mode-based robust tracking control of quadrotor uav with gaussian random disturbances and uncertainties. IEEE Trans. Aerosp. Electron. Syst. (2021)

  22. Lu, Q., Ren, B., Parameswaran, S.: Uncertainty and disturbance estimator-based global trajectory tracking control for a quadrotor. IEEE/ASME Trans. Mechatron. 25(3), 1519–1530 (2020)

    Article  Google Scholar 

  23. Cheng, P., He, S., Stojanovic, V., Luan, X., Liu, F.: Fuzzy fault detection for markov jump systems with partly accessible hidden information: An event-triggered approach. IEEE Transactions on Cybernetics (2021)

  24. Falanga, D., Kleber, K., Mintchev, S., Floreano, D., Scaramuzza, D.: The foldable drone: A morphing quadrotor that can squeeze and fly. IEEE Robot. Autom. Lett. 4(2), 209–216 (2018)

    Article  Google Scholar 

  25. Mintchev, S., Daler, L., L’Eplattenier, G., Saint-Raymond, L., Floreano, D.: Foldable and self-deployable pocket sized quadrotor. In: 2015 IEEE International Conference on Robotics and Automation (ICRA), pp. 2190–2195. IEEE (2015)

  26. Bai, Y., Gururajan, S.: Evaluation of a baseline controller for autonomous “figure-8” flights of a morphing geometry quadcopter: Flight performance. Drones 3(3), 70 (2019)

    Article  Google Scholar 

  27. Desbiez, A., Expert, F., Boyron, M., Diperi, J., Viollet, S., Ruffier, F.: X-morf: A crash-separable quadrotor that morfs its x-geometry in flight. In: 2017 Workshop on Research, Education and Development of Unmanned Aerial Systems (RED-UAS), pp. 222–227. IEEE (2017)

  28. Wallace, D.A.: Dynamics and control of a quadrotor with active geometric morphing. Ph.D. Thesis, University of Washington (2016)

  29. Kamil, Y., Hazry, D., Wan, K., Razlan, Z.M., AB, S.: Design a new model of unmanned aerial vehicle quadrotor using the variation in the length of the arm. In: 2017 International Conference on Artificial Life and Robotics (ICAROB), pp. 723–726 (2017)

  30. Shi, F., Zhao, M., Murooka, M., Okada, K., Inaba, M.: Aerial regrasping: Pivoting with transformable multilink aerial robot. In: 2020 IEEE International Conference on Robotics and Automation (ICRA), pp. 200–207. IEEE (2020)

  31. Avant, T., Lee, U., Katona, B., Morgansen, K.: Dynamics, hover configurations, and rotor failure restabilization of a morphing quadrotor. In: 2018 Annual American Control Conference (ACC), pp. 4855–4862. IEEE (2018)

  32. Barbaraci, G.: Modeling and control of a quadrotor with variable geometry arms. J. Unmanned Veh. Syst. 3(2), 35–57 (2015)

    Article  Google Scholar 

  33. Zhao, M., Kawasaki, K., Chen, X., Noda, S., Okada, K., Inaba, M.: Whole-body aerial manipulation by transformable multirotor with two-dimensional multilinks. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), pp. 5175–5182. IEEE (2017)

  34. Raj, N., Banavar, R., Abhishek, Kothari, M.: Attitude control of novel tail sitter: Swiveling biplane–quadrotor. J. Guid. Control. Dyn. 43(3), 599–607 (2020)

    Article  Google Scholar 

  35. Wei, T., Li, X., Stojanovic, V.: Input-to-state stability of impulsive reaction–diffusion neural networks with infinite distributed delays. Nonlinear Dyn. 103(2), 1733–1755 (2021)

    Article  Google Scholar 

  36. Stojanovic, V., Nedic, N., Prsic, D., Dubonjic, L., Djordjevic, V.: Application of cuckoo search algorithm to constrained control problem of a parallel robot platform. Int. J. Adv. Manuf. Technol. 87 (9), 2497–2507 (2016)

    Article  Google Scholar 

  37. El Gmili, N., Mjahed, M., El Kari, A., Ayad, H.: Particle swarm optimization and cuckoo search-based approaches for quadrotor control and trajectory tracking. Appl. Sci. 9(8), 1719 (2019)

    Article  Google Scholar 

  38. Chen, C-C, Chen, Y-T: Feedback linearized optimal control design for quadrotor with multi-performances. IEEE Access 9, 26674–26695 (2021)

    Article  Google Scholar 

  39. Chiou, J-S, Tran, H-K, Shieh, M-Y, Nguyen, T-N: Particle swarm optimization algorithm reinforced fuzzy proportional–integral–derivative for a quadrotor attitude control. Adv. Mech. Eng. 8 (9), 1687814016668705 (2016)

    Article  Google Scholar 

  40. Nazaruddin, Y.Y., Andrini, A.D., Anditio, B.: Pso based pid controller for quadrotor with virtual sensor. IFAC-PapersOnLine 51(4), 358–363 (2018)

    Article  Google Scholar 

  41. Mohammadi, V., Ghaemi, S., Kharrati, H.: Pso tuned flc for full autopilot control of quadrotor to tackle wind disturbance using bond graph approach. Appl. Soft Comput. 65, 184–195 (2018)

    Article  Google Scholar 

  42. Sun, C., Liu, M., Liu, C., Feng, X., Wu, H.: An industrial quadrotor uav control method based on fuzzy adaptive linear active disturbance rejection control. Electronics 10(4), 376 (2021)

    Article  Google Scholar 

  43. Tran, V.P., Santoso, F., Garratt, M.A.: Adaptive trajectory tracking for quadrotor systems in unknown wind environments using particle swarm optimization-based strictly negative imaginary controllers. IEEE Trans. Aerosp. Electron. Syst. (2021)

  44. Márquez-Vega, L.A., Aguilera-Ruiz, M., Torres-Trevi no, L.M.: Multi-objective optimization of a quadrotor flock performing target zone search. Swarm Evol. Comput. 60, 100733 (2021)

    Article  Google Scholar 

  45. Lou, Y., Zhang, Y., Huang, R., Chen, X., Li, Z.: Optimization algorithms for kinematically optimal design of parallel manipulators. IEEE Trans. Autom. Sci. Eng. 11(2), 574–584 (2013)

    Article  Google Scholar 

  46. Tuna, T., Ovur, S.E., Gokbel, E., Kumbasar, T.: Folly: A self foldable and self deployable autonomous quadcopter. In: 2018 6th International Conference on Control Engineering & Information Technology (CEIT), pp. 1–6. IEEE (2018)

  47. Derrouaoui, S.H., Bouzid, Y., Guiatni, M., Kada, H., Dib, I., Moudjari, N.: Backstepping controller applied to a foldable quadrotor for 3d trajectory tracking. In: Proc. 17th Int. Conf. Informatics in Control, Automation and Robotics, vol. 1, pp. 537–544 (2020)

  48. Derafa, L., Madani, T., Benallegue, A.: Dynamic modelling and experimental identification of four rotors helicopter parameters. In: 2006 IEEE International Conference on Industrial Technology, pp. 1834–1839. IEEE (2006)

  49. Bangura, M., Mahony, R.: Nonlinear Dynamic Modeling for High Performance Control of a Quadrotor. In: Proceedings Australasian Conference on Robotics and Automation 2012. Australian Robotics and Automation Association (2012)

  50. Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39–43. IEEE (1995)

  51. Shi, Y., Eberhart, R.C.: Empirical study of particle swarm optimization. In: Proceedings of the 1999 congress on evolutionary computation-CEC99 (Cat. No. 99TH8406), vol. 3, pp. 1945–1950. IEEE (1999)

Download references

Author information

Authors and Affiliations

Authors

Contributions

Saddam Hocine Derrouaoui, Yasser Bouzid and Mohamed Guiatni, made this manuscript and did the research.

Corresponding author

Correspondence to Saddam Hocine Derrouaoui.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Consent for publication

All authors have read and agreed to publish this work.

Consent to participate

All authors have read and agreed to publish this work.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Derrouaoui, S.H., Bouzid, Y. & Guiatni, M. PSO Based Optimal Gain Scheduling Backstepping Flight Controller Design for a Transformable Quadrotor. J Intell Robot Syst 102, 67 (2021). https://doi.org/10.1007/s10846-021-01422-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-021-01422-1

Keywords

Navigation