Skip to main content
SpringerLink
Log in

Nonlinear Model Predictive Control on SE(3) for Quadrotor Aggressive Maneuvers

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

Abstract

Applications involving Unmanned Aerial Vehicles (UAVs) have increasingly required faster and more accurate movements to reduce flight time and to improve efficiency in the obstacle avoidance capability. In this context, this work proposes a nonlinear model predictive control (NMPC) strategy formulated on the Special Euclidean group SE(3) for quadrotor trajectory tracking within cluttered environments with unknown obstacles. The approach considers constraints in the states and inputs, with constant disturbance rejection and capable of executing aggressive maneuvers. The UAV attitude is considered as an optimization variable within the control problem thanks to an algebraic ellipsoidal set approach. As a consequence, the collision check takes the UAV attitude into account, allowing aggressive maneuvers. Numerical experiments under realistic conditions allow evaluating the performance of the proposed approach for the UAV. The tested maneuvers are throwing a narrow gap, passing by a nonconvex obstacle gap, avoiding a convex obstacle, and doing slalom movements. In all cases, uncertainties are considered. The achieved results indicate the advantages of executing aggressive maneuvers.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Similar content being viewed by others

Data Availability

All data necessary to reproduce the results are given in the paper.

References

  1. Alexis, K., Nikolakopoulos, G., Tzes, A.: Switching model predictive attitude control for a quadrotor helicopter subject to atmospheric disturbances. Control. Eng. Pract. 19(10), 1195–1207 (2011)

    Article  Google Scholar 

  2. Andersson, J.A.E., Gillis, J., Horn, G., Rawlings, J.B., Diehl, M.: CasADi – a software framework for nonlinear optimization and optimal control. Mathematical Programming Computation 11(1), 1–36 (2019)

    Article  MathSciNet  Google Scholar 

  3. Bock, H., Plitt, K.: A multiple shooting algorithm for direct solution of optimal control problems. IFA Proceedings Volumes 17(2), 1603–1608 (1984). 9th IFAC World congress: A Bridge Between Control Science and Technology, Budapest, Hungary, 2-6 July 1984

    Article  Google Scholar 

  4. Caravantes, J., Gonzalez-Vega, L.: On the interference problem for ellipsoids: experiments and applications. In: Mathematical Software – ICMS 2018, pp 89–97. Springer International Publishing, Berlin (2018)

  5. Castilho, A., Sanz, R., Garcia, P., Qiu, W., Wang, H., Xu, C.: Disturbance observer-based quadrotor attitude tracking control for aggressive maneuvers. Control. Eng. Pract. 82, 14–23 (2019)

    Article  Google Scholar 

  6. Eskandarpour, A., Sharf, I.: A constrained error-based MPC for path following of quadrotor with stability analysis. Nonlinear Dynamics 99, 899–918 (2020)

    Article  Google Scholar 

  7. Ferreau, H.J., Kirches, C., Potschka, A., Bock, H.G., Diehl, M.: qpoases: a parametric active-set algorithm for quadratic programming. Math. Program. Comput. 6(4), 327–363 (2014)

    Article  MathSciNet  Google Scholar 

  8. Foehn, P., Scaramuzza, D.: Onboard state dependent LQR for agile quadrotors. In: IEEE International Conference on Robotics and Automation (ICRA), pp 6566–6572 (2018)

  9. Goodarzi, F., Lee, D., Lee, T.: Geometric adaptive tracking control of a quadrotor unmanned aerial vehicle on SE(3) for agile maneuvers. Journal of Dynamic Systems, Measurement, and Control 137(9), 1–12 (2015)

    Article  Google Scholar 

  10. Kamel, M., Alexis, K., Achtelik, M., Siegwart, R.: Fast nonlinear model predictive control for multicopter attitude tracking on SO(3). In: 2015 IEEE Conference on Control Applications (CCA), pp 1160–1166. IEEE (2015)

  11. Lee, T.: Global exponential attitude tracking controls on SO(3). IEEE Trans. Autom. Control 60(10), 2837–2842 (2015)

    Article  MathSciNet  Google Scholar 

  12. Liu, S., Mohta, K., Atanasov, N., Kumar, V.: Search-based motion planning for aggressive flight in SE(3). IEEE Robotics and Automation Letters 3(3), 2439–2446 (2018)

    Article  Google Scholar 

  13. Loianno, G., Brunner, C., McGrath, G., Kumar, V.: Estimation, control, and planning for aggressive flight with a small quadrotor with a single camera and IMU. IEEE Robotics and Automation Letters 2(2), 404–411 (2017)

    Article  Google Scholar 

  14. Lu, G.: Aggressive attitude control of unmanned rotor helicopters using a robust controller. Journal of Intelligent & Robotic Systems 80(1), 165–180 (2015)

    Article  Google Scholar 

  15. Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M.: Constrained model predictive control: stability and optimality. Automatica 36(6), 789–814 (2000)

    Article  MathSciNet  Google Scholar 

  16. Mellinger, D., Michael, N., Kumar, V.: Trajectory generation and control for precise aggressive maneuvers with quadrotors. The International Journal of Robotics Research 31(5), 664–674 (2012)

    Article  Google Scholar 

  17. Morrell, B., Rigter, M., Merewether, G., Reid, R., Thakker, R., Tzanetos, T., Rajur, V., Chamitoff, G.: Differential flatness transformations for aggressive quadrotor flight. In: IEEE International Conference on Robotics and Automation (ICRA), pp 1–7 (2018)

  18. Murilo, A., Lopes, R.V.: Unified NMPC framework for attitude and position control for a VTOL UAV. Proceedings of the Institution of Mechanical Engineers Part I: Journal of Systems and Control Engineering (2019)

  19. Nascimento, I.B.P., Ferramosca, A., Pimenta, L.C.A., Raffo, G.V.: NMPC strategy for a quadrotor UAV in a 3D unknown environment. In: 2019 19th International Conference on Advanced Robotics (ICAR) (2019)

  20. Paul, R.P.: Robot Manipulators - Mathematics, Programming and Control. MIT Press, Cambridge (1981)

    Google Scholar 

  21. Pereira, J.C., Leite, V.J.S., Raffo, G.V.: Nonlinear model predictive control on SE(3) for quadrotor trajectory tracking and obstacle avoidance. In: 2019 19th International Conference on Advanced Robotics (ICAR), pp 155–160 (2019)

  22. Raffo, G.V.: Robust control strategies for a quadrotor helicopter: an underactuated mechanical system. PhD Thesis, Universid de Sevilha (2011)

  23. Raffo, G.V., Ortega, M.G., Rubio, F.: An integral predictive/nonlinear \({\mathscr{H}}_{\infty }\) control structure for a quadrotor helicopter. Automatica 46(1), 29–39 (2010)

    Article  MathSciNet  Google Scholar 

  24. Rawlings, J.B., Mayne, D.Q., Diehl, M.: Model Predictive control: Theory, Computation and Design. Nob Hill Publishing, LLC, 2nd edition (2017)

  25. Ru, P., Subbarao, K.: Nonlinear model predictive control for unmanned aerial vehicles. Aerospace 4(2) (2017)

  26. Santos, M.A.: Tube-based MPC with economical criteria for load transportation tasks using tilt-rotor UAVs. Master Thesis, UFMG (2018)

  27. Sathya, A., Sopasakis, P., Parys, R.V., Themelis, A., Pipeleers, G., Patrinos, P.: Embedded nonlinear model predictive control for obstacle avoidance using panoc. In: 2018 European Control Conference (ECC), pp. 1523–1528 (2018)

  28. Shim, D.H., Kim, H.J., Sastry, S.: Decentralized nonlinear model predictive control of multiple flying robots. In: 42nd IEEE International Conference on Decision and Control, vol. 4, pp. 3621–3626 (2003)

  29. Simo, J., u-Quoc, L.: On the dynamics in space of rods undergoing large motions — a geometrically exact approach. Comput. Methods Appl. Mech. Eng. 66(2), 125–161 (1988)

    Article  MathSciNet  Google Scholar 

  30. Small, E., Sopasakis, P., Fresk, E., Patrinos, P., Nikolakopoulos, G.: Aerial navigation in obstructed environments with embedded nonlinear model predictive control. In: 2019 18th European Control Conference (ECC), pp. 3556–3563 (2019)

  31. Sánchez, I., Ferramosca, A., Raffo, G.V., González, A.H., D’Jorge, A.: Obstacle avoiding path following based on nonlinear model predictive control using artificial variables. In: 2019 19th International Conference on Advanced Robotics (ICAR), pp. 254–259 (2019)

  32. Wang, W., Wang, J., Kim, M.: An algebraic condition for the separation of two ellipsoids. Computer Aided Geometric Design 18(6), 531–539 (2001)

    Article  MathSciNet  Google Scholar 

  33. Wang, Y., Ramirez-Jaime, A., Xu, F., Puig, V.: Nonlinear model predictive control with constraint satisfactions for a quadcopter. In: Journal of Physics: Conference Series, vol. 783, pp. 012–025 (2017)

  34. Wächter, A.: An interior point algorithm for large-scale non linear optimization with applications in process engineering. PhD Dissertation, Carnegie Mellon University (2002)

  35. Yu, G., Cabecinhas, D., Cunha, R., Silvestre, C.: Quadrotor trajectory generation and tracking for aggressive maneuvers with attitude constraints. IFAC-PapersOnLine 52(12), 55–60 (2019). 21st IFAC Symposium on Automatic Control in Aerospace ACA 2019

    Article  Google Scholar 

Download references

Funding

This work was in part supported by the project INCT (National Institute of Science and Technology) under the grant CNPq (Brazilian National Research Council) 465755/2014-3, FAPESP, Brazil 2014/50851-0. This work was also partially supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil (Finance Code 88887.136349/2017-00), CNPq, Brazil (grant numbers 426392/2016-7, 313568/2017-0, 311208/2019-3), and FAPEMIG, Brazil (grant number APQ-03090-17).

Author information

Authors and Affiliations

  1. Graduate Program in Electrical Engineering, Federal University of Minas Gerais (UFMG), Belo Horizonte, MG, 31270-901, Brazil

    Jean C. Pereira & Guilherme V. Raffo

  2. Department of Mechatronics Engineering, CEFET-MG/Campus Divinopolis, Divinopolis, MG, 35503-822, Brazil

    Jean C. Pereira & Valter J. S. Leite

  3. Department of Electronic Engineering, Federal University of Minas Gerais (UFMG), Belo Horizonte, MG, 31270-901, Brazil

    Guilherme V. Raffo

Authors
  1. Jean C. Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Valter J. S. Leite
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guilherme V. Raffo
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception, control design and analysis. Coding and numerical experiments were performed by Jean Carlos Pereira. The first draft of the manuscript was written by Jean Carlos Pereira and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Jean C. Pereira.

Ethics declarations

Conflict of Interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Ethical approval

Not applicable.

Consent to participate

Not applicable.

Consent to publish

Not applicable.

Additional information

Publisher’s Note

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

Electronic supplementary material

Below is the link to the electronic supplementary material.

(MP4 10.1 MB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pereira, J.C., Leite, V.J.S. & Raffo, G.V. Nonlinear Model Predictive Control on SE(3) for Quadrotor Aggressive Maneuvers. J Intell Robot Syst 101, 62 (2021). https://doi.org/10.1007/s10846-021-01310-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-021-01310-8

Keywords

Search

Navigation