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Stabilization and Tracking Control Algorithms for VTOL Aircraft: Theoretical and Practical Overview

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Abstract

Control theory applied to multirotor aerial systems (MAS) has gained attention with the recent increase on the power computation for embedded systems. These systems are now able to perform the calculations needed for a variety of control techniques, with lower cost of sensors and actuators. These types of control algorithms are applied to the position and the attitude of MAS. In this paper, a brief overview evaluation of popular control algorithms for multirotor aerial systems, especially for VTOL - Vertical Take-Off and Landing aircraft, is presented. The main objective is to provide a unified and accessible analysis, placing the classical model of the VTOL vehicle and the studied control methods into a proper context. In addition, to provide the basis for beginner users working in aerial vehicles. In addition, this work contributes in presenting a comprehensive analysis of the implementation for the Nonlinear and Linear Backstepping, Nested Saturation and the Hyperbolic Bounded Controllers. These techniques are selected and compared to evaluate the performance of the aircraft, by simulations and experimental studies.

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References

  1. Abaunza, H., Ibarra, E., Castillo, P., Victorino, A.: Quaternion based control for circular uav trajectory tracking, following a ground vehicle: Real-time validation. IFAC-PapersOnLine 50(1), 11,453–11,458 (2017). https://doi.org/10.1016/j.ifacol.2017.08.1816. 20th IFAC World Congress

    Article  Google Scholar 

  2. Ailon, A.: Simple tracking controllers for autonomous vtol aircraft with bounded inputs. IEEE Trans. Autom. Control 55(3), 737–743 (2010). https://doi.org/10.1109/TAC.2010.2040493

    Article  MathSciNet  MATH  Google Scholar 

  3. Amin, R., Aijun, L., Shamshirband, S.: A review of quadrotor uav: control methodologies and performance evaluation. International Journal of Automation and Control 10(2), 87–103 (2016). https://doi.org/10.1504/IJAAC.2016.076453. PMID: 76453

    Article  Google Scholar 

  4. Ansari, U., Bajodah, A. H.: Tracking control of quadrotor using generalized dynamic inversion with constant-proportional rate reaching law. In: 2019 1st International Conference on Unmanned Vehicle Systems-Oman (UVS), pp. 1–7. https://doi.org/10.1109/UVS.2019.8658292 (2019)

  5. Antonio-Toledo, M.E., Sanchez, E.N., Alanis, A.Y., Flórez, J., Perez-Cisneros, M.A.: Real-time integral backstepping with sliding mode control for a quadrotor uav. IFAC-PapersOnLine 51(13), 549–554 (2018). https://doi.org/10.1016/j.ifacol.2018.07.337. 2nd IFAC Conference on Modelling, Identification and Control of Nonlinear Systems MICNON 2018

    Article  Google Scholar 

  6. Beikzadeh, H., Liu, G.: Trajectory tracking of quadrotor flying manipulators using l1 adaptive control. J. Franklin Inst. 355(14), 6239–6261 (2018). https://doi.org/10.1016/j.jfranklin.2018.06.011https://doi.org/10.1016/j.jfranklin.2018.06.011

    Article  MathSciNet  Google Scholar 

  7. Castillo, P., Lozano, R., Dzul, A. E.: Modelling and Control of Mini-Flying Machines. Springer, London (2006)

    Google Scholar 

  8. Chen, F., Lu, F., Jiang, B., Tao, G.: Adaptive compensation control of the quadrotor helicopter using quantum information technology and disturbance observer. J. Franklin Inst. 351(1), 442–455 (2014). https://doi.org/10.1016/j.jfranklin.2013.09.009

    Article  MATH  Google Scholar 

  9. Das, A., Subbarao, K., Lewis, F.: Dynamic inversion with zero-dynamics stabilisation for quadrotor control. IET Control Theory Applications 3(3), 303–314 (2009). https://doi.org/10.1049/iet-cta:20080002

    Article  MathSciNet  Google Scholar 

  10. de Crousaz, C., Farshidian, F., Neunert, M., Buchli, J.: Unified motion control for dynamic quadrotor maneuvers demonstrated on slung load and rotor failure tasks. In: 2015 IEEE International Conference on Robotics and Automation (ICRA), pp. 2223–2229. https://doi.org/10.1109/ICRA.2015.7139493 (2015)

  11. Escareño, J., Salazar, S., Romero, H., Lozano, R.: Trajectory control of a quadrotor subject to 2d wind disturbances. Journal of Intelligent & Robotic Systems 70(1), 51–63 (2013). https://doi.org/10.1007/s10846-012-9734-1

    Article  Google Scholar 

  12. Faessler, M., Falanga, D., Scaramuzza, D.: Thrust mixing, saturation, and body-rate control for accurate aggressive quadrotor flight. IEEE Robotics and Automation Letters 2(2), 476–482 (2017). https://doi.org/10.1109/LRA.2016.2640362

    Article  Google Scholar 

  13. Faessler, M., Franchi, A., Scaramuzza, D.: Differential flatness of quadrotor dynamics subject to rotor drag for accurate tracking of high-speed trajectories. IEEE Robotics and Automation Letters 3(2), 620–626 (2018). https://doi.org/10.1109/LRA.2017.2776353

    Article  Google Scholar 

  14. Gandolfo, D. C., Salinas, L. R., Toibero, J.M.: Stable path-following control for a quadrotor helicopter considering energy consumption. IEEE Transactions on Control Systems Technology 25(4), 1423–1430 (2017). https://doi.org/10.1109/TCST.2016.2601288

    Article  Google Scholar 

  15. Guerrero-Castellanos, J., Marchand, N., Hably, A., Lesecq, S., Delamare, J.: Bounded attitude control of rigid bodies: Real-time experimentation to a quadrotor mini-helicopter. Control. Eng. Pract. 19(8), 790–797 (2011). https://doi.org/10.1016/j.conengprac.2011.04.004

    Article  Google Scholar 

  16. Hehn, M., D’Andrea, R.: Real-time trajectory generation for interception maneuvers with quadrocopters. In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4979–4984. https://doi.org/10.1109/IROS.2012.6386093 (2012)

  17. Heredia, G., Jimenez-Cano, A. E., Sanchez, I., Llorente, D., Vega, V., Braga, J., Acosta, J. A., Ollero, A.: Control of a multirotor outdoor aerial manipulator. In: 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3417–3422. https://doi.org/10.1109/IROS.2014.6943038 (2014)

  18. Ibarra-Jimenez, E., Castillo, P.: Aerial autonomous catching ball using a nested second order sliding mode control. IFAC-PapersOnLine 50(1), 11,415–11,420 (2017). https://doi.org/10.1016/j.ifacol.2017.08.1805. 20th IFAC World Congress

    Article  Google Scholar 

  19. Kara-Mohamed, M.: Advanced trajectory tracking for uavs using combined feedforward/feedback control design. Robot. Auton. Syst. 96, 143–156 (2017). https://doi.org/10.1016/j.robot.2017.07.009

    Article  Google Scholar 

  20. Khalil, H. K.: Nonlinear Systems, 3rd edn. Prentice Hall, Upper Saddle River (2002)

    MATH  Google Scholar 

  21. Lab, H.: Fl-air - framework libre air. https://devel.hds.utc.fr/software/flair (2012)

  22. L’Afflitto, A., Anderson, R.B., Mohammadi, K.: An introduction to nonlinear robust control for unmanned quadrotor aircraft: How to design control algorithms for quadrotors using sliding mode control and adaptive control techniques. IEEE Control. Syst. Mag. 38(3), 102–121 (2018). https://doi.org/10.1109/MCS.2018.2810559

    Article  MathSciNet  Google Scholar 

  23. Lee, H., Kim, H. J.: Trajectory tracking control of multirotors from modelling to experiments: A survey. International Journal of Control, Automation and Systems 15(1), 281–292 (2017). https://doi.org/10.1007/s12555-015-0289-3

    Article  Google Scholar 

  24. Lei, W., Li, C., Chen, M. Z. Q.: Robust adaptive tracking control for quadrotors by combining pi and self-tuning regulator. IEEE Trans. Control Syst. Technol. 27(6), 2663–2671 (2019). https://doi.org/10.1109/TCST.2018.2872462

    Article  Google Scholar 

  25. 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). https://doi.org/10.1109/LRA.2016.2633290

    Article  Google Scholar 

  26. Lu, H., Liu, C., Coombes, M., Guo, L., Chen, W.: Online optimisation-based backstepping control design with application to quadrotor. IET Control Theory Applications 10(14), 1601–1611 (2016). https://doi.org/10.1049/iet-cta.2015.0976

    Article  MathSciNet  Google Scholar 

  27. Ma, D., Xia, Y., Shen, G., Jia, Z., Li, T.: Flatness-based adaptive sliding mode tracking control for a quadrotor with disturbances. J. Franklin Inst. 355(14), 6300–6322 (2018). https://doi.org/10.1016/j.jfranklin.2018.06.018

    Article  MathSciNet  MATH  Google Scholar 

  28. Mac, T. T., Copot, C., Keyser, R. D., Ionescu, C. M.: The development of an autonomous navigation system with optimal control of an uav in partly unknown indoor environment. Mechatronics 49, 187–196 (2018). https://doi.org/10.1016/j.mechatronics.2017.11.014

    Article  Google Scholar 

  29. Mellinger, D., Kumar, V.: Minimum snap trajectory generation and control for quadrotors. In: 2011 IEEE International Conference on Robotics and Automation, pp. 2520–2525. https://doi.org/10.1109/ICRA.2011.5980409(2011)

  30. Mian, A. A., Daobo, W.: Modeling and backstepping-based nonlinear control strategy for a 6 dof quadrotor helicopter. Chin. J. Aeronaut. 21(3), 261–268 (2008). https://doi.org/10.1016/S1000-9361(08)60034-5

    Article  Google Scholar 

  31. Nascimento, T. P., Saska, M.: Position and attitude control of multi-rotor aerial vehicles: A survey. Annu. Rev. Control. 52(7), 1367–5788 (2019)

    MathSciNet  Google Scholar 

  32. Nayak, V., Karaya, R.R.: Target tracking by a quadrotor using proximity sensor fusion based on a sigmoid function. IFAC-PapersOnLine 51(1), 154–159 (2018). https://doi.org/10.1016/j.ifacol.2018.05.026. 5th IFAC Conference on Advances in Control and Optimization of Dynamical Systems ACODS 2018

    Article  Google Scholar 

  33. Nazaruddin, Y.Y., Andrini, A.D., Anditio, B.: Pso based pid controller for quadrotor with virtual sensor. IFAC-PapersOnLine 51(4), 358–363 (2018). https://doi.org/10.1016/j.ifacol.2018.06.091. 3rd IFAC Conference on Advances in Proportional-Integral-Derivative Control PID 2018

    Article  Google Scholar 

  34. Olfati-Saber, R.: Global configuration stabilization for the vtol aircraft with strong input coupling. IEEE Trans. Autom. Control 47(11), 1949–1952 (2002). https://doi.org/10.1109/TAC.2002.804457

    Article  MathSciNet  Google Scholar 

  35. Purwin, O., D’Andrea, R.: Performing and extending aggressive maneuvers using iterative learning control. Robot. Auton. Syst. 59(1), 1–11 (2011). https://doi.org/10.1016/j.robot.2010.09.004

    Article  Google Scholar 

  36. Ríos, H., Falcón, R., González, O.A., Dzul, A.: Continuous sliding-mode control strategies for quadrotor robust tracking: Real-time application. IEEE Trans. Ind. Electron. 66(2), 1264–1272 (2019). https://doi.org/10.1109/TIE.2018.2831191

    Article  Google Scholar 

  37. Rosaldo-Serrano, M., Aranda-Bricaire, E.: Trajectory tracking for a commercial quadrotor via time-varying backstepping. IFAC-PapersOnLine 51(13), 532–536 (2018). https://doi.org/10.1016/j.ifacol.2018.07.334. 2nd IFAC Conference on Modelling, Identification and Control of Nonlinear Systems MICNON 2018

    Article  Google Scholar 

  38. Sanahuja, G., Castillo, P., Sanchez, A.: Stabilization of n integrators in cascade with bounded input with experimental application to a vtol laboratory system. International Journal of Robust and Nonlinear Control 20(10), 1129–1139 (2010). https://doi.org/10.1002/rnc.1494

    Article  MathSciNet  MATH  Google Scholar 

  39. Santiaguillo-Salinas, J., Rosaldo-Serrano, M., Aranda-Bricaire, E.: Observer-based time-varying backstepping control for parrot’s ar.drone 2.0. IFAC-PapersOnLine 50(1), 10,305 – 10,310 (2017). https://doi.org/10.1016/j.ifacol.2017.08.1497. 20th IFAC World Congress

    Article  Google Scholar 

  40. Shraim, H., Awada, A., Youness, R.: A survey on quadrotors: Configurations, modeling and identification, control, collision avoidance, fault diagnosis and tolerant control. IEEE Aerosp. Electron. Syst. Mag. 33 (7), 14–33 (2018). https://doi.org/10.1109/MAES.2018.160246

    Article  Google Scholar 

  41. Subudhi, C.S., Ezhilarasi, D.: Modeling and trajectory tracking with cascaded pd controller for quadrotor. Procedia Computer Science 133, 952–959 (2018). https://doi.org/10.1016/j.procs.2018.07.082. International Conference on Robotics and Smart Manufacturing (RoSMa2018)

    Article  Google Scholar 

  42. Tamayo, A.J.M., Ríos, C.A.V., Zannatha, J.M.I., Soto, S.M.O.: Quadrotor input-output linearization and cascade control. IFAC-PapersOnLine 51(13), 437–442 (2018). https://doi.org/10.1016/j.ifacol.2018.07.317. 2nd IFAC Conference on Modelling, Identification and Control of Nonlinear Systems MICNON 2018

    Article  Google Scholar 

  43. Teel, A. R.: Global stabilization and restricted tracking for multiple integrators with bounded controls. Systems & Control Letters 18(3), 165–171 (1992). https://doi.org/10.1016/0167-6911(92)90001-9

    Article  MathSciNet  Google Scholar 

  44. Tomashevich, S., Belyavskyi, A.: Passification based simple adaptive control of quadrotor. IFAC-PapersOnLine 49(13), 281–286 (2016). https://doi.org/10.1016/j.ifacol.2016.07.974. 12th IFAC Workshop on Adaptation and Learning in Control and Signal Processing ALCOSP 2016

    Article  Google Scholar 

  45. Tomić, T., Maier, M., Haddadin, S.: Learning quadrotor maneuvers from optimal control and generalizing in real-time. In: 2014 IEEE International Conference on Robotics and Automation (ICRA), pp. 1747–1754. https://doi.org/10.1109/ICRA.2014.6907087 (2014)

  46. Tran, T. T., Shuzhi Sam, G., Wei, H.: Adaptive control of a quadrotor aerial vehicle with input constraints and uncertain parameters. International Journal of Control (2018)

  47. Villagómez, J., Vargas, M., Ortega, M., Rubio, F.: Modeling and control of the pvtol. IFAC-PapersOnLine 48(9), 150–155 (2015). https://doi.org/10.1016/j.ifacol.2015.08.075

    Article  Google Scholar 

  48. Wang, R., Liu, J.: Trajectory tracking control of a 6-dof quadrotor uav with input saturation via backstepping. J. Franklin Inst. 355(7), 3288–3309 (2018). https://doi.org/10.1016/j.jfranklin.2018.01.039

    Article  MathSciNet  Google Scholar 

  49. Warier, R.R., Sanyal, A.K., Dhullipalla, M.H., Viswanathan, S.P.: Trajectory tracking control for underactuated thrust-propelled aerial vehicles. IFAC-PapersOnLine 51(13), 555 – 560 (2018). https://doi.org/10.1016/j.ifacol.2018.07.338. 2nd IFAC Conference on Modelling, Identification and Control of Nonlinear Systems MICNON 2018

    Article  Google Scholar 

  50. Xu, Z., Nian, X., Wang, H., Chen, Y.: Robust guaranteed cost tracking control of quadrotor uav with uncertainties. ISA Trans. 69, 157–165 (2017). https://doi.org/10.1016/j.isatra.2017.03.023

    Article  Google Scholar 

  51. Yao, X., Chen, Z.: Sliding mode control with deep learning method for rotor trajectory control of active magnetic bearing system. Trans. Inst. Meas. Control. 41(5), 1383–1394 (2019). https://doi.org/10.1177/0142331218778324

    Article  Google Scholar 

  52. Zagaris, A., Kaper, H. G., Kaper, T. J.: Fast and slow dynamics for the computational singular perturbation method. arXiv Mathematics e-prints math/0401206 (2004)

  53. Özbek, N. S., Önkol, M., Önder Efe, M.: Feedback control strategies for quadrotor-type aerial robots: a survey. Trans. Inst. Meas. Control. 38(5), 529–554 (2016). https://doi.org/10.1177/0142331215608427

    Article  Google Scholar 

  54. Zhang, Y., Chen, Z., Zhang, X., Sun, Q., Sun, M.: A novel control scheme for quadrotor uav based upon active disturbance rejection control. Aerosp. Sci. Technol. 79, 601–609 (2018). https://doi.org/10.1016/j.ast.2018.06.017

    Article  Google Scholar 

  55. Zhao, B., Tang, Y., Wu, C., Du, W.: Vision-based tracking control of quadrotor with backstepping sliding mode control. IEEE Access 6, 72,439–72,448 (2018). https://doi.org/10.1109/ACCESS.2018.2882241

    Article  Google Scholar 

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Acknowledgements

This work was supported by CONACyT (Consejo Nacional de Ciencia y Tecnología), Mexico. This work has been also sponsored by the French government research programm Investissements d’avenir through the Robotex Equipment of Excellence (ANR-10-EQPX-44). Theirs supports are gratefully acknowledge

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  1. Université de Technologie de Compiègne, CNRS, Heudiasyc (Heuristics and Diagnosis of Complex Systems), CS 60 319 - 60 203, Compiègne Cedex, France

    J. Betancourt, P. Castillo & R. Lozano

  2. UMI-LAFMIA 3175 CNRS, CINVESTAV, Mexico, Mexico

    R. Lozano

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  1. J. Betancourt
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Correspondence to P. Castillo.

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Betancourt, J., Castillo, P. & Lozano, R. Stabilization and Tracking Control Algorithms for VTOL Aircraft: Theoretical and Practical Overview. J Intell Robot Syst 100, 1249–1263 (2020). https://doi.org/10.1007/s10846-020-01252-7

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