Skip to main content
SpringerLink
Log in

Trajectory tracking control of multirotors from modelling to experiments: A survey

  • Regular Papers
  • Robot and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

Multirotors have received a great attention from researchers and the general public, as a platform on which various ideas can be easily demonstrated. This paper aims to provide background materials by categorizing various representations of multirotor dynamics and existing control approaches for multirotor control. First, many ways of expressing the translation and the attitude dynamics of a quadrotor UAV are described. Second, linear and nonlinear control laws are reviewed considerably. Finally, we show various types of flight test-beds configured for validating the controller. In experiments, the performance of linear and nonlinear controller are described.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Leishman, “The breguet-richet quad-rotor helicopter of 1907,” Vertiflite, vol. 47, no. 3, pp. 58–60, 2002.

    Google Scholar 

  2. D. Mellinger, N. Michael, and V. Kumar, “Trajectory generation and control for precise aggressive maneuvers with quadrotors,” The International Journal of Robotics Research, vol. 31, no. 5, pp. 664–674, 2012.

    Article  Google Scholar 

  3. G. Hoffmann, S. Waslander, and C. Tomlin, “Quadrotor helicopter trajectory tracking control,” in Proc. of AIAA Guidance, Navigation and Control Conference and Exhibit, Honolulu, Hawaii, 2008, pp. 1–14.

    Google Scholar 

  4. S. Bouabdallah, A. Noth, and R. Siegwart, “PID vs LQ control techniques applied to an indoor micro quadrotor,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 3, pp. 2451–2456, Sept.-2 Oct. 2004.

    Google Scholar 

  5. P. Pounds, R. Mahony, and P. Corke, “Modelling and control of a quad-rotor robot,” Proceedings Australasian Conference on Robotics and Automation, 2006.

    Google Scholar 

  6. I. Cowling, O. Yakimenko, J. Whidborne, and A. Cooke, “Direct method based control system for an autonomous quadrotor,” Journal of Intelligent & Robotic Systems, vol. 60, no. 2, pp. 285–316, 2010.

    Article  MATH  Google Scholar 

  7. M. Valenti, B. Bethke, G. Fiore, J. How, and E. Feron, “Indoor multi-vehicle flight testbed for fault detection, isolation, and recovery,” Proc. of the AIAA Guidance, Navigation, and Control Conference, vol. 63, 2006.

  8. Z. T. Dydek, A. M. Annaswamy, and E. Lavretsky, “Adaptive control of quadrotor uavs: A design trade study with flight evaluations,” IEEE Transactions on Control Systems Technology, vol. 21, no. 4, pp. 1400–1406, 2013.

    Article  Google Scholar 

  9. M. Chen and M. Huzmezan, “A Combined MBPC/2 DOF H ∞ Controller for a Quad Rotor UAV,” Proc. of AIAA Guidance, Navigation, and Control Conference and Exhibit, AAS Astrodynamics Specialist Conference, 2003.

    Google Scholar 

  10. G. Raffo, M. Ortega, and F. Rubio, “An integral predictive/ nonlinear control structure for a quadrotor helicopter,” Automatica, vol. 46, no. 1, pp. 29–39, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Mokhtari, A. Benallegue, and B. Daachi, “Robust feedback linearization and GH ∞ controller for a quadrotor unmanned aerial vehicle,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1198–1203, Aug. 2005.

    Google Scholar 

  12. T. Ryan and H. J. Kim, “Approximate feedback linearization and LMI based gain synthesis for robust VTOL UAV control,” IEEE Transactions on Automation Science and Engineering, vol. 10, no. 4, pp. 1173–1178, 2013.

    Article  Google Scholar 

  13. F. Yacef, O. Bouhali, H. Khebbache, and F. Boudjema, “Takagi-sugeno model for quadrotor modelling and control using nonlinear state feedback controller,” International Journal of Control Theory and Computer Modelling, vol. 2, no. 3, pp. 9–24, 2012.

    Article  Google Scholar 

  14. H. Lee and H. J. Kim, “Robust control of a quadrotor using takagi-sugeno fuzzy model and an lmi approach,” Proc. of International Conference on Control, Automation and Systems, pp. 370–374, 2014.

    Google Scholar 

  15. M. Sanchez, J. Acosta, and A. Ollero, “Integral action in first-order closed-loop inverse kinematics. application to aerial manipulators,” Proc. of IEEE International Conference on Robotics and Automation, 2015., pp. 5297–5302

    Google Scholar 

  16. “Ar drone by parrot,” http://ardrone2.parrot.com/.

  17. “Indago VTOL quadrotor by lockheed martin,” http://www.lockheedmartin.com/.

  18. D. Scaramuzza et al., “Vision-controlled micro flying robots: From system design to autonomous navigation and mapping in gps-denied environments,” IEEE Robotics Automation Magazine, vol. 21, no. 3, pp. 26–40, Sept 2014.

    Article  Google Scholar 

  19. M. Henson and D. Seborg, “Feedback linearizing control,” Nonlinear Process Control, pp. 149–231, 1997

    Google Scholar 

  20. D. Lee., H. J. Kim, and S. Sastry, “Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter,” International Journal of Control, Automation and Systems, vol. 7, no. 3, pp. 419–428, 2009.

    Article  Google Scholar 

  21. A. Mokhtari, N. M’Sirdi, K. Meghriche, and A. Belaidi, “Feedback linearization and linear observer for a quadrotor unmanned aerial vehicle,” Advanced Robotics, vol. 20, no. 1, pp. 71–91, 2006.

    Article  Google Scholar 

  22. O. Härkegård and S. Glad, Flight Control Design Using Backstepping, Linköping University Electronic Press, 2001.

    Google Scholar 

  23. T. Madani and A. Benallegue, “Control of a quadrotor mini-helicopter via full state backstepping technique,” Proc. of IEEE Conference on Decision and Control, pp. 1515–1520, 2006.

    Chapter  Google Scholar 

  24. P. Castillo, P. Albertos, P. Garcia, and R. Lozano, “Simple real-time attitude stabilization of a quad-rotor aircraft with bounded signals,” Proc. of IEEE Conference on Decision and Control, pp. 1533–1538, 2006.

    Chapter  Google Scholar 

  25. S. Bouabdallah and R. Siegwart, “Backstepping and sliding-mode techniques applied to an indoor micro quadrotor,” Proc. of IEEE International Conference on Robotics and Automation, pp. 2247–2252, April 2005.

    Google Scholar 

  26. P. Adigbli, C. Gr, J. Mouret, and S. Doncieux, “Nonlinear attitude and position control of a micro quadrotor using sliding mode and backstepping techniques,” European Micro Air Vehicle Conference, pp. 1–9, 2007.

    Google Scholar 

  27. A. Das, F. Lewis, and K. Subbarao, “Backstepping approach for controlling a quadrotor using lagrange form dynamics,” Journal of Intelligent & Robotic Systems, vol. 56, no. 1, pp. 127–151, 2009.

    Article  MATH  Google Scholar 

  28. A. Das, K. Subbarao, and F. Lewis, “Dynamic inversion with zero-dynamics stabilisation for quadrotor control,” IET Control Theory & Applications, vol. 3, no. 3, pp. 303–314, 2009.

    Article  MathSciNet  Google Scholar 

  29. T. Lee, M. Leoky, and N. McClamroch, “Geometric tracking control of a quadrotor uav on SE(3),” Proc. of IEEE Conference on Decision and Control, pp. 5420–5425, Dec. 2010.

    Google Scholar 

  30. D. Mellinger and V. Kumar, “Minimum snap trajectory generation and control for quadrotors,” Proc. of IEEE International Conference on Robotics and Automation, pp. 2520–2525, May 2011.

    Google Scholar 

  31. A. Kushleyev, D. Mellinger, and V. Kumar, “Towards a swarm of agile micro quadrotors,” in Robotics: Science and Systems, 2012.

    Google Scholar 

  32. K. Rudin, M. Hua, G. Ducard, and S. Bouabdallah, “A robust attitude controller and its application to quadrotor helicopters,” Proc. of 18th IFAC World Congress, pp. 10379–10384, 2011.

    Google Scholar 

  33. T. Fernando, J. Chandiramani, T. Lee, and H. Gutierrez, “Robust adaptive geometric tracking controls on SO(3) with an application to the attitude dynamics of a quadrotor uav,” Proc. of IEEE Conference on Decision and Control and European Control Conference, pp. 7380–7385, 2011.

    Chapter  Google Scholar 

  34. T. Lee, M. Leok, and N. McClamroch, “Nonlinear robust tracking control of a quadrotor UAV on SE(3),” Asian Journal of Control, vol. 15, no. 3, pp. 391–498, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  35. F. Goodarzi, D. Lee, and T. Lee, “Geometric control of a quadrotor UAV transporting a payload connected via flexible cable,” International Journal of Control, Automation, and Systems, vol. 13, no. 6, pp. 1486–1498, 2016.

    Article  Google Scholar 

  36. H. Lee, S. Kim, T. Ryan, and H. J. Kim, “Backstepping control based on SE(3) of a micro quadrotor for stable trajectory tracking,” Proc. of IEEE International Conference on Systems, Man, and Cybernetics, pp. 4522–4527, 2013.

    Google Scholar 

  37. T. Dierks and S. Jagannathan, “Output feedback control of a quadrotor UAV using neural networks,” IEEE Transactions on Neural Networks, vol. 21, no. 1, pp. 50–66, 2010.

    Article  Google Scholar 

  38. S. Lupashin, A. Schoellig, M. Sherback, and R. D’Andrea, “A simple learning strategy for high-speed quadrocopter multi-flips,” in IEEE International Conference on Robotics and Automation, pp. 1642–1648, 2010.

    Google Scholar 

  39. T. Tomic, M. Maier and S. Haddadin, “Learning quadrotor maneuvers from optimal control and generalizing in realtime,” Proc. of IEEE International Conference on Robotics and Automation, pp. 1747–1754, 2014.

    Google Scholar 

  40. X. Zhao, P. Shi, X. Zheng, and J. Zhang, “Intelligent tracking control for a class of uncertain high-order nonlinear systems,” IEEE Transactions on Neural Networks and Learning Systems, vol. 27, no. 9, pp. 1976–1982, 2016.

    Article  MathSciNet  Google Scholar 

  41. V. Kumar and N. Michael, “Opportunities and challenges with autonomous micro aerial vehicles,” The International Journal of Robotics Research, vol. 31, no. 11, pp. 1279–1291, 2012.

    Article  Google Scholar 

  42. R. Mahony, V. Kumar, and P. Corke, “Multirotor aerial vehicles: Modeling, estimation, and control of quadrotor,” IEEE Robotics & Automation Magazine, vol. 19, no. 3, pp. 20–32, sept. 2012.

    Article  Google Scholar 

  43. F. Kendoul, “Survey of advances in guidance, navigation, and control of unmanned rotorcraft systems,” Journal of Field Robotics, vol. 29, no. 2, pp. 315–378, 2012.

    Article  Google Scholar 

  44. M.-D. Hua, T. Hamel, P. Morin, and C. Samson, “Feedback control of underactuated VTOL vehicles,” IEEE Control Systems, vol. 33, no. 1, pp. 61–75, 2013.

    Article  MathSciNet  Google Scholar 

  45. D. Mellinger, M. Shomin, N. Michael, and V. Kumar, “Cooperative grasping and transport using multiple quadrotors,” Distributed Autonomous Robotic Systems, pp. 545–558, 2010.

    Google Scholar 

  46. I. Palunko, P. Cruz, and R. Fierro, “Agile load transportation: Safe and efficient load manipulation with aerial robots,” IEEE Robotics & Automation Magazine, vol. 19, no. 3, pp. 69–79, 2012.

    Article  Google Scholar 

  47. G. Antonelli, E. Cataldi, P. Giordano, S. Chiaverini, and A. Franchi, “Experimental validation of a new adaptive control scheme for quadrotors MAVs,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2439–2444, 2013.

    Google Scholar 

  48. M. Orsag, C. Korpela, and P. Oh, “Modeling and control of MM-UAV: Mobile manipulating unmanned aerial vehicle,” Journal of Intelligent & Robotic Systems, vol. 69, no. 1, pp. 227–240, 2013.

    Article  Google Scholar 

  49. A. Jimenez-Cano, J. Martin, G. Heredia, A. Ollero, and R. Cano, “Control of an aerial robot with multi-link arm for assembly tasks,” Proc. of IEEE International Conference on Robotics and Automation, pp. 4916–4921, 2013.

    Google Scholar 

  50. S. Kim, S. Choi, and H. J. Kim, “Aerial manipulation using a quadrotor with a two dof robotic arm,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4990–4995, 2013.

    Google Scholar 

  51. H. Huang, G. Hoffmann, S. Waslander, and C. Tomlin, “Aerodynamics and control of autonomous quadrotor helicopters in aggressive maneuvering,” Proc. of IEEE International Conference on Robotics and Automation, pp. 3277–3282, 2009.

    Google Scholar 

  52. A. Schöllig and R. D’Andrea, “Optimization-based iterative learning control for trajectory tracking,” Proceedings of the European Control Conference, pp. 1505–1510, 2009.

    Google Scholar 

  53. F. Kendoul, Z. Yu, and K. Nonami, “Guidance and nonlinear control system for autonomous flight of minirotorcraft unmanned aerial vehicles,” Journal of Field Robotics, vol. 27, no. 3, pp. 311–334, 2010.

    Google Scholar 

  54. J. How, B. Bethke, A. Frank, D. Dale, and J. Vian, “Realtime indoor autonomous vehicle test environment,” IEEE Control Systems, vol. 28, no. 2, pp. 51–64, 2008.

    Article  MathSciNet  Google Scholar 

  55. D. Zhou and M. Schwager, “Vector field following for quadrotors using differential flatness,” Proc. of IEEE International Conference on Robotics and Automation, pp. 6567–6572, 2014.

    Google Scholar 

  56. J. Stowers, M. Hayes, and A. Bainbridge-Smith, “Altitude control of a quadrotor helicopter using depth map from microsoft kinect sensor,” Proc. of IEEE International Conference on Mechatronics, pp. 358–362, 2011.

    Google Scholar 

  57. F. Fraundorfer, L. Heng, D. Honegger, G. H. Lee, L. Meier, P. Tanskanen, and M. Pollefeys, “Vision-based autonomous mapping and exploration using a quadrotor MAV,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4557–4564, 2012.

    Google Scholar 

  58. N. Michael, et al., “Collaborative mapping of an earthquake-damaged building via ground and aerial robots,” Journal of Field Robotics, vol. 29, no. 5, pp. 832–841, 2012.

    Article  Google Scholar 

  59. S. Shen, N. Michael, and V. Kumar, “Autonomous multifloor indoor navigation with a computationally constrained MAV,” Proc. of IEEE international conference on Robotics and automation, pp. 20–25, 2011.

    Google Scholar 

  60. M. Achtelik, S. Lynen, M. Chli, and R. Siegwart, “Inversion based direct position control and trajectory following for micro aerial vehicles,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2933–2939, 2013.

    Google Scholar 

  61. G. M. Hoffmann, H. Huang, S. L. Waslander, and C. J. Tomlin, “Quadrotor helicopter flight dynamics and control: Theory and experiment,” Proc. of the AIAA Guidance, Navigation, and Control Conference, pp. 1–20, 2007.

    Google Scholar 

  62. P. Castillo, R. Lozano, and A. Dzul, “Stabilization of a mini-rotorcraft having four rotors,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 3, pp. 2693–2698, 2005.

    Google Scholar 

  63. S. Bouabdallah, Design and Control of Quadrotors with Application to Autonomous Flying, Lausanne Polytechnic University, 2007.

    Google Scholar 

  64. J. Gillula, H. Huang, M. Vitus, and C. Tomlin, “Design of guaranteed safe maneuvers using reachable sets: Autonomous quadrotor aerobatics in theory and practice,” IEEE International Conference on Robotics and Automation, pp. 1649–1654, 2010.

    Google Scholar 

  65. S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design, vol. 2, Wiley, 2007.

  66. K. Lee, J. Back, and I. Choy, “Nonlinear disturbance observer based robust attitude tracking controller for quadrotor UAVs,” International Journal of Control, Automation and Systems, vol. 12, no. 6, pp. 1266–1275, 2014.

    Article  Google Scholar 

  67. J. Back and H. Shim, “An inner-loop controller guaranteeing robust transient performance for uncertain mimo nonlinear systems,” IEEE Transactions on Automatic Control, vol. 54, no. 7, pp. 1601–1607, 2009.

    Article  MathSciNet  Google Scholar 

  68. S. Kim, H. Seo, and H. J. Kim, “Operating an unknown drawer using an aerial manipulator,” Proc. of IEEE International Conference on Robotics and Automation, pp. 5503–5508, 2015.

    Google Scholar 

  69. H. Lee, S. Kim, and H. J. Kim, “Control of an aerial manipulator using on-line parameter estimator for an unknown payload,” Proc. of IEEE International Conference on Automation Science and Engineering, pp. 316–321, 2015.

    Google Scholar 

  70. H. Lee, H. Kim, and H. J. Kim, “Path planning and control of multiple aerial manipulators for a cooperative transportation,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2386–2391, 2015.

    Google Scholar 

  71. A. Tayebi and S. McGilvray, “Attitude stabilization of a VTOL quadrotor aircraft,” IEEE Transactions on Control System Technology, vol. 14, no. 3, pp. 562–571, 2006.

    Article  Google Scholar 

  72. M. Turpin, N. Michael, and V. Kumar, “Trajectory design and control for aggressive formation flight with quadrotors,” Autonomous Robots, vol. 33, no. 1, pp. 143–156, 2012.

    Article  Google Scholar 

  73. K. Sreenath, T. Lee, and V. Kumar, “Geometric control and differential flatness of a quadrotor UAV with a cablesuspended load,” Proc. of IEEE 52nd Annual Conference on Decision and Control, pp. 2269–2274, 2013.

    Chapter  Google Scholar 

  74. H. Lim, J. Park, D. Lee, and H. J. Kim, “Build your own quadrotor: Open-source projects on unmanned aerial vehicles,” IEEE Robotics & Automation Magazine, vol. 19, no. 3, pp. 33–45, 2012.

    Article  Google Scholar 

  75. C. Lehnert and P. Corke, “mAV-design and implementation of an open source micro quadrotor,” AC on Robotics and Automation, Eds, 2013.

    Google Scholar 

  76. M. Asadpour, B. Van den Bergh, D. Giustiniano, K. A. Hummel, S. Pollin, and B. Plattner, “Micro aerial vehicle networks: An experimental analysis of challenges and opportunities,” IEEE Communications Magazine, vol. 52, no. 7, pp. 141–149, 2014.

    Article  Google Scholar 

  77. J. Engel, J. Sturm, and D. Cremers, “Camera-based navigation of a low-cost quadrocopter,” Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2815–2821, 2012.

    Google Scholar 

  78. C. Bills, J. Chen, and A. Saxena, “Autonomous MAV flight in indoor environments using single image perspective cues,” Proc. of IEEE international Conference on Robotics and Automation, pp. 5776–5783, 2011.

    Google Scholar 

  79. P.-J. Bristeau, F. Callou, D. Vissiere, N. Petit, et al., “The navigation and ontrol technology inside the ar. drone micro UAV,” Proc of 18th IFAC World Congress, vol. 18, no. 1, pp. 1477–1484, 2011.

    Google Scholar 

  80. “Matrice 100, DJI,” http://dev.dji.com.

  81. “Vicon system,” http://www.vicon.com.

  82. S. Grzonka, G. Grisetti, and W. Burgard, “Towards a navigation system for autonomous indoor flying,” Proc. of IEEE International Conference on Robotics and Automation, pp. 2878–2883, 2009

    Google Scholar 

  83. “Endurance R/C,” http://www.endurance-rc.com.

  84. “Robot operating system,” http://www.ros.org.

  85. “Ardrone autonomy,” http://wiki.ros.org/ardrone_autonomy.

  86. “Asctec mav framework,” http://wiki.ros.org/asctec_mav_ framework.

  87. “Odroid,” http://www.hardkernel.com.

Download references

Author information

Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Seoul National University, 1 Gwanack-ro, Gwanack-gu, Seoul, Korea

    Hyeonbeom Lee & H. Jin Kim

Authors
  1. Hyeonbeom Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Jin Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Jin Kim.

Additional information

Recommended by Associate Editor DaeEun Kim under the direction of Editor Euntai Kim. This work was supported by the Technology Innovation Program (10051673) funded by the Ministry of Trade, industry and Energy(MI, Korea) and the program of Development of Space Core Technology through the National Research Foundation of Korea funded by the Ministry of Science, ICT and Future Planning (NRF-2015M1A3A3A05027630).

Hyeonbeom Lee received the B.S. degree in Mechanical and Control Engineering from Handong Global University in 2011, and the M.S. degree in Mechanical and Aerospace Engineering from Seoul National University in 2013. He is currently pursuing the Ph.D. degree in the Department of Mechanical and Ae-rospace Engineering at Seoul National University. His research interests include aerial manipulation and motion planning of aerial robots.

H. Jin Kim received the B.S. degree from Korea Advanced Institute of Technology (KAIST) in 1995, and the M.S. and Ph.D. degrees in Mechanical Engineering from University of California, Berkeley (UC Berkeley), in 1999 and 2001, respectively. From 2002 to 2004, she was a Postdoctoral Researcher in Electrical Engineering and Computer Science (EECS), UC Berkeley. In September 2004 she joined the Department of Mechanical and Aerospace Engineering at Seoul National University, Seoul, Korea, as an Assistant Professor where she is currently a Professor. Her research interests include intelligent control of robotic systems and motion planning.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, H., Kim, H.J. Trajectory tracking control of multirotors from modelling to experiments: A survey. Int. J. Control Autom. Syst. 15, 281–292 (2017). https://doi.org/10.1007/s12555-015-0289-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-015-0289-3

Keywords

Search

Navigation