Skip to main content
SpringerLink
Log in

Geometric control of a quadrotor UAV transporting a payload connected via flexible cable

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

Abstract

We derived a coordinate-free form of equations of motion for a complete model of a quadrotor UAV with a payload which is connected via a flexible cable according to Lagrangian mechanics on a manifold. The flexible cable is modeled as a system of serially-connected links and has been considered in the full dynamic model. A geometric nonlinear control system is presented to asymptotically stabilize the position of the quadrotor while aligning the links to the vertical direction below the quadrotor. Numerical simulation and experimental results are presented and a rigorous stability analysis is provided to confirm the accuracy of our derivations. These results will be particularly useful for aggressive load transportation that involves large deformation of the cable.

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. L. Cicolani, G. Kanning, and R. Synnestvedt, “Simulation of the dynamics of helicopter slung load systems,” Journal of the American Helicopter Society, vol. 40, no. 4, pp. 44–61, 1995.

    Article  Google Scholar 

  2. M. Bernard, “Generic slung load transportation system using small size helicopters,” Proc. of the International Conference on Robotics and Automation, pp. 3258–3264, 2009.

    Google Scholar 

  3. I. Palunko, P. Cruz, and R. Fierro, “Agile load transportation,” IEEE Robotics and Automation Magazine, vol. 19, no. 3, pp. 69–79, 2012.

    Article  Google Scholar 

  4. N. Michael, J. Fink, and V. Kumar, “Cooperative manipulation and transportation with aerial robots,” Autonomous Robots, vol. 30, pp. 73–86, 2011.

    Article  Google Scholar 

  5. I. Maza, K. Kondak, M. Bernard, and A. Ollero, “Multi-UAV cooperation and control for load transportation and deployment,” Journal of Intelligent and Robotic Systems, vol. 57, pp. 417–449, 2010.

    Article  MATH  Google Scholar 

  6. D. Mellinger, M. Shomin, N. Michael, and V. Kumar, “Cooperative grasping and transport using multiple quadrotors,” Distributed Autonomous Robotic Systems, Springer Tracts in Advanced Robotics, vol. 83, pp. 545–558, 2013.

    Article  Google Scholar 

  7. D. Zameroski, G. Starr, J. Wood, and R. Lumia, “Rapid swing-free transport of nonlinear payloads using dynamic programming,” Journal of Dynamic Systems, Measurement, and Control, vol. 130, no. 4, p. 041001, June 2008.

    Article  Google Scholar 

  8. J. Schultz and T. Murphey, “Trajectory generation for underactuated control of a suspended mass,” Proc. of IEEE International Conference on Robotics and Automation, pp. 123–129, May 2012.

    Google Scholar 

  9. I. Palunko, R. Fierro, and P. Cruz, “Trajectory generation for swing-free maneuvers of a quadrotor with suspended payload: a dynamic programming approach,” Proc. of IEEE International Conference on Robotics and Automation, RiverCentre, Saint Paul, Minnesota, USA, May 14-18 2012.

    Google Scholar 

  10. T. Lee, M. Leok, and N. McClamroch, “Dynamics and control of a chain pendulum on a cart,” Proc. of the IEEE Conference on Decision and Control, pp. 2502–2508, 2012.

    Google Scholar 

  11. F. Goodarzi, D. Lee, and T. Lee, “Geometric stabilization of a quadrotor UAV with a payload connected by flexible cable,” Proc. of the American Control Conference, Portland, OR, pp. 4925–4930, 2014.

    Google Scholar 

  12. T. Lee, M. Leok, and N. McClamroch, “Geometric tracking control of a quadrotor UAV on SE(3),” Proc. of the IEEE Conference on Decision and Control, pp. 5420–5425, 2010.

    Google Scholar 

  13. M. L. T. Lee and N. McClamroch, “Nonlinear robust tracking control of a quadrotor UAV on SE(3),” Asian Journal of Control, vol. 15, no. 2, pp. 391–408, March 2013.

    Article  MathSciNet  Google Scholar 

  14. F. Goodarzi, D. Lee, and T. Lee, “Geometric nonlinear PID control of a quadrotor UAV on SE(3),” Proc. of the European Control Conference, Zurich, July 2013.

    Google Scholar 

  15. T. Lee, Computational Geometric Mechanics and Control of Rigid Bodies, Ph. D. dissertation, University of Michigan, 2008.

    Google Scholar 

  16. T. Lee, M. Leok, and N. H. McClamroch, “Lagrangian mechanics and variational integrators on twospheres,” International Journal for Numerical Methods in Engineering, vol. 79, no. 9, pp. 1147–1174, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  17. H. Khalil, Nonlinear Systems, 2nd ed., Prentice Hall, 1996.

    Google Scholar 

  18. 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 the IEEE Conference on Decision and Control, 7380–7385, 2011.

    Google Scholar 

  19. F. Goodarzi, D. Lee, and T. Lee, “Geometric control of a quadrotor UAV transporting a payload connected via flexible cable,” ArXiv, 2014. [Online]. Available: http://arxiv.org/abs/1407.164v1

Download references

Author information

Authors and Affiliations

  1. School of Mechanical and aerospace Engineering, The George Washington University, Washington DC, 20052, USA

    Farhad A. Goodarzi, Daewon Lee & Taeyoung Lee

Authors
  1. Farhad A. Goodarzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daewon Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Taeyoung Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Farhad A. Goodarzi.

Additional information

Recommended by Associate Editor Sung Jin Yoo under the direction of Editor Myotaeg Lim.

This research has been supported in part by NSF under the grants CMMI-1243000 (transferred from 1029551), CMMI-1335008, and CNS-1337722.

Farhad A. Goodarzi received his B.S. and M.S. degrees in Mechanical Engineering from Sharif University of Technology and Santa Clara University, CA, in 2009 and 2011, respectively. Currently, he is a Ph.D. candidate in ME department at The George Washington University. His research interests include control of complex systems and its application such as autonomous load transportation using multiple quadrotor UAV’s.

Daewon Lee received his B.S., M.S. and Ph.D. degrees in Mechanical Engineering from Seoul National University. He is currently a Post doctoral fellow in Mechanical and Aerospace Engineering Department at The George Washington University. His research interests include control theory and its application to control of the quadrotor UAV’s.

Taeyoung Lee is an assistant professor of the Department of Mechanical and Aerospace Engineering at the George Washington University. He received his doctoral degree in Aerospace Engineering and his master’s degree in Mathematics at the University of Michigan in 2008. His research interests include computational geometric mechanics and control of complex systems.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goodarzi, F.A., Lee, D. & Lee, T. Geometric control of a quadrotor UAV transporting a payload connected via flexible cable. Int. J. Control Autom. Syst. 13, 1486–1498 (2015). https://doi.org/10.1007/s12555-014-0304-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-014-0304-0

Keywords

Search

Navigation