Abstract
In this paper, we consider the problem of trajectory tracking of a multirotor Unmanned Aerial Vehicle carrying a suspended payload. The movement of the suspended payload influences the dynamics of the multirotor, which must be appropriately handled by the controller to achieve satisfactory tracking results. We derive a mathematical model of the interconnected multi-body system using Kane’s equations, and develop a non-linear tracking controller based on the backstepping technique. In addition to suppressing the effects of the swinging payload, the controller also compensates for an unknown constant wind disturbance. The origin of the tracking error is proven UGAS (Uniformly Globally Asymptotically Stable) and ULES (Uniformly Locally Exponentially Stable) through Lyapunov analysis. To reduce the swing motion of the suspended load, a nominal swing-free path is generated through open loop shaping filters, then further perturbed through a delayed feedback approach from measured load deflection angles to achieve robustness. The proposed controller structure is verified by simulations and experiments.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abdel-Rahman, E., Nayfeh, A., Masoud, Z.: Dynamics and control of cranes: a review. J. Vib. Control. 9(7), 863–908 (2003). doi:10.1177/107754603031852
Amazon: Amazon.com (2016). http://www.amazon.com/b?node=8037720011
Angeli, D., Sontag, E. D.: Forward completeness, unboundedness observability, and their Lyapunov characterizations. Syst. Control Lett. 38(4), 209–217 (1999). doi:10.1016/S0167-6911(99)00055-9
Ardupilot.com: Ardupilot - Open source autopilot (2016). http://ardupilot.com
Bernard, M., Kondak, K.: Generic slung load transportation system using small size helicopters. In: 2009 IEEE International Conference on Robotics and Automation. doi:10.1109/ROBOT.2009.5152382, pp 3258–3264 (2009)
Bernard, M., Kondak, K., Maza, I., Ollero, A.: Autonomous transportation and deployment with aerial robots for search and rescue missions. J. Field Rob. 28(6), 914–931 (2011). doi:10.1002/rob
Bisgaard, M., la Cour-Harbo, A., Bendtsen, J.: Input Shaping for Helicopter Slung Load Swing Reduction. In: AIAA Guidance, Navigation and Control Conference and Exhibit. Honolulu, Hawai (2008)
Bisgaard, M., Cour-harbo, A., Bendtsen, J. D.: Swing damping for helicopter slung load systems using delayed feedback. In: Proceedings of AIAA Conference on Guidance, Navigation, and Control, pp 1–11 (2009)
Cicolani, L., Kanning, G.: Equations of motion of slung-load systems, including multilift systems. NASA Office of Management Scientific and Technical Information Program Technical(3280) (1992)
Egeland, O., Gravdahl, J. T.: Modeling and simulation for automatic control. Marine Cybernetics (2002)
Fossen, T., Breivik, M., Skjetne, R.: Line-of-sight path following of underactuated marine craft. In: Proceedings of the IFAC MCMC’03, pp 1–6. IFAC MCMC’03, Girona, Spain (2003)
Fossen, T. I.: Marine Craft Hydrodynamics and Motion Control. Wiley (2011)
Fossen, T. I., Lori̇a, A., Teel, A.: Theorem for UGAS and ULES of (passive) nonautonomous systems: robust control of mechanical systems and ships. Int. J. Robust Nonlinear Control 11(2), 95–108 (2001). doi:10.1002/rnc.551
Goodarzi, F. A., Lee, D., Lee, T.: Geometric stabilization of quadrotor UAV with a payload connected by flexible cable. In: American Control Conference (ACC), pp. 4925–4930. IEEE (2014)
Guerrero, M. E., Mercado, D. A., Lozano, R., Garc, C. D.: IDA-PBC methodology for a quadrotor UAV transporting a cable-suspended payload. In: International Conference on Unmanned Aircraft Systems (ICUAS), 2015. doi:10.1109/ICUAS.2015.7152325, pp 470–476. IEEE, Denver, CO (2015)
Khalil, H. K.: Nonlinear Systems, 3rd edn. Prentice Hall (2002)
Klausen, K., Fossen, T. I., Johansen, T. A.: Nonlinear control of a multirotor UAV with suspended load. In: International Conference on Unmanned Aircraft Systems (ICUAS), 2015. doi:10.1109/ICUAS.2015.7152289, pp 176–184. IEEE, Denver, CO (2015)
Krstic, M., Kanellakopoulos, I., Kokotovic, P.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)
Mahony, R., Kumar, V., Corke, P.: Modeling, estimation, and control of quadrotor. IEEE Robot. Autom. Mag. 19(3), 20–32 (2012). doi:10.1109/MRA.2012.2206474
Palunko, I., Cruz, P., Fierro, R.: Agile load transportation - safe and efficient load manipulation with aerial robots. IEEE Robot. Autom. Mag., 69–79 (2012)
Palunko, I., Fierro, R., Cruz, P.: Trajectory generation for swing-free maneuvers of a quadrotor with suspended payload: a dynamic programming approach. In: 2012 IEEE International Conference on Robotics and Automation. doi:10.1109/ICRA.2012.6225213, pp 2691–2697 (2012)
Piher.net: MTS-360 (2016). http://www.piher.net/
Pinto, J., Dias, P. S., Martins, R., Fortuna, J., Marques, E., Sousa, J.: The LSTS toolchain for networked vehicle systems. OCEANS 2013 MTS/IEEE Bergen: the Challenges of the Northern Dimension. doi:10.1109/OCEANS-Bergen.2013.6608148 (2013)
Pixhawk.ethz.ch: PX4 Pixhawk (2016). https://pixhawk.ethz.ch/
Singh, T., Singhose, W.: Input shaping / time delay control of maneuvering flexible structures. In: American Control Conference, 2002. Proceedings of the 2002, pp. 1717–1731 (3). NY, USA (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Klausen, K., Fossen, T.I. & Johansen, T.A. Nonlinear Control with Swing Damping of a Multirotor UAV with Suspended Load. J Intell Robot Syst 88, 379–394 (2017). https://doi.org/10.1007/s10846-017-0509-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10846-017-0509-6