Skip to main content

Advertisement

SpringerLink
Log in

Controlling Draft Interactions Between Quadcopter Unmanned Aerial Vehicles with Physics-aware Modeling

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

Abstract

In this paper, we address the problem of multiple quadcopter control, where the quadcopters maneuver in close proximity resulting in interference due to air-drafts. We use sparse experimental data to estimate the interference area between palm sized quadcopters and to derive physics-infused models that describe how the air-draft generated by two quadcopters (flying one above the other) affect each other. The observed significant altitude deviations due to airdraft interactions, mainly in the lower quadcopter, is adequately captured by our physics infused machine learning model. We use two strategies to mitigate these effects. First, we propose non-invasive, online and offline trajectory re-planning strategies that allow avoiding the interference zone while reducing the deviations from desired minimum snap trajectories. Second, we propose invasive strategies that re-design control algorithms by incorporating the interference model. We demonstrate how to modify the standard quadcopter PID controller, and how to formulate a model predictive control approach when considering the interference model. Both invasive and non-invasive strategies show significant reduction in tracking error and control signal energy as compared to the case where the interference area is ignored.

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. Crazyfly 2.0 design specifications: https://www.bitcraze.io/crazyflie-2/. Accessed 22 Jul 2019

  2. 1, 000 drones decorate the sky to celebrate hit’s 100th anniversary: https://news.cgtn.com/news/2020-06-08/1-000-drones-decorate-the-sky-to-celebrate-HIT-s-100th-anniversary-R9tddkPzgc/index.htmlhttps://news.cgtn.com/news/2020-06-08/1-000-drones-decorate-the-sky-to-celebrate-HIT-s-100th-anniversary-R9tddkPzgc/index.html (2020)

  3. Abaee Shoushtary, M., Hoseini Nasab, H., Fakhrzad, M.B.: Team robot motion planning in dynamics environments using a new hybrid algorithm (honey bee mating optimization-tabu list). Chinese J. Eng. 2014 (2014)

  4. Al-Aradi, A., Correia, A., Naiff, D., Jardim, G., Saporito Y.: Solving nonlinear and high-dimensional partial differential equations via deep learning (2018)

  5. Andrade, R., Raffo, G.V., Normey-Rico, J.E.: Model predictive control of a Tilt-Rotor Uav for load transportation. In: 2016 European Control Conference (ECC), pp 2165–2170 (2016)

  6. Behjat, A., Paul, S., Chowdhury, S.: Learning reciprocal actions for cooperative collision avoidance in quadrotor unmanned aerial vehicles. Robot. Auton. Syst. 121, 103270 (2019)

    Article  Google Scholar 

  7. Bekmezci, I., Sahingoz, O.K., Temel, Ş.: Flying ad-hoc networks (fanets): a survey. Ad Hoc Netw. 11(3), 1254–1270 (2013)

    Article  Google Scholar 

  8. Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E.N.: The explicit linear quadratic regulator for constrained systems. Automatica 38(1), 3–20 (2002). https://doi.org/10.1016/S0005-1098(01)00174-1. http://www.sciencedirect.com/science/article/pii/S0005109801001741

    Article  MathSciNet  Google Scholar 

  9. Bouabdallah, S., Siegwart, R.: Full control of a quadrotor. In: 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems. https://doi.org/10.1109/IROS.2007.4399042, pp 153–158 (2007)

  10. Bradbury, J., Frostig, R., Hawkins, P., Johnson, M.J., Leary, C., Maclaurin, D., Wanderman-Milne, S.: JAX: composable transformations of Python+NumPy programs. http://github.com/google/jax (2018)

  11. Carrillo, J.A., Fornasier, M., Toscani, G., Vecil, F.: Particle, Kinetic, and Hydrodynamic Models of Swarming, pp 297–336. Birkhäuser, Boston (2010)

    MATH  Google Scholar 

  12. Causa, F., Vetrella, A.R., Fasano, G., Accardo, D.: Multi-uav formation geometries for cooperative navigation in Gnss-challenging environments. In: 2018 IEEE/ION Position, Location and Navigation Symposium (PLANS), pp 775–785 (2018)

  13. Costa, F.G., Ueyama, J., Braun, T., Pessin, G., Osório, F.S., Vargas, P.A.: The use of unmanned aerial vehicles and wireless sensor network in agricultural applications. In: 2012 IEEE International Geoscience and Remote Sensing Symposium, IEEE, pp 5045–5048 (2012)

  14. Dentler, J., Rosalie, M., Danoy, G., Bouvry, P., Kannan, S., Olivares-Mendez, M.A., Voos, H.: Collision avoidance effects on the mobility of a uav swarm using chaotic ant colony with model predictive control. J.Intell. Robot. Syst. 93(1-2), 227–243 (2019)

    Article  Google Scholar 

  15. Finegan, F., Higgins, R., Nichols, F.: Runway acceptance rate improvements. In: 8Th Aerospace Sciences Meeting, p 74 (1970)

  16. Förster, J.: System Identification of the Crazyflie 2.0 Nano Quadrocopter. B.S. thesis, ETH Zurich (2015)

  17. Garcia, C.E., Prett, D.M., Morari, M.: Model predictive control: Theory and practice - A survey. Automatica 25(3), 335–348 (1989). http://www.sciencedirect.com/science/article/pii/0005109889900022

    Article  Google Scholar 

  18. Giernacki, W., Skwierczyński, M., Witwicki, W., Wroński, P., Kozierski, P.: Crazyflie 2.0 Quadrotor as a platform for research and education in robotics and control engineering. In: 2017 22Nd International Conference on Methods and Models in Automation and Robotics (MMAR), pp 37–42. IEEE (2017)

  19. Giones, F., Brem, A.: From toys to tools: the co-evolution of technological and entrepreneurial developments in the drone industry. Bus. Horiz. 60(6), 875–884 (2017)

    Article  Google Scholar 

  20. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning, 1st edn. Addison-wesley Longman Publishing Co., Inc, USA (1989)

    MATH  Google Scholar 

  21. Griffiths, D.A.: A study of dual-rotor interference and ground effect using a Free-Vortex wake model. In: American Helicopter Society 58th Annual Forum, Montreal, Canada, June 11-13, 2002 (2002)

  22. Hansson, A.: A primal-dual interior-point method for robust optimal control of linear discrete-time systems. IEEE Trans. Autom. Control 45(9), 1639–1655 (2000)

    Article  MathSciNet  Google Scholar 

  23. Hönig, W., Preiss, J.A., Kumar, T.S., Sukhatme, G.S., Ayanian, N.: Trajectory planning for quadrotor swarms. IEEE Trans. Robot. 34(4), 856–869 (2018)

    Article  Google Scholar 

  24. Huang, H., Hoffmann, G.M., Waslander, S.L., Tomlin, C.J.: Aerodynamics and control of autonomous Quadrotor helicopters in aggressive maneuvering. In: 2009 IEEE International Conference on Robotics and Automation, pp 3277–3282. IEEE (2009)

  25. Jain, K.P., Fortmuller, T., Byun, J., Mäkiharju, S.A., Mueller, M.W.: Modeling of aerodynamic disturbances for proximity flight of multirotors. In: 2019 International Conference on Unmanned Aircraft Systems (ICUAS), pp 1261–1269. IEEE (2019)

  26. Kelly, M.: An introduction to trajectory optimization: How to do your own direct collocation. SIAM Rev. 59(4), 849–904 (2017). https://doi.org/10.1137/16M1062569

    Article  MathSciNet  MATH  Google Scholar 

  27. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN’95 - International Conference on Neural Networks, vol. 4, pp 1942–1948 (1995)

  28. Kim, J., Khosla, P.K.: Real-time obstacle avoidance using harmonic potential functions. IEEE Trans. Robot. Autom. 8(3), 338–349 (1992)

    Article  Google Scholar 

  29. Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. In: arXiv:1412.6980. Cite arxiv:1412.6980comment: Published as a Conference Paper at the 3rd International Conference for Learning Representations San Diego, 2015 (2014)

  30. Koo, S., Kim, S., Suk, J.: Model predictive control for uav automatic landing on moving carrier deck with heave motion. IFAC-PapersOnLine 48(5), 59–64 (2015). https://doi.org/10.1016/j.ifacol.2015.06.464. http://www.sciencedirect.com/science/article/pii/S240589631500703X. 3rd IFAC Workshop on Multivehicle Systems

    Article  Google Scholar 

  31. Kuriki, Y., Namerikawa, T.: Consensus-Based cooperative formation control with collision avoidance for a Multi-Uav system. In: 2014 American Control Conference, pp 2077–2082. IEEE (2014)

  32. Leese, G.W.: Helicopter downwash blast effects study. 3 US Army Engineer Waterways Experiment Station (1964)

  33. Lei, Y., Bai, Y., Xu, Z.: Wind effect on aerodynamic optimization for non-planar rotor pairs using full-scale measurements. J. Intell. Robot. Syst. 87(3-4), 615–626 (2017)

    Article  Google Scholar 

  34. Matei, I., Baras, J.: Distributed algorithms for optimization problems with equality constraints. In: Decision and Control (CDC), 2013 IEEE 52nd Annual Conference On, pp 2352–2357 (2013), https://doi.org/10.1109/CDC.2013.6760232

  35. Matei, I., Baras, J., Nabi, M., Kurtoglu, T.: An extension of the method of multipliers for distributed nonlinear programming. In: Decision and Control (CDC), 2014 IEEE 53nd Annual Conference On, pp 6951–6956 (2014)

  36. Mellinger, D., Kumar, V.: Minimum snap trajectory generation and control for Quadrotors. In: 2011 IEEE International Conference on Robotics and Automation, pp 2520–2525 (2011)

  37. Morabito, B., Kögel, M., Bullinger, E., Pannocchia, G., Findeisen, R.: Simple and efficient moving horizon estimation based on the fast gradient method. IFAC-PapersOnLine 48(23), 428–433 (2015). https://doi.org/10.1016/j.ifacol.2015.11.316. http://www.sciencedirect.com/science/article/pii/S2405896315026002. 5th IFAC Conference on Nonlinear Model Predictive Control NMPC 2015

    Article  Google Scholar 

  38. Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7, 308–313 (1965)

    Article  MathSciNet  Google Scholar 

  39. Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, USA (2006)

    MATH  Google Scholar 

  40. Odonkor, P., Ball, Z., Chowdhury, S.: Distributed operation of collaborating unmanned aerial vehicles for time-sensitive oil spill mapping. Swarm Evol. Comput. 46, 52–68 (2019)

    Article  Google Scholar 

  41. Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch (2017)

  42. Patnaik, B., Wei, G.: Controlling wake turbulence. Phys. Rev. Lett. 88(5), 054502 (2002)

    Article  Google Scholar 

  43. Qu, Z., Jin, Y.F.: Robust control of nonlinear systems in the presence of unknown exogenous dynamics. vol. 3 pp. 2784–2790, https://doi.org/10.1109/.2001.980695 (2001)

  44. Radhakrishnan, A., Schmitz, F.: An experimental investigation of a quad tilt rotor in ground effect. In: 21st AIAA Applied Aerodynamics Conference, p 3517 (2003)

  45. Rao, C.V., Wright, S.J., Rawlings, J.B.: Application of interior-point methods to model predictive control. J. Opt. Theory Appl. 99, 723–757 (1998)

    Article  MathSciNet  Google Scholar 

  46. Sa, I., Kamel, M., Khanna, R., Popoviċ, M., Nieto, J., Siegwart, R.: Dynamic System Identification, and Control for a Cost-Effective and Open-Source Multi-Rotor Mav. In: Hutter, M., Siegwart, R. (eds.) Field and Service Robotics, pp 605–620. Springer International Publishing, Cham (2018)

  47. Sartori, D., Yu, W.: Experimental characterization of a propulsion system for multi-rotor uavs. J. Intell. Robot. Syst. 96(3-4), 529–540 (2019)

    Article  Google Scholar 

  48. Shi, G., Hönig, W., Yue, Y., Chung, S.J.: Neural-swarm:, Decentralized close-proximity multirotor control using learned interactions. arXiv:2003.02992 (2020)

  49. Shin, H.S., Antoniadis, A.F., Tsourdos, A.: Parametric study on formation flying effectiveness for a blended-wing uav. J. Intell. Robot. Syst. 93(1-2), 179–191 (2019)

    Article  Google Scholar 

  50. Shukla, D., Hiremath, N., Patel, S., Komerath, N.: Aerodynamic interactions study on low-re coaxial and quad-rotor configurations. In: ASME International Mechanical Engineering Congress and Exposition, vol. 58424, p V007t09a023. American Society of Mechanical Engineers (2017)

  51. Shukla, D., Komerath, N.: Multirotor drone aerodynamic interaction investigation. Drones 2 (4), 43 (2018)

    Article  Google Scholar 

  52. Silano, G., Aucone, E., Iannelli, L.: Crazys: a software-in-the-loop platform for the Crazyflie 2.0 Nano-Quadcopter. In: 2018 26Th Mediterranean Conference on Control and Automation (MED), pp 1–6. IEEE (2018)

  53. Stojanovic, V., He, S., Zhang, B.: State and parameter joint estimation of linear stochastic systems in presence of faults and non-gaussian noises. International Journal of Robust and Nonlinear Control. https://doi.org/10.1002/rnc.5131 (2020)

  54. Stojanovic, V., Nedic, N., Prsic, D., Dubonjic, L., Djordjevic, V.: Application of cuckoo search algorithm to constrained control problem of a parallel robot platform. Int. J. Adv. Manuf. Technol. 87 https://doi.org/10.1007/s00170-016-8627-z (2016)

  55. Stojanovic, V., Prsic, D.: Robust identification for fault detection in the presence of non-gaussian noises: application to hydraulic servo drives. Nonlinear Dyn. 100 https://doi.org/10.1007/s11071-020-05616-4(2020)

  56. Sun, K., Liu, L., Qiu, J., Feng, G.: Fuzzy adaptive finite-time fault-tolerant control for strict-feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 1–1 (2020)

  57. Tazibt, C.Y., Achir, N., Muhlethaler, P., Djamah, T.: uav-based data gathering using an artificial potential fields approach. In: 2018 IEEE 88Th Vehicular Technology Conference (VTC-Fall), pp 1–5 (2018)

  58. Wang, Z., Spica, R., Schwager, M.: Game theoretic motion planning for multi-robot racing. In: Distributed Autonomous Robotic Systems, pp 225–238. Springer, New York (2019)

  59. Yeo, D., Shrestha, E., Paley, D.A., Atkins, E.M.: An empirical model of rotorcraft Uav Downwash for disturbance localization and avoidance. In: AIAA Atmospheric Flight Mechanics Conference, p 1685 (2015)

  60. Yoon, S., Lee, H.C., Pulliam, T.H.: Computational analysis of multi-rotor flows. In: 54Th AIAA Aerospace Sciences Meeting, p 0812 (2016)

Download references

Acknowledgements

This material is based upon work supported by the Defense Advanced Research Projects Agency (DARPA) under Agreement No. HR0011-18-9-0037. Any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the DARPA.

Author information

Authors and Affiliations

  1. Palo Alto Research Center, Inc. (PARC), Palo Alto, CA, 94304, USA

    Ion Matei & Johan de Kleer

  2. Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY, 14260, USA

    Chen Zeng, Souma Chowdhury & Rahul Rai

Authors
  1. Ion Matei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chen Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Souma Chowdhury
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rahul Rai
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Johan de Kleer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Souma Chowdhury.

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Matei, I., Zeng, C., Chowdhury, S. et al. Controlling Draft Interactions Between Quadcopter Unmanned Aerial Vehicles with Physics-aware Modeling. J Intell Robot Syst 101, 21 (2021). https://doi.org/10.1007/s10846-020-01295-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-020-01295-w

Keywords

Search

Navigation