Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Predictive control of aerial swarms in cluttered environments

Nature Machine Intelligence volume 3, pages 545–554 (2021)Cite this article

Subjects

Abstract

Classical models of aerial swarms often describe global coordinated motion as the combination of local interactions that happen at the individual level. Mathematically, these interactions are represented with potential fields. Despite their explanatory success, these models fail to guarantee rapid and safe collective motion when applied to aerial robotic swarms flying in cluttered environments of the real world, such as forests and urban areas. Moreover, these models necessitate a tight coupling with the deployment scenarios to induce consistent swarm behaviours. Here, we propose a predictive model that incorporates the local principles of potential field models in an objective function and optimizes those principles under the knowledge of the agents’ dynamics and environment. We show that our approach improves the speed, order and safety of the swarm, it is independent of the environment layout and is scalable in the swarm speed and inter-agent distance. Our model is validated with a swarm of five quadrotors that can successfully navigate in a real-world indoor environment populated with obstacles.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Experimental set-up of drone swarm flight in cluttered environments.
Fig. 2: Comparison of the PF and NMPC aerial swarms in simulation experiments.
Fig. 3: Comparison of the PF and NMPC swarm deployment in environments with different obstacle densities.
Fig. 4: Scalability of the NMPC swarm in inter-agent distance and speed.
Fig. 5: Real-world experiment with the NMPC swarm.

Similar content being viewed by others

Data availability

Complementary data for reproducing the experiments are available in the Supplementary Information. Simulation and hardware experimental data that support the findings of this study can be downloaded from ref. 54.

Code availability

The code that supports the findings of this study can be downloaded from ref. 55.

References

  1. Couzin, I. D., Krause, J., Franks, N. R. & Levin, S. A. Effective leadership and decision-making in animal groups on the move. Nature 433, 513–516 (2005).

    Article  Google Scholar 

  2. Hildenbrandt, H., Carere, C. & Hemelrijk, C. K. Self-organized aerial displays of thousands of starlings: a model. Behav. Ecol. 21, 1349–1359 (2010).

    Article  Google Scholar 

  3. Young, G. F., Scardovi, L., Cavagna, A., Giardina, I. & Leonard, N. E. Starling flock networks manage uncertainty in consensus at low cost. PLoS Comput. Biol. 9, e1002894 (2013).

    Article  MathSciNet  Google Scholar 

  4. Dell’Ariccia, G., Dell’Omo, G., Wolfer, D. P. & Lipp, H.-P. Flock flying improves pigeons’ homing: GPS track analysis of individual flyers versus small groups. Anim. Behav. 76, 1165–1172 (2008).

    Article  Google Scholar 

  5. Nagy, M., Ákos, Z., Biro, D. & Vicsek, T. Hierarchical group dynamics in pigeon flocks. Nature 464, 890–893 (2010).

    Article  Google Scholar 

  6. Yomosa, M., Mizuguchi, T., Vásárhelyi, G. & Nagy, M. Coordinated behaviour in pigeon flocks. PLoS ONE 10, e0140558 (2015).

    Article  Google Scholar 

  7. Ballerini, M. et al. Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study. Proc. Natl. Acad. Sci. USA 105, 1232–1237 (2008).

    Article  Google Scholar 

  8. Floreano, D. & Wood, R. J. Science, technology and the future of small autonomous drones. Nature 521, 460–466 (2015).

    Article  Google Scholar 

  9. Stirling, T., Roberts, J., Zufferey, J.-C. & Floreano, D. Indoor navigation with a swarm of flying robots. In Proc. IEEE International Conference on Robotics and Automation (ICRA) 4641–4647 (IEEE, 2012).

  10. McGuire, K. N., Wagter, C. D., Tuyls, K., Kappen, H. J. & de Croon, G. C. H. E. Minimal navigation solution for a swarm of tiny flying robots to explore an unknown environment. Sci. Robot. 4, eaaw9710 (2019).

    Article  Google Scholar 

  11. Erman, A. T., van Hoesel, L., Havinga, P. & Wu, J. Enabling mobility in heterogeneous wireless sensor networks cooperating with UAVs for mission-critical management. IEEE Wirel. Commun. 15, 38–46 (2008).

    Article  Google Scholar 

  12. Tagliabue, A., Kamel, M., Siegwart, R. & Nieto, J. Robust collaborative object transportation using multiple MAVs. Int. J. Robot. Res. 38, 1020–1044 (2019).

    Article  Google Scholar 

  13. Augugliaro, F. et al. The flight assembled architecture installation: cooperative construction with flying machines. IEEE Control Syst. Mag. 34, 46–64 (2014).

    Article  MathSciNet  Google Scholar 

  14. Intel drone light show: Intel’s 50th anniversary (Intel, 21 November 2019); https://www.intel.com/content/www/us/en/technology-innovation/videos/drone-light-show-50th-anniversary-video.html

  15. EHang Egret’s 1,374 drones dancing over the City Wall of Xian, achieving a Guinness World Records title (EHang, 2 May 2018); https://www.ehang.com/news/365.html

  16. The Globe and Mail: mini-drone use on the rise to light up big concerts like Celine Dion and Drake (Verity, 6 December 2019); https://veritystudios.com/news/globe-and-mail-celine

  17. Chen, D., Liu, X., Xu, B. & Zhang, H.-T. Intermittence and connectivity of interactions in pigeon flock flights. Sci. Rep. 7, 10452 (2017).

    Article  Google Scholar 

  18. Berdahl, A., Torney, C. J., Ioannou, C. C., Faria, J. J. & Couzin, I. D. Emergent sensing of complex environments by mobile animal groups. Science 339, 574–576 (2013).

    Article  Google Scholar 

  19. Couzin, I. D. Synchronization: the key to effective communication in animal collectives. Trends Cogn. Sci. 22, 844–846 (2018).

    Article  Google Scholar 

  20. Reynolds, C. W. Flocks, herds and schools: a distributed behavioral model. Comput. Graph. 21, 25–43 (1987).

    Article  Google Scholar 

  21. Hauert, S. et al. Reynolds flocking in reality with fixed-wing robots: communication range versus maximum turning rate. In Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 5015–5020 (IEEE, 2011).

  22. Schilling, F., Lecoeur, J., Schiano, F. & Floreano, D. Learning vision-based flight in drone swarms by imitation. IEEE Robot. Autom. Lett. 4, 4523–4530 (2019).

    Article  Google Scholar 

  23. Olfati-Saber, R. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control 51, 401–420 (2006).

    Article  MathSciNet  Google Scholar 

  24. Vásárhelyi, G. et al. Optimized flocking of autonomous drones in confined environments. Sci. Robot. 3, eaat3536 (2018).

    Article  Google Scholar 

  25. Vasarhelyi, G. et al. Outdoor flocking and formation flight with autonomous aerial robots. In Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 3866–3873 (IEEE, 2014).

  26. Koren, Y. & Borenstein, J. Potential field methods and their inherent limitations for mobile robot navigation. In Proc. IEEE International Conference on Robotics and Automation (ICRA) 1398–1404 (IEEE, 1991).

  27. Soria, E., Floreano, D. & Schiano, F. The influence of limited visual sensing on the Reynolds flocking algorithm. In Proc. Third IEEE International Conference on Robotic Computing (IRC) 138–145 (IEEE, 2019).

  28. Borrelli, F., Bemporad, A. & Morari, M. Predictive Control for Linear and Hybrid Systems 1st edn (Cambridge Univ. Press, 2017).

  29. Grune, L. & Pannek, J. Nonlinear Model Predictive Control. Theory and Algorithms (Springer, 2011).

  30. Baca, T., Hert, D., Loianno, G., Saska, M. & Kumar, V. Model predictive trajectory tracking and collision avoidance for reliable outdoor deployment of unmanned aerial vehicles. In Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 6753–6760 (IEEE, 2018).

  31. Falanga, D., Foehn, P., Lu, P. & Scaramuzza, D. PAMPC: Perception-Aware Model Predictive Control for quadrotors. In Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 1–8 (IEEE, 2018).

  32. Luis, C. E., Vukosavljev, M. & Schoellig, A. P. Online trajectory generation with distributed model predictive control for multi-robot motion planning. IEEE Robot. Autom. Lett. 5, 604–611 (2020).

    Article  Google Scholar 

  33. Keviczky, T., Borrelli, F., Fregene, K., Godbole, D. & Balas, G. J. Decentralized receding horizon control and coordination of autonomous vehicle formations. IEEE Trans. Control Syst. Technol. 16, 19–33 (2008).

    Article  Google Scholar 

  34. Van Parys, R. Distributed MPC for multi-vehicle systems moving in formation. Robot. Auton. Syst 97, 144–152 (2017).

    Article  Google Scholar 

  35. Eren, U. et al. Model predictive control in aerospace systems: current state and opportunities. J. Guid. Control Dyn. 40, 1541–1566 (2017).

    Article  Google Scholar 

  36. Dunbar, W. B. & Murray, R. M. Distributed receding horizon control for multi-vehicle formation stabilization. Automatica 42, 549–558 (2006).

    Article  MathSciNet  Google Scholar 

  37. Raffard, R. L., Tomlin, C. J. & Boyd, S. P. Distributed optimization for cooperative agents: application to formation flight. IEEE Conf. Decision Control 3, 2453–2459 (2004).

    Google Scholar 

  38. Schouwenaars, T., How, J. & Feron, E. Decentralized cooperative trajectory planning of multiple aircraft with hard safety guarantees. In Proc. AIAA Guidance, Navigation and Control Conference (AIAA, 2004); https://doi.org/10.2514/6.2004-5141

  39. Richards, A. & How, J. Implementation of robust decentralized model predictive control. In Proc. AIAA Guidance, Navigation and Control Conference (AIAA, 2005); https://doi.org/10.2514/6.2005-6366

  40. Kuwata, Y. & How, J. P. Robust cooperative decentralized trajectory optimization using receding horizon MILP. In Proc. 2007 American Control Conference 522–527 (IEEE, 2007); https://doi.org/10.1109/ACC.2007.4283003

  41. Erunsal, I. K., Martinoli, A. & Ventura, R. Decentralized nonlinear model predictive control for 3D formation of multirotor micro aerial vehicles with relative sensing and estimation. In Proc. 2019 International Symposium on Multi-Robot and Multi-Agent Systems (MRS) 176–178 (IEEE, 2019).

  42. Zhao, W. & Go, T. H. Quadcopter formation flight control combining MPC and robust feedback linearization. J. Frankl. Inst. 351, 1335–1355 (2014).

    Article  MathSciNet  Google Scholar 

  43. Ren, W. & Sorensen, N. Distributed coordination architecture for multi-robot formation control. Robot. Auton. Syst. 56, 324–333 (2008).

    Article  Google Scholar 

  44. Kamel, M., Alonso-Mora, J., Siegwart, R. & Nieto, J. Robust collision avoidance for multiple micro aerial vehicles using nonlinear model predictive control. In Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 236–243 (IEEE, 2017).

  45. Kumar, V. & Michael, N. Opportunities and challenges with autonomous micro aerial vehicles. Int. J. Robot. Res. 31, 1279–1291 (2012).

    Article  Google Scholar 

  46. Petrlík, M. et al. A robust UAV system for operations in a constrained environment. IEEE Robot. Autom. Lett. 5, 2169–2176 (2020).

    Article  Google Scholar 

  47. Sapkota, K. R. et al. Vision-based unmanned aerial vehicle detection and tracking for sense and avoid systems. In Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 1556–1561 (IEEE, 2016).

  48. Hunt, E. R. & Hauert, S. A checklist for safe robot swarms. Nat. Mach. Intell. 2, 420–422 (2020).

    Article  Google Scholar 

  49. Lindqvist, B., Mansouri, S. S., Agha-mohammadi, A. & Nikolakopoulos, G. Nonlinear MPC for collision avoidance and control of UAVs with dynamic obstacles. IEEE Robot. Autom. Lett. 5, 6001–6008 (2020).

    Article  Google Scholar 

  50. Strandburg-Peshkin, A. et al. Visual sensory networks and effective information transfer in animal groups. Curr. Biol. 23, 709–711 (2013).

    Article  Google Scholar 

  51. Chen, Z. & Chu, T. Multi-agent system model with mixed coupling topologies for pattern formation and formation splitting. Math. Comput. Model. Dyn. Syst. 19, 388–400 (2013).

    Article  MathSciNet  Google Scholar 

  52. Verschueren, R. et al. Towards a modular software package for embedded optimization. IFAC-PapersOnLine 51, 374–380 (2018).

    Article  Google Scholar 

  53. Frison, G., Kufoalor, D. K. M., Imsland, L. & Jørgensen, J. B. Efficient implementation of solvers for linear model predictive control on embedded devices. In Proc. IEEE Conference on Control Applications (CCA) 1954–1959 (IEEE, 2014).

  54. Soria, E., Schiano, F. & Floreano, D. Predictive control of aerial swarms in cluttered environments [dataset]. Zenodo https://doi.org/10.5281/zenodo.4379168 (2020).

  55. Soria, E., Schiano, F. & Floreano, D. Predictive control of aerial swarms in cluttered environments [code repository]. Zenodo https://doi.org/10.5281/zenodo.4379503 (2020).

Download references

Acknowledgements

We thank A. De Bortoli, M. Pfister and F. Schilling for helpful discussions. This work was supported by the Swiss National Science Foundation under grant no. 200020_188457. This work was also partially funded by the European Union’s Horizon 2020 research and innovation programme under grant agreement ID 871479 AERIAL-CORE.

Author information

Authors and Affiliations

  1. Laboratory of Intelligent Systems (LIS), École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Enrica Soria, Fabrizio Schiano & Dario Floreano

Authors
  1. Enrica Soria
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fabrizio Schiano
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dario Floreano
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the conception of the project and were involved in the analysis of the results. E.S. designed, implemented and performed software and hardware experiments of the NMPC algorithm for the navigation of drone swarms in cluttered environments. All authors contributed to the writing of the manuscript.

Corresponding authors

Correspondence to Enrica Soria, Fabrizio Schiano or Dario Floreano.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Machine Intelligence thanks George Nikolakopoulos, Shan Luo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Soria, E., Schiano, F. & Floreano, D. Predictive control of aerial swarms in cluttered environments. Nat Mach Intell 3, 545–554 (2021). https://doi.org/10.1038/s42256-021-00341-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s42256-021-00341-y

This article is cited by

Search

Advanced search

Quick links

Nature Briefing AI and Robotics

Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research, free to your inbox weekly.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing: AI and Robotics