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Decentralized progressive shape formation with robot swarms

  • Guannan Li
  • David St-Onge
  • Carlo Pinciroli
  • Andrea Gasparri
  • Emanuele Garone
  • Giovanni Beltrame
Article

Abstract

We address the problem of progressively deploying a set of robots to a formation defined as a point cloud, in a decentralized manner. To achieve this, we present an algorithm that transforms a given point cloud into an acyclic directed graph. This graph is used by the control law to allow a swarm of robots to progressively form the target shape based only on local decisions. This means that free robots (i.e., not yet part of the formation) find their location based on the perceived location of the robots already in the formation. We prove that for a 2D shape it is sufficient for a free robot to compute its distance from two robots in the formation to achieve this objective. We validate our method using physics-based simulations and robotic experiments, showing consistent convergence and minimal formation placement error.

Keywords

Swarm robotics Pattern formation Progressive deployment Buzz 

Notes

Acknowledgements

We would like to thank the people who provided technical assistance for this work: Vivek Shankar Varadharajan, Cao Yanjun and Chao Chen, Polytechnique Montreal. This work was funded by the NSERC Strategic Partnership Grant No. 479149-2015 and by the NSERC Research Tools and Infrastructure Grant No. 2016-00599. This work is also sponsored by the China Scholarship Council.

Supplementary material

Supplementary material 1 (avi 206231 KB)

References

  1. Alonso-Mora, J., Breitenmoser, A., Rufli, M., Siegwart, R., & Beardsley, P. (2011). Multi-robot system for artistic pattern formation. In IEEE international conference on robotics and automation (ICRA) (pp. 4512–4517).Google Scholar
  2. Anand, A., Nithya, M., & Sudarshan, T. (2014). Coordination of mobile robots with master-slave architecture for a service application. In IEEE international conference on contemporary computing and informatics (IC3I) (pp. 539–543).Google Scholar
  3. Beal, J. (2011). Functional blueprints: An approach to modularity in grown systems. Swarm Intelligence, 5(3), 257–281.CrossRefGoogle Scholar
  4. Belta, C., & Kumar, V. (2002). Trajectory design for formations of robots by kinetic energy shaping. In IEEE international conference on robotics and automation (ICRA) (Vol. 3, pp. 2593–2598).Google Scholar
  5. Bonani, M., Longchamp, V., Magnenat, S., Rétornaz, P., Burnier, D., Roulet, G., et al. (2010). The marXbot, a miniature mobile robot opening new perspectives for the collective-robotic research. In IEEE international conference on intelligent robots and systems (IROS) (pp. 4187–4193).Google Scholar
  6. Brambilla, M., Ferrante, E., Birattari, M., & Dorigo, M. (2013). Swarm robotics: A review from the swarm engineering perspective. Swarm Intelligence, 7(1), 1–41.CrossRefGoogle Scholar
  7. Cheah, C. C., Hou, S. P., & Slotine, J. J. E. (2009). Region-based shape control for a swarm of robots. Automatica, 45(10), 2406–2411.MathSciNetCrossRefGoogle Scholar
  8. Chen, Z., & Chu, T. (2013). Multi-agent system model with mixed coupling topologies for pattern formation and formation splitting. Mathematical and Computer Modelling of Dynamical Systems, 19(4), 388–400.MathSciNetCrossRefGoogle Scholar
  9. Cowley, A., & Taylor, C. J. (2007). Orchestrating concurrency in robot swarms. In IEEE international conference on intelligent robots and systems (IROS) (pp. 945–950).Google Scholar
  10. Desai, J. P., Ostrowski, J. P., & Kumar, V. (2001). Modeling and control of formations of nonholonomic mobile robots. IEEE Transactions on Robotics and Automation, 17(6), 905–908.CrossRefGoogle Scholar
  11. Dieudonné, Y., & Petit, F. (2007). Deterministic leader election in anonymous sensor networks without common coordinated system. In International conference on principles of distributed systems (ICPDS) (pp. 132–142).Google Scholar
  12. Fierro, R., Belta, C., Desai, J. P., & Kumar, V. (2001a). On controlling aircraft formations. In IEEE conference on decision and control (Vol. 2, pp. 1065–1070).Google Scholar
  13. Fierro, R., Das, A. K., Kumar, V., & Ostrowski, J. P. (2001b). Hybrid control of formations of robots. In IEEE International Conference on Robotics and Automation (ICRA) (Vol. 1, pp. 157–162).Google Scholar
  14. Güzel, M. S., Gezer, E. C., Ajabshir, V. B., & Bostancı, E. (2017). An adaptive pattern formation approach for swarm robots. In IEEE international conference on electrical and electronic engineering (ICEEE) (pp. 194–198).Google Scholar
  15. Hsieh, A., & Kumar, V. (2006). Pattern generation with multiple robots. In IEEE international conference on robotics and automation (pp. 2442–2447).Google Scholar
  16. Hsieh, M. A., Kumar, V., & Chaimowicz, L. (2008). Decentralized controllers for shape generation with robotic swarms. Robotica, 26(5), 691–701.CrossRefGoogle Scholar
  17. Karpov, V., & Karpova, I. (2015). Leader election algorithms for static swarms. Biologically Inspired Cognitive Architectures, 12, 54–64.CrossRefGoogle Scholar
  18. Li, G., Sogor, I., & Beltrame, G. (2017). Self-adaptive pattern formation with battery-powered robot swarms. In NASA/ESA Adaptive Hardware and Systems Conference (AHS).Google Scholar
  19. Liu, L., & Shell, D. A. (2014). Multi-robot formation morphing through a graph matching problem. In International symposium on distributed autonomous robotic systems (DARS) (pp. 291–306).Google Scholar
  20. Majid, M., & Arshad, M. (2015). Hydrodynamic effect on V-shape pattern formation of swarm autonomous surface vehicles (ASVs). Procedia Computer Science, 76, 186–191.CrossRefGoogle Scholar
  21. Michael, N., Fink, J., & Kumar, V. (2007). Controlling a team of ground robots via an aerial robot. In IEEE international conference on intelligent robots and systems (IROS) (pp. 965–970).Google Scholar
  22. Michael, N., Fink, J., & Kumar, V. (2008a). Controlling ensembles of robots via a supervisory aerial robot. Advanced Robotics, 22(12), 1361–1377.CrossRefGoogle Scholar
  23. Michael, N., Zavlanos, M. M., Kumar, V., & Pappas, G. J. (2008b). Distributed multi-robot task assignment and formation control. In IEEE international conference on robotics and automation (ICRA) (pp. 128–133).Google Scholar
  24. Mondada, F., Bonani, M., Raemy, X., Pugh, J., Cianci, C., Klaptocz, A., et al. (2006). The e-puck: A robot designed for education in engineering. In Conference on autonomous robot systems and competitions (Robotica) (Vol. 1, pp. 59–65).Google Scholar
  25. Paley, D. A., Leonard, N. E., & Sepulchre, R. (2008). Stabilization of symmetric formations to motion around convex loops. Systems & Control Letters, 57(3), 209–215.MathSciNetCrossRefGoogle Scholar
  26. Petit, F. (2009). Tutorial 1–3: Leader election and pattern formation in swarms of deterministic robots. In International conference on parallel and distributed computing, applications and technologies (PDCAT).Google Scholar
  27. Pinciroli, C., & Beltrame, G. (2016). Buzz: An extensible programming language for heterogeneous swarm robotics. In IEEE international conference on intelligent robots and systems (IROS) (pp. 3794–3800).Google Scholar
  28. Pinciroli, C., Gasparri, A., Garone, E., & Beltrame, G. (2016). Decentralized progressive shape formation with robot swarms. In International symposium on distributed autonomous robotic systems (DARS) (pp. 433–445).CrossRefGoogle Scholar
  29. Pinciroli, C., Trianni, V., O’Grady, R., Pini, G., Brutschy, A., Brambilla, M., et al. (2012). ARGoS: A modular, parallel, multi-engine simulator for multi-robot systems. Swarm Intelligence, 6(4), 271–295.CrossRefGoogle Scholar
  30. Ravichandran, R., Gordon, G., & Goldstein, S. (2007). A scalable distributed algorithm for shape transformation in multi-robot systems. In International conference on intelligent robots and systems (IROS) (pp. 4188–4193).Google Scholar
  31. Rubenstein, M., Cornejo, A., & Nagpal, R. (2014). Programmable self-assembly in a thousand-robot swarm. Science, 345(6198), 795–799.CrossRefGoogle Scholar
  32. Rubenstein, M., & Shen, W. M. (2008). A scalable and distributed model for self-organization and self-healing. In International joint conference on autonomous agents and multiagent systems (AAMAS) (pp. 1179–1182).Google Scholar
  33. Seibert, P., & Suarez, R. (1990). Global stabilization of nonlinear cascade systems. Systems & Control Letters, 14(4), 347–352.MathSciNetCrossRefGoogle Scholar
  34. Sepulchre, R., Paley, D. A., & Leonard, N. E. (2008). Stabilization of planar collective motion with limited communication. IEEE Transactions on Automatic Control, 53(3), 706–719.MathSciNetCrossRefGoogle Scholar
  35. Spears, W. M., Spears, D. F., Hamann, J. C., & Heil, R. (2004). Distributed, physics-based control of swarms of vehicles. Autonomous Robots, 17(2/3), 137–162.CrossRefGoogle Scholar
  36. Spletzer, J., & Fierro, R. (2005). Optimal positioning strategies for shape changes in robot teams. In IEEE International conference on robotics and automation (pp. 742–747).Google Scholar
  37. Støy, K. (2001). Using situated communication in distributed autonomous mobile robots. In Scandinavian conference on artificial intelligence (SCAI) (pp. 44–52).Google Scholar
  38. Tanner, H. G., Kumar, V., & Pappas, G. J. (2002). The effect of feedback and feedforward on formation iss. In IEEE international conference on robotics and automation (ICRA) (Vol. 4, pp. 3448–3453).Google Scholar
  39. Turpin, M., Michael, N., & Kumar, V. (2012a). Decentralized formation control with variable shapes for aerial robots. In IEEE international conference on robotics and automation (ICRA) (pp. 23–30).Google Scholar
  40. Turpin, M., Michael, N., & Kumar, V. (2012b). Trajectory design and control for aggressive formation flight with quadrotors. Autonomous Robots, 33(1–2), 143–156.CrossRefGoogle Scholar
  41. Turpin, M., Michael, N., & Kumar, V. (2013). Trajectory planning and assignment in multirobot systems. In E. Frazzoli, T. Lozano-Perez, N. Roy, & D. Rus (Eds.), Algorithmic foundations of robotics X (pp. 175–190). Berlin: Springer.CrossRefGoogle Scholar
  42. Yang, H., & Zhang, F. (2010). Geometric formation control for autonomous underwater vehicles. In IEEE international conference on robotics and automation (ICRA) (pp. 4288–4293).Google Scholar
  43. Yu, C. H., & Nagpal, R. (2008). Sensing-based shape formation on modular multi-robot systems: A theoretical study. In International joint conference on autonomous agents and multiagent systems (AAMAS) (pp. 71–78).Google Scholar
  44. Zhang, F. (2007). Cooperative shape control of particle formations. In IEEE conference on decision and control (pp. 2516–2521).Google Scholar
  45. Zhang, F., Fratantoni, D. M., Paley, D. A., Lund, J. M., & Leonard, N. E. (2007). Control of coordinated patterns for ocean sampling. International Journal of Control, 80(7), 1186–1199.MathSciNetCrossRefGoogle Scholar
  46. Zhang, F., & Haq, S. (2008). Boundary following by robot formations without GPS. In IEEE international conference on robotics and automation (pp. 152–157).Google Scholar
  47. Zhang, F., & Leonard, N. E. (2006). Coordinated patterns on smooth curves. In IEEE international conference on networking, sensing and control (ICNSC) (pp. 434–439).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of RoboticsShenyang Institute of Automation, CASShenyangChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.Worcester Polytechnic InstituteWorcesterUSA
  4. 4.Department of EngineeringUniversità Roma TreRomeItaly
  5. 5.Université Libre de BruxellesBrusselsBelgium
  6. 6.Polytechnique MontréalMontréalCanada

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