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.
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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).
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).
Beal, J. (2011). Functional blueprints: An approach to modularity in grown systems. Swarm Intelligence, 5(3), 257–281.
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).
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).
Brambilla, M., Ferrante, E., Birattari, M., & Dorigo, M. (2013). Swarm robotics: A review from the swarm engineering perspective. Swarm Intelligence, 7(1), 1–41.
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.
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.
Cowley, A., & Taylor, C. J. (2007). Orchestrating concurrency in robot swarms. In IEEE international conference on intelligent robots and systems (IROS) (pp. 945–950).
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.
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).
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).
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).
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).
Hsieh, A., & Kumar, V. (2006). Pattern generation with multiple robots. In IEEE international conference on robotics and automation (pp. 2442–2447).
Hsieh, M. A., Kumar, V., & Chaimowicz, L. (2008). Decentralized controllers for shape generation with robotic swarms. Robotica, 26(5), 691–701.
Karpov, V., & Karpova, I. (2015). Leader election algorithms for static swarms. Biologically Inspired Cognitive Architectures, 12, 54–64.
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).
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).
Majid, M., & Arshad, M. (2015). Hydrodynamic effect on V-shape pattern formation of swarm autonomous surface vehicles (ASVs). Procedia Computer Science, 76, 186–191.
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).
Michael, N., Fink, J., & Kumar, V. (2008a). Controlling ensembles of robots via a supervisory aerial robot. Advanced Robotics, 22(12), 1361–1377.
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).
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).
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.
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).
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).
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).
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.
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).
Rubenstein, M., Cornejo, A., & Nagpal, R. (2014). Programmable self-assembly in a thousand-robot swarm. Science, 345(6198), 795–799.
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).
Seibert, P., & Suarez, R. (1990). Global stabilization of nonlinear cascade systems. Systems & Control Letters, 14(4), 347–352.
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.
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.
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).
Støy, K. (2001). Using situated communication in distributed autonomous mobile robots. In Scandinavian conference on artificial intelligence (SCAI) (pp. 44–52).
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).
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).
Turpin, M., Michael, N., & Kumar, V. (2012b). Trajectory design and control for aggressive formation flight with quadrotors. Autonomous Robots, 33(1–2), 143–156.
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.
Yang, H., & Zhang, F. (2010). Geometric formation control for autonomous underwater vehicles. In IEEE international conference on robotics and automation (ICRA) (pp. 4288–4293).
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).
Zhang, F. (2007). Cooperative shape control of particle formations. In IEEE conference on decision and control (pp. 2516–2521).
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.
Zhang, F., & Haq, S. (2008). Boundary following by robot formations without GPS. In IEEE international conference on robotics and automation (pp. 152–157).
Zhang, F., & Leonard, N. E. (2006). Coordinated patterns on smooth curves. In IEEE international conference on networking, sensing and control (ICNSC) (pp. 434–439).
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.
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Li, G., St-Onge, D., Pinciroli, C. et al. Decentralized progressive shape formation with robot swarms. Auton Robot 43, 1505–1521 (2019). https://doi.org/10.1007/s10514-018-9807-5
- Swarm robotics
- Pattern formation
- Progressive deployment