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Stochastic Nonlinear Ensemble Modeling and Control for Robot Team Environmental Monitoring

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Distributed Autonomous Robotic Systems (DARS 2022)

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Abstract

We seek methods to model, control, and analyze robot teams performing environmental monitoring tasks. During environmental monitoring, the goal is to have teams of robots collect various data throughout a fixed region for extended periods of time. Standard bottom-up task assignment methods do not scale as the number of robots and task locations increases and require computationally expensive replanning. Alternatively, top-down methods have been used to combat computational complexity, but most have been limited to the analysis of methods which focus on transition times between tasks. In this work, we study a class of nonlinear macroscopic models which we use to control a time-varying distribution of robots performing different tasks throughout an environment. Our proposed ensemble model and control maintains desired time-varying populations of robots by leveraging naturally occurring interactions between robots performing tasks. We validate our approach at multiple fidelity levels including experimental results, suggesting the effectiveness of our approach to perform environmental monitoring.

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References

  1. Almadhoun, R., Taha, T., Seneviratne, L., Zweiri, Y.: A survey on multi-robot coverage path planning for model reconstruction and mapping. SN Appl. Sci. 1(8), 1–24 (2019)

    Article  Google Scholar 

  2. Berman, S., Halász, A., Hsieh, M.A., Kumar, V.: Optimized stochastic policies for task allocation in swarms of robots. IEEE Trans. Rob. 25(4), 927–937 (2009)

    Article  Google Scholar 

  3. Biswal, S., Elamvazhuthi, K., Berman, S.: Decentralized control of multi-agent systems using local density feedback. IEEE Trans. Autom. Control 67(8), 3920–3932 (2021)

    Article  Google Scholar 

  4. Deshmukh, V., Elamvazhuthi, K., Biswal, S., Kakish, Z., Berman, S.: Mean-field stabilization of Markov chain models for robotic swarms: computational approaches and experimental results. IEEE Robot. Autom. Lett. 3(3), 1985–1992 (2018). https://doi.org/10.1109/LRA.2018.2792696

    Article  Google Scholar 

  5. Dey, B., Franci, A., Özcimder, K., Leonard, N.E.: Feedback controlled bifurcation of evolutionary dynamics with generalized fitness. In: 2018 Annual American Control Conference (ACC), pp. 6049–6054. IEEE (2018)

    Google Scholar 

  6. Elamvazhuthi, K., Berman, S.: Mean-field models in swarm robotics: a survey. Bioinspiration Biomimetics 15(1), 015001 (2019). https://doi.org/10.1088/1748-3190/ab49a4

  7. Gerkey, B.P., Mataric, M.J.: Multi-robot task allocation: analyzing the complexity and optimality of key architectures. In: 2003 IEEE International Conference on Robotics and Automation (ICRA), vol. 3, pp. 3862–3868. IEEE (2003)

    Google Scholar 

  8. Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)

    Article  Google Scholar 

  9. Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, vol. 42. Springer, Cham (2013). https://doi.org/10.1007/978-1-4612-1140-2

  10. Harwell, J., Sylvester, A., Gini, M.: Characterizing the limits of linear modeling of non-linear swarm behaviors. arXiv preprint arXiv:2110.12307 (2021)

  11. Hofbauer, J.: On the occurrence of limit cycles in the Volterra-Lotka equation. Nonlinear Anal. Theory Methods Appl. 5(9), 1003–1007 (1981)

    Article  MathSciNet  Google Scholar 

  12. Hsieh, M.A., Halász, Á., Berman, S., Kumar, V.: Biologically inspired redistribution of a swarm of robots among multiple sites. Swarm Intell. 2(2), 121–141 (2008)

    Article  Google Scholar 

  13. Hsieh, M.A., Halasz, A., Cubuk, E.D., Schoenholz, S., Martinoli, A.: Specialization as an optimal strategy under varying external conditions. In: 2009 IEEE International Conference on Robotics and Automation (ICRA), pp. 1941–1946 (2009). https://doi.org/10.1109/ROBOT.2009.5152798

  14. Khamis, A., Hussein, A., Elmogy, A.: Multi-robot task allocation: a review of the state-of-the-art. Coop. Robots Sens. Netw. 2015, 31–51 (2015)

    Google Scholar 

  15. Lee, W., Kim, D.: Adaptive approach to regulate task distribution in swarm robotic systems. Swarm Evol. Comput. 44, 1108–1118 (2019)

    Article  Google Scholar 

  16. Leonard, N.E.: Multi-agent system dynamics: bifurcation and behavior of animal groups. Annu. Rev. Control. 38(2), 171–183 (2014)

    Article  Google Scholar 

  17. Lerman, K., Jones, C., Galstyan, A., Matarić, M.J.: Analysis of dynamic task allocation in multi-robot systems. Int. J. Robot. Re. 25(3), 225–241 (2006). https://doi.org/10.1177/0278364906063426

  18. Lerman, K., Martinoli, A., Galstyan, A.: A review of probabilistic macroscopic models for swarm robotic systems. In: Şahin, E., Spears, W.M. (eds.) Swarm Robotics, pp. 143–152. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30552-1_12

    Chapter  Google Scholar 

  19. Mather, T.W., Hsieh, M.A.: Distributed robot ensemble control for deployment to multiple sites. In: Robotics: Science and Systems VII (2011)

    Google Scholar 

  20. Nam, C., Shell, D.A.: Analyzing the sensitivity of the optimal assignment in probabilistic multi-robot task allocation. IEEE Robot. Autom. Lett. 2(1), 193–200 (2017). https://doi.org/10.1109/LRA.2016.2588138

    Article  Google Scholar 

  21. Pais, D., Caicedo-Nunez, C.H., Leonard, N.E.: Hopf bifurcations and limit cycles in evolutionary network dynamics. SIAM J. Appl. Dyn. Syst. 11(4), 1754–1784 (2012)

    Article  MathSciNet  Google Scholar 

  22. Prorok, A., Hsieh, M.A., Kumar, V.: The impact of diversity on optimal control policies for heterogeneous robot swarms. IEEE Trans. Rob. 33(2), 346–358 (2017)

    Article  Google Scholar 

  23. Ravichandar, H., Shaw, K., Chernova, S.: STRATA: unified framework for task assignments in large teams of heterogeneous agents. Auton. Agents Multi Agent Syst. 34(2), 38 (2020)

    Article  Google Scholar 

  24. Schuster, P., Sigmund, K., Hofbauer, J., Gottlieb, R., Merz, P.: Selfregulation of behaviour in animal societies. Biol. Cybern. 40(1), 17–25 (1981)

    Article  Google Scholar 

  25. Sigmund, K.: A survey of replicator equations. In: Casti, J.L., Karlqvist, A. (eds.) Complexity, Language, and Life: Mathematical Approaches. Biomathematics, vol. 16, pp. 88–104. Springer, Heidelberg (1986). https://doi.org/10.1007/978-3-642-70953-1_4

Download references

Acknowledgement

We gratefully acknowledge the support of ARL DCIST CRA W911NF-17-2-0181, Office of Naval Research (ONR) Award No. N00014-22-1-2157, and the National Defense Science & Engineering Graduate (NDSEG) Fellowship Program.

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Correspondence to Victoria Edwards .

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Edwards, V., Silva, T.C., Hsieh, M.A. (2024). Stochastic Nonlinear Ensemble Modeling and Control for Robot Team Environmental Monitoring. In: Bourgeois, J., et al. Distributed Autonomous Robotic Systems. DARS 2022. Springer Proceedings in Advanced Robotics, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-031-51497-5_7

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