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A Case Study of Policy Synthesis for Swarm Robotics

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12477)

Abstract

Continuous time Markov chain models, derived from process algebraic descriptions of systems are a powerful method for studying the dynamics of collective adaptive systems. Here, we study a formal modelling framework, based on the CARMA process algebra, where information about the possible control actions of individual components in such systems can be incorporated in the process algebraic description. The formal semantics for such specifications are defined to give rise to continuous time Markov decision processes. Here we show how, together with a given specification of desired collective behaviour, such models can be readily treated as stochastic policy or control synthesis problems. This is demonstrated through an example scenario from swarm robotics.

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Notes

  1. 1.

    Note that the above construction could equivalently be done directly in the definition of the rates of \( random ^*\) and \( directed ^*\) actions.

References

  1. Baier, C., Hermanns, H., Katoen, J., Haverkort, B.R.: Efficient computation of time-bounded reachability probabilities in uniform continuous-time Markov decision processes. Theor. Comput. Sci. 345(1), 2–26 (2005)

    MathSciNet  CrossRef  Google Scholar 

  2. Bartocci, E., Bortolussi, L., Brázdil, T., Milios, D., Sanguinetti, G.: Policy learning in continuous-time Markov decision processes using Gaussian processes. Perform. Eval. 116, 84–100 (2017)

    CrossRef  Google Scholar 

  3. Bernardo, M., Gorrieri, R.: Extended Markovian process algebra. In: Montanari, U., Sassone, V. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 315–330. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61604-7_63

    CrossRef  Google Scholar 

  4. Bortolussi, L., Milios, D., Sanguinetti, G.: Smoothed model checking for uncertain continuous-time Markov chains. Inf. Comput. 247, 235–253 (2016)

    MathSciNet  CrossRef  Google Scholar 

  5. Bortolussi, L., Policriti, A., Silvetti, S.: Logic-based multi-objective design of chemical reaction networks. In: Cinquemani, E., Donzé, A. (eds.) HSB 2016. LNCS, vol. 9957, pp. 164–178. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-47151-8_11

    CrossRef  Google Scholar 

  6. Bortolussi, L., Silvetti, S.: Bayesian statistical parameter synthesis for linear temporal properties of stochastic models. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10806, pp. 396–413. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89963-3_23

    CrossRef  MATH  Google Scholar 

  7. Brambilla, M., Brutschy, A., Dorigo, M., Birattari, M.: Property-driven design for robot swarms: a design method based on prescriptive modeling and model checking. ACM Trans. Auton. Adapt. Syst. 9(4), 17:1–17:28 (2014)

    Google Scholar 

  8. Butkova, Y., Hatefi, H., Hermanns, H., Krčál, J.: Optimal continuous time Markov decisions. In: Finkbeiner, B., Pu, G., Zhang, L. (eds.) ATVA 2015. LNCS, vol. 9364, pp. 166–182. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24953-7_12

    CrossRef  Google Scholar 

  9. Češka, M., Dannenberg, F., Paoletti, N., Kwiatkowska, M., Brim, L.: Precise parameter synthesis for stochastic biochemical systems. Acta Informatica 54(6), 589–623 (2016). https://doi.org/10.1007/s00236-016-0265-2

    MathSciNet  CrossRef  MATH  Google Scholar 

  10. De Nicola, R., Latella, D., Loreti, M., Massink, M.: A uniform definition of stochastic process calculi. ACM Comput. Surv. 46(1), 5:1–5:35 (2013)

    CrossRef  Google Scholar 

  11. Galpin, V.: Modelling ambulance deployment with Carma. In: Lluch Lafuente, A., Proença, J. (eds.) COORDINATION 2016. LNCS, vol. 9686, pp. 121–137. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39519-7_8

    CrossRef  Google Scholar 

  12. Galpin, V., Zon, N., Wilsdorf, P., Gilmore, S.: Mesoscopic modelling of pedestrian movement using CARMA and its tools. ACM Trans. Model. Comput. Simul. 28(2), 1–26 (2018)

    MathSciNet  CrossRef  Google Scholar 

  13. Georgoulas, A., Hillston, J., Milios, D., Sanguinetti, G.: Probabilistic programming process algebra. In: Norman, G., Sanders, W. (eds.) QEST 2014. LNCS, vol. 8657, pp. 249–264. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10696-0_21

    CrossRef  Google Scholar 

  14. Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, New York (1996)

    CrossRef  Google Scholar 

  15. Kwiatkowska, M., Norman, G., Parker, D.: PRISM: probabilistic symbolic model checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 200–204. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46029-2_13

    CrossRef  Google Scholar 

  16. Legay, A., Delahaye, B., Bensalem, S.: Statistical model checking: an overview. In: Barringer, H., et al. (eds.) RV 2010. LNCS, vol. 6418, pp. 122–135. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16612-9_11

    CrossRef  Google Scholar 

  17. Lerman, K., Galstyan, A.: Mathematical model of foraging in a group of robots: effect of interference. Auton. Robots 13(2), 127–141 (2002). https://doi.org/10.1023/A:1019633424543

    CrossRef  MATH  Google Scholar 

  18. Loreti, M., Hillston, J.: Modelling and analysis of collective adaptive systems with CARMA and its tools. In: Bernardo, M., De Nicola, R., Hillston, J. (eds.) SFM 2016. LNCS, vol. 9700, pp. 83–119. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-34096-8_4

    CrossRef  Google Scholar 

  19. Luckcuck, M., Farrell, M., Dennis, L.A., Dixon, C., Fisher, M.: Formal specification and verification of autonomous robotic systems: a survey. ACM Comput. Surv. 52(5), 1–14 (2019)

    CrossRef  Google Scholar 

  20. Lv, H., Hillston, J., Piho, P., Wang, H.: An attribute-based availability model for large scale IaaS clouds with CARMA. IEEE Trans. Parallel Distrib. Syst. 31(3), 733–748 (2020)

    CrossRef  Google Scholar 

  21. Soriano Marcolino, L., Tavares dos Passos, Y., Fonseca de Souza, Á.A., dos Santos Rodrigues, A., Chaimowicz, L.: Avoiding target congestion on the navigation of robotic swarms. Auton. Robots 41(6), 1297–1320 (2016). https://doi.org/10.1007/s10514-016-9577-x

    CrossRef  Google Scholar 

  22. Piho, P., Hillston, J.: Policy synthesis for collective dynamics. In: McIver, A., Horvath, A. (eds.) QEST 2018. LNCS, vol. 11024, pp. 356–372. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99154-2_22

    CrossRef  Google Scholar 

  23. Rackauckas, C., Nie, Q.: DifferentialEquations.jl – a performant and feature-rich ecosystem for solving differential equations in Julia. J. Open Res. Softw. 5, 15 (2017)

    CrossRef  Google Scholar 

  24. Schroeder, A., Trease, B., Arsie, A.: Balancing robot swarm cost and interference effects by varying robot quantity and size. Swarm Intell. 13(1), 1–19 (2018). https://doi.org/10.1007/s11721-018-0161-1

    CrossRef  Google Scholar 

  25. Zon, N., Gilmore, S.: Data-driven modelling and simulation of urban transportation systems using Carma. In: Margaria, T., Steffen, B. (eds.) ISoLA 2018, Part III. LNCS, vol. 11246, pp. 274–287. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03424-5_18

    CrossRef  Google Scholar 

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Piho, P., Hillston, J. (2020). A Case Study of Policy Synthesis for Swarm Robotics. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation: Engineering Principles. ISoLA 2020. Lecture Notes in Computer Science(), vol 12477. Springer, Cham. https://doi.org/10.1007/978-3-030-61470-6_29

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  • DOI: https://doi.org/10.1007/978-3-030-61470-6_29

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