Sampling-Based Reactive Motion Planning with Temporal Logic Constraints and Imperfect State Information

  • Felipe J. MontanaEmail author
  • Jun Liu
  • Tony J. Dodd
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10471)


This paper presents a method that allows mobile systems with uncertainty in motion and sensing to react to unknown environments while high-level specifications are satisfied. Although previous works have addressed the problem of synthesising controllers under uncertainty constraints and temporal logic specifications, reaction to dynamic environments has not been considered under this scenario. The method uses feedback-based information roadmaps (FIRMs) to break the curse of history associated with partially observable systems. A transition system is incrementally constructed based on the idea of FIRMs by adding nodes on the belief space. Then, a policy is found in the product Markov decision process created between the transition system and a Rabin automaton representing a linear temporal logic formula. The proposed solution allows the system to react to previously unknown elements in the environment. To achieve fast reaction time, a FIRM considering the probability of violating the specification in each transition is used to drive the system towards local targets or to avoid obstacles. The method is demonstrated with an illustrative example.


  1. 1.
    Agha-Mohammadi, A.A., Chakravorty, S., Amato, N.M.: FIRM: sampling-based feedback motion-planning under motion uncertainty and imperfect measurements. Int. J. Robot. Res. 33(2), 268–304 (2014)CrossRefGoogle Scholar
  2. 2.
    Ayala, A.M., Andersson, S.B., Belta, C.: Temporal logic motion planning in unknown environments. In: Proceedings of IROS, pp. 5279–5284. IEEE (2013)Google Scholar
  3. 3.
    Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)zbMATHGoogle Scholar
  4. 4.
    Bauer, A., Leucker, M., Schallhart, C.: Runtime verification for LTL and TLTL. In: Proceedings of FSTTCS, vol. 20, pp. 1–68. ACM (2006)Google Scholar
  5. 5.
    Bry, A., Roy, N.: Rapidly-exploring random belief trees for motion planning under uncertainty. In: Proceedings of ICRA, pp. 723–730. IEEE (2011)Google Scholar
  6. 6.
    Chatterjee, K., Chmelík, M., Gupta, R., Kanodia, A.: Qualitative analysis of POMDPs with temporal logic specifications for robotics applications. In: Procedings of ICRA, pp. 325–330. IEEE (2015)Google Scholar
  7. 7.
    Cormen, T.H.: Introduction to Algorithms. MIT press, Cambridge (2009)zbMATHGoogle Scholar
  8. 8.
    Fu, J., Topcu, U.: Integrating active sensing into reactive synthesis with temporal logic constraints under partial observations. In: Proceedings of ACC, pp. 2408–2413. IEEE (2015)Google Scholar
  9. 9.
    Horowitz, M.B., Wolff, E.M., Murray, R.M.: A compositional approach to stochastic optimal control with co-safe temporal logic specifications. In: Proceedings of IROS, pp. 1466–1473. IEEE (2014)Google Scholar
  10. 10.
    Kallman, M., Mataric, M.: Motion planning using dynamic roadmaps. In: Proceedings of ICRA, vol. 5, pp. 4399–4404. IEEE (2004)Google Scholar
  11. 11.
    Karaman, S., Frazzoli, E.: Sampling-based motion planning with deterministic \(\mu \)-calculus specifications. In: Proceedings of CDC/CCC, pp. 2222–2229. IEEE (2009)Google Scholar
  12. 12.
    Kavraki, L.E., Svestka, P., Latombe, J.C., Overmars, M.H.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans. Robot. Autom. 12(4), 566–580 (1996)CrossRefGoogle Scholar
  13. 13.
    Leven, P., Hutchinson, S.: Toward real-time path planning in changing environments. In: Algorithmic and Computational Robotics: New Directions, pp. 363–376. A K Peters (2000)Google Scholar
  14. 14.
    Littman, M.L., Dean, T.L., Kaelbling, L.P.: On the complexity of solvingMarkov decision problems. In: Proceedings of UAI, pp. 394–402. Morgan Kaufmann Publishers Inc. (1995)Google Scholar
  15. 15.
    Montana, F.J., Liu, J., Dodd, T.J.: Sampling-based stochastic optimal control with metric interval temporal logic specifications. In: Proceedings of CCA, pp. 767–773. IEEE (2016)Google Scholar
  16. 16.
    Pineau, J., Gordon, G., Thrun, S., et al.: Point-based value iteration: An anytime algorithm for POMDPs. In: Proceedings of IJCAI, vol. 3, pp. 1025–1032 (2003)Google Scholar
  17. 17.
    Prentice, S., Roy, N.: The belief roadmap: efficient planning in linear POMDPs by factoring the covariance. In: Kaneko, M., Nakamura, Y. (eds.) Robotics Research, pp. 293–305. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-14743-2_25 CrossRefGoogle Scholar
  18. 18.
    Svoreňová, M., Chmelík, M., Leahy, K., Eniser, H.F., Chatterjee, K., Černá, I., Belta, C.: Temporal logic motion planning using POMDPs with parity objectives: case study paper. In: Proceedings of HSCC, pp. 233–238. ACM (2015)Google Scholar
  19. 19.
    Vasile, C.I., Belta, C.: Reactive sampling-based temporal logic path planning. In: Proceedings of ICRA, pp. 4310–4315. IEEE (2014)Google Scholar
  20. 20.
    Vasile, C.I., Leahy, K., Cristofalo, E., Jones, A., Schwager, M., Belta, C.: Control in belief space with temporal logic specifications. In: Proceedings of CDC, pp. 7419–7424. IEEE (2016)Google Scholar
  21. 21.
    Wongpiromsarn, T., Frazzoli, E.: Control of probabilistic systems under dynamic, partially known environments with temporal logic specifications. In: Proceedings of CDC, pp. 7644–7651. IEEE (2012)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Automatic Control and Systems EngineeringUniversity of SheffieldSheffieldUK
  2. 2.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

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