Decoupled Formal Synthesis for Almost Separable Systems with Temporal Logic Specifications

  • Scott C. LivingstonEmail author
  • Pavithra Prabhakar
Conference paper
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 112)


We consider the problem of synthesizing controllers automatically for distributed robots that are loosely coupled using a formal synthesis approach. Formal synthesis entails construction of game strategies for a discrete transition system such that the system under the strategy satisfies a specification, given for instance in linear temporal logic (LTL). The general problem of automated synthesis for distributed discrete transition systems suffers from state-space explosion because the combined state-space has size exponential in the number of subsystems. Motivated by multi-robot motion planning problems, we focus on distributed systems whose interaction is nearly decoupled, allowing the overall specification to be decomposed into specifications for individual subsystems and a specification about the joint system. We treat specifically reactive synthesis for the GR(1) fragment of LTL. Each robot is subject to a GR(1) formula, and a safety formula describes constraints on their interaction. We propose an approach wherein we synthesize strategies independently for each subsystem; then we patch the separate controllers around interaction regions such that the specification about the joint system is satisfied.


Reactive synthesis LTL Collision avoidance Motion planning 


  1. 1.
    Alur, R., Henzinger, T.A., Lafferriere, G., Pappas, G.J.: Discrete abstractions of hybrid systems. Proc. IEEE 88(7), 971–984 (2000)CrossRefGoogle Scholar
  2. 2.
    Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press (2008)Google Scholar
  3. 3.
    Belta, C., Bicchi, A., Egerstedt, M., Frazzoli, E., Klavins, E., Pappas, G.J.: Symbolic planning and control of robot motion: finding the missing pieces of current methods and ideas. IEEE Robot. Autom. Mag. 61–70 (2007)Google Scholar
  4. 4.
    Bloem, R., Jobstmann, B., Piterman, N., Pnueli, A., Sa’ar, Y.: Synthesis of reactive(1) designs. J. Comput. Syst. Sci. 78, 911–938 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bullo, F., Cortés, J., Martínez, S.: Distributed Control of Robotic Networks. Applied Mathematics Series. Princeton University Press (2009).
  6. 6.
    Chen, Y., Ding, X.C., Stefanescu, A., Belta, C.: Formal approach to the deployment of distributed robotic teams. IEEE Trans. Robot. 28(1), 158–171 (2012)CrossRefGoogle Scholar
  7. 7.
    Emerson, E.A.: Handbook of Theoretical Computer Science (vol. B): Formal Models and Semantics, chapter Temporal and Modal Logic, pp. 995–1072. MIT Press (1990)Google Scholar
  8. 8.
    Gerkey, B.P., Matarić, M.J.: A formal analysis and taxonomy of task allocation in multi-robot systems. Int. J. Robot. Res. 23(9), 939–954 (2004)CrossRefGoogle Scholar
  9. 9.
    Karaman, S., Frazzoli, E.: Vehicle routing problem with metric temporal logic specifications. In: Proceedings of the 47th IEEE Conference on Decision and Control (CDC), pp. 3953–3958, Cancun, Mexico, December (2008)Google Scholar
  10. 10.
    Karaman, S., Frazzoli, E.: Sampling-based algorithms for optimal motion planning with deterministic \(\mu \)-calculus specifications. In: Proceedings of the American Control Conference (ACC), pp. 735–742, Montréal, Canada, June (2012)Google Scholar
  11. 11.
    Lindemann, S.R., LaValle, S.M.: Simple and efficient algorithms for computing smooth, collision-free feedback laws over given cell decompositions. Int. J. Robot. Res. 28(5), 600–621 (2009)CrossRefGoogle Scholar
  12. 12.
    Livingston, S.C., Murray, R.M.: Hot-swapping robot task goals in reactive formal synthesis. Technical report, California Institute of Technology, September (2014).
  13. 13.
    Livingston, S.C., Prabhakar, P., Jose, A.B., Murray, R.M.: Patching task-level robot controllers based on a local \(\mu \)-calculus formula. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 4573–4580, Karlsruhe, Germany, May (2013)Google Scholar
  14. 14.
    Ozay, N., Topcu, U., Wongpiromsarn, T., Murray, R.M.: Distributed synthesis of control protocols for smart camera networks. In: International Conference on Cyber-physical Systems (2011)Google Scholar
  15. 15.
    Parker, L.E.: Current state of the art in distributed autonomous mobile robotics. In: Proceedings of Distributed Autonomous Robotic Systems, vol. 4, pp. 3–12. Springer, Japan (2000)Google Scholar
  16. 16.
    Parker, L.E.: Distributed intelligence: overview of the field and its application in multi-robot systems. J. Phys. Agents 2(1), 5–14 (2008)Google Scholar
  17. 17.
    Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proceedings of the 16th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL ’89, pp. 179–190, New York, USA. ACM (1989)Google Scholar
  18. 18.
    Pnueli, A., Rosner, R.: Distributed reactive systems are hard to synthesize. In: Proceedings of the 31st Annual Symposium on Foundations of Computer Science, October (1990)Google Scholar
  19. 19.
    Tabuada, P.: Verification and Control of Hybrid Systems: A Symbolic Approach. Springer (2009)Google Scholar
  20. 20.
    Zhu, M., Otte, M., Chaudhari, P., Frazzoli, E.: Game theoretic controller synthesis for multi-robot motion planning, Part I: trajectory based algorithms. In: Proceedings of the 2014 IEEE International Conference on Robotics and Automation (ICRA), pp. 1646–1651, Hong Kong, China (2014)Google Scholar

Copyright information

© Springer Japan 2016

Authors and Affiliations

  1. 1.California Institute of TechnologyPasadenaUSA
  2. 2.IMDEA Software InstituteMadridSpain

Personalised recommendations