Hybrid Systems: From Verification to Falsification

  • Erion Plaku
  • Lydia E. Kavraki
  • Moshe Y. Vardi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4590)


We propose HyDICE, Hybrid DIscrete Continuous Exploration, a multi-layered approach for hybrid-system testing that integrates continuous sampling-based robot motion planning with discrete searching. The discrete search uses the discrete transitions of the hybrid system and coarse-grained decompositions of the continuous state spaces or related projections to guide the motion planner during the search for witness trajectories. Experiments presented in this paper, using a hybrid system inspired by robot motion planning and with nonlinear dynamics associated with each of several thousand modes, provide an initial validation of HyDICE and demonstrate its promise as a hybrid-system testing method. Comparisons to related work show computational speedups of up to two orders of magnitude.


Model Check Hybrid System Motion Planning Discrete Transition Hybrid Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Glover, W., Lygeros, J.: A stochastic hybrid model for air traffic control simulation. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 372–386. Springer, Heidelberg (2004)Google Scholar
  2. 2.
    Pepyne, D., Cassandras, C.: Optimal control of hybrid systems in manufacturing. Proceedings of IEEE 88(7), 1108–1123 (2000)CrossRefGoogle Scholar
  3. 3.
    Johansson, R., Rantzer, A. (eds.): Nonlinear and Hybrid Systems in Automotive Control. Springer, London, UK (2003)zbMATHGoogle Scholar
  4. 4.
    Dounias, G., Linkens, D.A.: Adaptive systems and hybrid computational intelligence in medicine. Artificial Intelligence in Medicine 32(3), 151–155 (2004)CrossRefGoogle Scholar
  5. 5.
    Piazza, C., Antoniotti, M., Mysore, V., Policriti, A., Winkler, F., Mishra, B.: Algorithmic algebraic model checking I: Challenges from systems biology. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 5–19. Springer, Heidelberg (2005)Google Scholar
  6. 6.
    Alur, R., Courcoubetis, C., Henzinger, T., Ho, P.H.: Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) Hybrid Systems. LNCS, vol. 736, pp. 209–229. Springer, Heidelberg (1993)Google Scholar
  7. 7.
    Henzinger, T., Kopke, P., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? In: STOC, pp. 373–382. ACM Press, New York (1995)Google Scholar
  8. 8.
    Henzinger, T.: The theory of hybrid automata. In: Proc. 11th IEEE Symp. on Logic in Computer Science, DIMACS, pp. 278–292. IEEE Computer Society Press, Los Alamitos (1996)CrossRefGoogle Scholar
  9. 9.
    Lafferriere, G., Pappas, G., Yovine, S.: A new class of decidable hybrid systems. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 137–151. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. 10.
    Puri, A.: Theory of Hybrid Systems and Discrete Event Systems. PhD thesis, University of California, Berkeley (1995)Google Scholar
  11. 11.
    Tomlin, C.J., Mitchell, I., Bayen, A., Oishi, M.: Computational techniques for the verification and control of hybrid systems. Proc. of IEEE 91(7), 986–1001 (2003)CrossRefGoogle Scholar
  12. 12.
    Chutinan, C., Krogh, B.H.: Computational techniques for hybrid system verification. IEEE Transactions on Automatic Control 48(1), 64–75 (2003)CrossRefGoogle Scholar
  13. 13.
    Silva, B., Stursberg, O., Krogh, B., Engell, S.: An assessment of the current status of algorithmic approaches to the verification of hybrid systems. In: IEEE Conf. on Decision and Control. vol. 3, pp. 2867–2874 (2001)Google Scholar
  14. 14.
    Esposito, J.M., Kim, J., Kumar, V.: Adaptive RRTs for validating hybrid robotic control systems. In: WAFR, Zeist, Netherlands, pp. 107–132 (2004)Google Scholar
  15. 15.
    Kim, J., Esposito, J.M., Kumar, V.: An RRT-based algorithm for testing and validating multi-robot controllers. In: RSS, Boston, MA, pp. 249–256 (2005)Google Scholar
  16. 16.
    Copty, F., Fix, L., Fraer, R., Giunchiglia, E., Kamhi, G., Tacchella, A., Vardi, M.: Benefits of bounded model checking at an industrial setting. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 436–453. Springer, Heidelberg (2001)Google Scholar
  17. 17.
    Choset, H., Lynch, K.M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L.E., Thrun, S.: Principles of Robot Motion: Theory, Algorithms, and Implementations. MIT Press, Cambridge, MA (2005)zbMATHGoogle Scholar
  18. 18.
    LaValle, S.M.: Planning Algorithms. Cambridge University Press, Cambridge (2006)zbMATHGoogle Scholar
  19. 19.
    LaValle, S.M., Kuffner, J.J.: Rapidly-exploring random trees: Progress and prospects. In: Donald, B.R., Lynch, K., Rus, D. (eds.) WAFR, pp. 293–308 (2000)Google Scholar
  20. 20.
    Hsu, D., Kindel, R., Latombe, J.C., Rock, S.: Randomized kinodynamic motion planning with moving obstacles. IJRR 21(3), 233–255 (2002)Google Scholar
  21. 21.
    Plaku, E., Bekris, K.E., Chen, B.Y., Ladd, A.M., Kavraki, L.E.: Sampling-based roadmap of trees for parallel motion planning. IEEE Trans. on Robotics 21(4), 597–608 (2005)CrossRefGoogle Scholar
  22. 22.
    Ladd, A.M., Kavraki, L.E.: Motion planning in the presence of drift, underactuation and discrete system changes. In: RSS, Boston, MA, pp. 233–241 (2005)Google Scholar
  23. 23.
    Bekris, K.E., Kavraki, L.E.: Greedy but safe replanning under kinodynamic constraints. In: IEEE ICRA, Rome, Italy (2007)Google Scholar
  24. 24.
    Plaku, E., Vardi, M.Y., Kavraki, L.E.: Discrete search leading continuous exploration for kinodynamic motion planning. In: RSS, Atlanta, GA (2007)Google Scholar
  25. 25.
    Kavraki, L.E., Švestka, P., Latombe, J.C., Overmars, M.H.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Transactions on Robotics and Automation 12(4), 566–580 (1996)CrossRefGoogle Scholar
  26. 26.
    Plaku, E., Kavraki, L.E., Vardi, M.Y.: A motion planner for a hybrid robotic system with kinodynamic constraints. In: IEEE ICRA, Rome, Italy (2007)Google Scholar
  27. 27.
    Zhang, W.: State-space Search: Algorithms, Complexity, Extensions, and Applications. Springer, New York (2006)Google Scholar
  28. 28.
    Biere, A., Cimatti, A., Clarke, E., Fujita, M., Zhu, Y.: Symbolic model checking using SAT procedures instead of BDDs. In: Proc. 36th Design Automation Conference, pp. 317–320. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  29. 29.
    Edelkamp, S., Jabbar, S.: Large-scale directed model checking ltl. In: Valmari, A. (ed.) Model Checking Software. LNCS, vol. 3925, pp. 1–18. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  30. 30.
    Burch, J., Clarke, E., McMillan, K., Dill, D., Hwang, L.: Symbolic model checking: 1020 states and beyond. Information and Computation 98(2), 142–170 (1992)zbMATHCrossRefGoogle Scholar
  31. 31.
    Ladd, A.M.: Motion Planning for Physical Simulation. PhD thesis, Rice University, Houston, TX (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Erion Plaku
    • 1
  • Lydia E. Kavraki
    • 1
  • Moshe Y. Vardi
    • 1
  1. 1.Department of Computer Science, Rice University, Houston TX 77005USA

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