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Counterexample-Guided Safety Contracts for Autonomous Driving

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Algorithmic Foundations of Robotics XIII (WAFR 2018)

Abstract

Ensuring the safety of autonomous vehicles is paramount for their successful deployment. However, formally verifying autonomous driving decisions systems is difficult. In this paper, we propose a framework for constructing a set of safety contracts that serve as design requirements for controller synthesis for a given scenario. The contracts guarantee that the controlled system will remain safe with respect to probabilistic models of traffic behavior, and, furthermore, that it will follow rules of the road. We create contracts using an iterative approach that alternates between falsification and reachable set computation. Counterexamples to collision-free behavior are found by solving a gradient-based trajectory optimization problem. We treat these counterexamples as obstacles in a reach-avoid problem that quantifies the set of behaviors an ego vehicle can make while avoiding the counterexample. Contracts are then derived directly from the reachable set. We demonstrate that the resulting design requirements are able to separate safe from unsafe behaviors in an interacting multi-car traffic scenario, and further illustrate their utility in analyzing the safety impact of relaxing traffic rules.

J. DeCastro and L. Liebenwein—Equal contribution.

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References

  1. Althoff, M.: An introduction to CORA 2015. In: Proceedings of the Workshop on Applied Verification for Continuous and Hybrid Systems, pp. 120–151 (2015)

    Google Scholar 

  2. Althoff, M., Dolan, J.: Online verification of automated road vehicles using reachability analysis. IEEE Trans. Rob. 30, 903–918 (2014)

    Article  Google Scholar 

  3. Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T., Ho, P.H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoret. Comput. Sci. 138(1), 3–34 (1995)

    Article  MathSciNet  Google Scholar 

  4. Alur, R., Dang, T., Ivančić, F.: Predicate abstraction for reachability analysis of hybrid systems. ACM Trans. Embedded Comput. Syst. (TECS) 5(1), 152–199 (2006)

    Article  Google Scholar 

  5. Baram, N., Anschel, O., Caspi, I., Mannor, S.: End-to-end differentiable adversarial imitation learning. In: ICML (2017)

    Google Scholar 

  6. Bhatia, A., Frazzoli, E.: Incremental search methods for reachability analysis of continuous and hybrid systems. In: Alur, R., Pappas, G.J. (eds.) Hybrid Systems: Computation and Control. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  7. Chen, M., Hu, Q., Fisac, J.F., Akametalu, K., Mackin, C., Tomlin, C.J.: Reachability-based safety and goal satisfaction of unmanned aerial platoons on air highways. J. Guid. Control Dynam. 40(6), 1360–1373 (2017)

    Article  Google Scholar 

  8. Chen, X., Ábrahám, E., Sankaranarayanan, S.: Flow*: an analyzer for non-linear hybrid systems. In: International Conference on Computer Aided Verification (2013)

    Google Scholar 

  9. Chen, X., Schupp, S., Makhlouf, I., Ábrahám, E., Frehse, G., Kowalewski, S.: A benchmark suite for hybrid systems reachability analysis. In: NASA Formal Methods Symposium (2015)

    Google Scholar 

  10. Cheng, P., Kumar, V.: Sampling-based falsification and verification of controllers for continuous dynamic systems. Int. J. Robot. Res. 27(11–12), 1232–1245 (2008)

    Article  Google Scholar 

  11. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: International Conference on Computer Aided Verification (2000)

    Google Scholar 

  12. Clarke, E., Grumberg, O., Long, D.: Verification tools for finite-state concurrent systems. In: Workshop/School/Symposium of the REX Project (Research and Education in Concurrent Systems) (1993)

    Google Scholar 

  13. Coulter, R.C.: Implementation of the pure pursuit path tracking algorithm. Technical report CMU-RI-TR-92-01, Carnegie Mellon University, Pittsburgh, PA (1992)

    Google Scholar 

  14. DeCastro, J.A., Kress-Gazit, H.: Nonlinear controller synthesis and automatic workspace partitioning for reactive high-level behaviors. In: ACM International Conference on Hybrid Systems: Computation and Control (HSCC), Vienna, Austria (2016)

    Google Scholar 

  15. Economic Commission for Europe – Inland Transport Committee, Vienna, Austria: Convention on Road Traffic, E/CONF.56/16/Rev.1/Amend.1 edn. (1968)

    Google Scholar 

  16. Erlien, S.M., Fujita, S., Gerdes, J.C.: Shared steering control using safe envelopes for obstacle avoidance and vehicle stability. IEEE Trans. Intell. Transp. Syst. 17, 441–451 (2016)

    Article  Google Scholar 

  17. Fisac, J., Bajcsy, A., Herbert, S., Fridovich-Keil, D., Wang, S., Tomlin, C., Dragan, A.: Probabilistically safe robot planning with confidence-based human predictions. In: Proceedings of Robotics: Science and Systems, Pittsburgh, PA, June 2018

    Google Scholar 

  18. Gill, P.E., Murray, W., Saunders, M.A.: SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev. 47(1), 99–131 (2005)

    Article  MathSciNet  Google Scholar 

  19. Hargraves, C.R., Paris, S.W.: Direct trajectory optimization using nonlinear programming and collocation. AIAA J. Guid. 10, 338–342 (1987)

    Article  Google Scholar 

  20. Ivanovic, B., Harrison, J., Sharma, A., Chen, M., Pavone, M.: BaRC: backward reachability curriculum for robotic reinforcement learning. arXiv:1806.06161 (2018)

  21. Kapinski, J., Deshmukh, J., Sankaranarayanan, S., Arechiga, N.: Simulation-guided Lyapunov analysis for hybrid dynamical systems. In: Proceedings of the International Conference on Hybrid Systems: Computation and Control (2014)

    Google Scholar 

  22. Karlsson, J., Vasile, C.I., Tumova, J., Karaman, S., Rus, D.: Multi-vehicle motion planning for social optimal mobility-on-demand. In: IEEE International Conference on Robotics and Automation (ICRA), Brisbane, Australia (2018)

    Google Scholar 

  23. Kim, E.S., Arcak, M., Seshia, S.A.: Compositional controller synthesis for vehicular traffic networks. In: IEEE Conference on Decision and Control (CDC), pp. 6165–6171 (2015)

    Google Scholar 

  24. Kim, E.S., Sadraddini, S., Belta, C., Arcak, M., Seshia, S.A.: Dynamic contracts for distributed temporal logic control of traffic networks. In: IEEE Conference on Decision and Control (CDC), pp. 3640–3645 (2017)

    Google Scholar 

  25. Kuefler, A., Morton, J., Wheeler, T.A., Kochenderfer, M.J.: Imitating driver behavior with generative adversarial networks. In: IEEE Intelligent Vehicles Symposium (IV), pp. 204–211 (2017)

    Google Scholar 

  26. Liebenwein, L., Baykal, C., Gilitschenski, I., Karaman, S., Rus, D.: Sampling-based approximation algorithms for reachability analysis with provable guarantees. In: Proceedings of Robotics: Science and Systems, Pittsburgh, PA, June 2018

    Google Scholar 

  27. Liebenwein, L., Schwarting, W., Vasile, C.I., DeCastro, J., Alonso-Mora, J., Karaman, S., Rus, D.: Compositional and contract-based verification for autonomous driving on road networks. In: International Symposium on Robotics Research (ISRR) (2017)

    Google Scholar 

  28. Mitchell, I.M., Bayen, A.M., Tomlin, C.J.: A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games. IEEE Trans. Autom. Control 50(7), 947–957 (2005)

    Article  MathSciNet  Google Scholar 

  29. Morton, J., Kochenderfer, M.J.: Simultaneous policy learning and latent state inference for imitating driver behavior. In: IEEE International Conference on Intelligent Transportation Systems (ITSC), pp. 1–6 (2017)

    Google Scholar 

  30. Plaku, E., Kavraki, L., Vardi, M.: Falsification of LTL safety properties in hybrid systems. In: International Conference on Tools and Algorithms for the Construction and Analysis of Systems (2009)

    Google Scholar 

  31. Sangiovanni-Vincentelli, A., Damm, W., Passerone, R.: Taming Dr. Frankenstein: contract-based design for cyber-physical systems. In: 2011 Control and Decision Conference and European Control Conference (2012)

    Google Scholar 

  32. Sankaranarayanan, S., Fainekos, G.: Falsification of temporal properties of hybrid systems using the cross-entropy method. In: ACM International Conference on Hybrid Systems: Computation and Control, pp. 125–134 (2012)

    Google Scholar 

  33. Schwarting, W., Alonso-Mora, J., Paull, L., Karaman, S., Rus, D.: Parallel autonomy in automated vehicles: safe motion generation with minimal intervention. In: IEEE International Conference on Robotics and Automation (ICRA) (2017)

    Google Scholar 

  34. Shalev-Shwartz, S., Shammah, S., Shashua, A.: Safe, multi-agent, reinforcement learning for autonomous driving. CoRR abs/1610.03295 (2016)

    Google Scholar 

  35. Russ Tedrake and the Drake Development Team: Drake: A planning, control, and analysis toolbox for nonlinear dynamical systems (2016). http://drake.mit.edu

  36. Treiber, M., Kesting, A.: Traffic Flow Dynamics. Springer, Heidelberg (2013)

    Book  Google Scholar 

  37. Vasile, C.I., Tumova, J., Karaman, S., Belta, C., Rus, D.: Minimum-violation scLTL motion planning for mobility-on-demand. In: IEEE International Conference on Robotics and Automation (ICRA), Singapore, pp. 1481–1488 (2017)

    Google Scholar 

  38. Wongpiromsarn, T., Topcu, U., Murray, R.M.: Receding horizon temporal logic planning for dynamical systems. In: IEEE Conference on Decision and Control (CDC) and Chinese Control Conference, pp. 5997–6004 (2009)

    Google Scholar 

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Acknowledgements

Toyota Research Institute (“TRI”) provided funds to assist the authors with their research, but this article solely reflects the opinions and conclusions of its authors, and not TRI or any other Toyota entity.

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Correspondence to Jonathan DeCastro .

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DeCastro, J., Liebenwein, L., Vasile, CI., Tedrake, R., Karaman, S., Rus, D. (2020). Counterexample-Guided Safety Contracts for Autonomous Driving. In: Morales, M., Tapia, L., Sánchez-Ante, G., Hutchinson, S. (eds) Algorithmic Foundations of Robotics XIII. WAFR 2018. Springer Proceedings in Advanced Robotics, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-44051-0_54

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