A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9690)


One barrier in introducing autonomous vehicle technology is the liability issue when these vehicles are involved in an accident. To overcome this, autonomous vehicle manufacturers should ensure that their vehicles always comply with traffic rules. This paper focusses on the safe distance traffic rule from the Vienna Convention on Road Traffic. Ensuring autonomous vehicles to comply with this safe distance rule is problematic because the Vienna Convention does not clearly define how large a safe distance is. We provide a formally proved prescriptive definition of how large this safe distance must be, and correct checkers for the compliance of this traffic rule. The prescriptive definition is obtained by: (1) identifying all possible relative positions of stopping (braking) distances; (2) selecting those positions from which a collision freedom can be deduced; and (3) reformulating these relative positions such that lower bounds of the safe distance can be obtained. These lower bounds are then the prescriptive definition of the safe distance, and we combine them into a checker which we prove to be sound and complete. Not only does our work serve as a specification for autonomous vehicle manufacturers, but it could also be used to determine who is liable in court cases and for online verification of autonomous vehicles’ trajectory planner.


Decision Procedure Theorem Prover Interval Arithmetic Safe Distance Autonomous Vehicle 
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.
    Aghabayk, K., Sarvi, M., Young, W.: A state-of-the-art review of car-following models with particular considerations of heavy vehicles. Transport Rev. 35(1), 82–105 (2015)CrossRefGoogle Scholar
  2. 2.
    Althoff, M., Dolan, J.: Online verification of automated road vehicles using reachability analysis. IEEE Trans. Robot. 30(4), 903–918 (2014)CrossRefGoogle Scholar
  3. 3.
    American Prosecutors Research Institute: Crash Reconstruction Basics for Prosecutors: Targeting Hardcore Impaired Drivers. Author (2003)Google Scholar
  4. 4.
    Chen, C., Liu, L., Du, X., Pei, Q., Zhao, X.: Improving driving safety based on safe distance design in vehicular sensor networks. Int. J. Distrib. Sens. Netw. 2012(469067), 13 (2012)Google Scholar
  5. 5.
    Eberl, M.: A decision procedure for univariate real polynomials in Isabelle/HOL. In: Proceedings of the 2015 Conference on Certified Programs and Proofs. CPP 2015, Mumbai, India, pp. 75–83. ACM, New York (2015).
  6. 6.
    Fricke, L.: Traffic Accident Reconstruction. The Traffic Accident Investigation Manual, vol. 2, Northwestern University Center for Public Safety (1990)Google Scholar
  7. 7.
    Gipps, P.: A behavioural car-following model for computer simulation. Transp. Res. B Methodological 15(2), 105–111 (1981)CrossRefGoogle Scholar
  8. 8.
    Goodloe, A.E., Muñoz, C., Kirchner, F., Correnson, L.: Verification of numerical programs: from real numbers to floating point numbers. In: Brat, G., Rungta, N., Venet, A. (eds.) NFM 2013. LNCS, vol. 7871, pp. 441–446. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  9. 9.
    Haftmann, F., Krauss, A., Kunčar, O., Nipkow, T.: Data refinement in Isabelle/HOL. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 100–115. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Haftmann, F., Nipkow, T.: Code generation via higher-order rewrite systems. In: Blume, M., Kobayashi, N., Vidal, G. (eds.) FLOPS 2010. LNCS, vol. 6009, pp. 103–117. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Harrison, J.: Verifying nonlinear real formulas via sums of squares. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 102–118. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Hölzl, J.: Proving inequalities over reals with computation in Isabelle/HOL. In: Proceedings of the ACM SIGSAM International Workshop on Programming Languages for Mechanized Mathematics Systems. pp. 38–45 (2009)Google Scholar
  13. 13.
    Immler, F.: Verified reachability analysis of continuous systems. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 37–51. Springer, Heidelberg (2015)Google Scholar
  14. 14.
    Kowshik, H., Caveney, D., Kumar, P.: Provable systemwide safety in intelligent intersections. IEEE Trans. Veh. Technol. 60(3), 804–818 (2011)CrossRefGoogle Scholar
  15. 15.
    Loos, S.M., Platzer, A., Nistor, L.: Adaptive cruise control: hybrid, distributed, and now formally verified. In: Butler, M., Schulte, W. (eds.) FM 2011. LNCS, vol. 6664, pp. 42–56. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  16. 16.
    Loos, S., Platzer, A.: Safe intersections: at the crossing of hybrid systems and verification. In: IEEE Conference on Intelligent Transportations Systems. pp. 1181–1186, October 2011Google Scholar
  17. 17.
    McLaughlin, S., Harrison, J.V.: A proof-producing decision procedure for real arithmetic. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 295–314. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL - A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  19. 19.
    Olsen, R.A.: Pedestrian injury issues in litigation. In: Karwowski, W., Noy, Y.I. (eds.) Handbook of Human Factors in Litigation, pp. 15-1–15-23. CRC Press, Boca Raton (2004)Google Scholar
  20. 20.
    Platzer, A.: Logical Analysis of Hybrid Systems. Springer, Heidelberg (2010)CrossRefzbMATHGoogle Scholar
  21. 21.
    Platzer, A.: A complete axiomatization of quantified differential dynamic logic for distributed hybrid systems. Logical Methods Comput. Sci. 8(4), 1–44 (2012)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Qu, D., Chen, X., Yang, W., Bian, X.: Modeling of car-following required safe distance based on molecular dynamics. Math. Probl. Eng. 2014(604023), 7 (2014)Google Scholar
  23. 23.
    Rizaldi, A., Althoff, M.: Formalising traffic rules for accountability of autonomous vehicles. In: IEEE Conference on Intelligent Transportation Systems. pp. 1658–1665 (2015)Google Scholar
  24. 24.
    Vanholme, B., Gruyer, D., Lusetti, B., Glaser, S., Mammar, S.: Highly automated driving on highways based on legal safety. IEEE Trans. Intell. Transp. Syst. 14(1), 333–347 (2013)CrossRefGoogle Scholar
  25. 25.
    Wilson, B.H.: How soon to brake and how hard to brake: unified analysis of the envelope of opportunity for rear-end collision warnings. In: Enhanced Safety of Vehicles. vol. 47 (2001)Google Scholar
  26. 26.
    Xiao, L., Gao, F.: A comprehensive review of the development of adaptive cruise control systems. Veh. Syst. Dyn. 48(10), 1167–1192 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institut für InformatikTechnische Universität MünchenMunichGermany

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