Skip to main content
SpringerLink
Log in

Automated Synthesis of Safe Autonomous Vehicle Control Under Perception Uncertainty

  • Conference paper
  • First Online:
NASA Formal Methods (NFM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9690))

Included in the following conference series:

Abstract

Autonomous vehicles have found wide-ranging adoption in aerospace, terrestrial as well as marine use. These systems often operate in uncertain environments and in the presence of noisy sensors, and use machine learning and statistical sensor fusion algorithms to form an internal model of the world that is inherently probabilistic. Autonomous vehicles need to operate using this uncertain world-model, and hence, their correctness cannot be deterministically specified. Even once probabilistic correctness is specified, proving that an autonomous vehicle will operate correctly is a challenging problem. In this paper, we address these challenges by proposing a correct-by-synthesis approach to autonomous vehicle control. We propose a probabilistic extension of temporal logic, named Chance Constrained Temporal Logic (C2TL), that can be used to specify correctness requirements in presence of uncertainty. We present a novel automated synthesis technique that compiles C2TL specification into mixed integer constraints, and uses second-order (quadratic) cone programming to synthesize optimal control of autonomous vehicles subject to the C2TL specification. We demonstrate the effectiveness of the proposed approach on a diverse set of illustrative examples.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    As discussed in Sect. 3.1, probabilistic negation is not the same as logical negation when violation probability (\(\delta \)) can be 0.5 or more, and hence, we will need two \(\{0,1\}\) integer variables to represent the truth value of each chance constraint, to account for four cases depending on the truth value of the chance constraint and its probabilistic negation. For likely (violation probability \(\delta < 0.5\)) chance constraints, one \(\{0,1\}\) integer variable is sufficient by Theorem 1.

References

  1. Abate, A., Prandini, M., Lygeros, J., Sastry, S.: Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems. Automatica 44(11), 2724–2734 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Acikmese, B., Acikmese, S.R.: Convex programming approach to powered descent guidance for mars landing. J. Guid. Control Dyn. 30(5), 1353–1366 (2007)

    Article  Google Scholar 

  3. Andersen, M.S., Dahl, J., Vandenberghe, L.: Cvxopt: a python package for convex optimization, version 1.1.6. (2013). cvxopt.org

  4. Åström, K.J.: Introduction to stochastic control theory. Courier Corporation (2012)

    Google Scholar 

  5. Bailey, T., Durrant-Whyte, H.: Simultaneous localization and mapping (SLAM): Part II. J. Guid. Control Dyn. 13(3), 108–117 (2006)

    Google Scholar 

  6. Barr, N.M., Gangsaas, D., Schaeffer, D.R.: Wind models for flight simulator certification of landing and approach guidance and control systems. Technical report, DTIC Document (1974)

    Google Scholar 

  7. Bellman, R.: Introduction to the mathematical theory of control processes, vol. 2. IMA (1971)

    Google Scholar 

  8. Belotti, P., Lee, J., Liberti, L., Margot, F., Wachter, A.: Branching and bounds tightening techniques for non-convex MINLP. Optim. Meth. Softw. 24, 597–634 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bernini, N., Bertozzi, M., Castangia, L., Patander, M., Sabbatelli, M.: Real-time obstacle detection using stereo vision for autonomous ground vehicles: a survey. In: ITSC, pp. 873–878. IEEE (2014)

    Google Scholar 

  10. Broggi, A.: Autonomous vehicles control in the vislab intercontinental autonomous challenge. J. Guid. Control Dyn. 36(1), 161–171 (2012)

    Google Scholar 

  11. Cassandras, C.G., Lygeros, J.: Stochastic hybrid systems, vol. 24. CRC Press (2006)

    Google Scholar 

  12. Charnes, A., Cooper, W.W., Symonds, G.H.: Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil. J. Guid. Control Dyn. 4(3), 235–263 (1958)

    Google Scholar 

  13. De Nijs, R., Ramos, S., Roig, G., Boix, X., Gool, L.V., Kuhnlenz, K.: On-line semantic perception using uncertainty. In: IROS, pp. 4185–4191. IEEE (2012)

    Google Scholar 

  14. Devroye, L., Györfi, L., Lugosi, G.: A Probabilistic Theory of Pattern Recognition, vol. 31. Springer Science & Business Media, New York (2013)

    MATH  Google Scholar 

  15. Donzé, A., Maler, O.: Robust satisfaction of temporal logic over real-valued signals. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 92–106. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  16. Raman, V., et al.: Model predictive control with signal temporal logic specifications. In: CDC, pp. 81–87, December 2014

    Google Scholar 

  17. Koutsoukos, X.D., Riley, D.: Computational methods for reachability analysis of stochastic hybrid systems. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 377–391. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. Kwiatkowska, M., Norman, G., Parker, D.: PRISM: probabilistic symbolic model checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, p. 200. Springer, Heidelberg (2002)

    Google Scholar 

  19. Li, P., Arellano-Garcia, H., Wozny, G.: Chance constrained programming approach to process optimization under uncertainty. Comput. Chem. Eng. 32(1–2), 25–45 (2008)

    Article  Google Scholar 

  20. Martinet, P., Laugier, C., Nunes, U.: Special issue on perception and navigation for autonomous vehicles (2014)

    Google Scholar 

  21. Mathys, C.D., et al.: Uncertainty in perception and the hierarchical gaussian filter. Front. Hum. Neurosci. 8(825) (2014)

    Google Scholar 

  22. McGee, T.G., Sengupta, R., Hedrick, K.: Obstacle detection for small autonomous aircraft using sky segmentation. In: ICRA 2005, pp. 4679–4684. IEEE (2005)

    Google Scholar 

  23. Meier, L., Tanskanen, P., Fraundorfer, F., Pollefeys, M.: PIXHAWK: a system for autonomous flight using onboard computer vision. In: ICRA, pp. 2992–2997. IEEE (2011)

    Google Scholar 

  24. Miller, B.L., Wagner, H.M.: Chance constrained programming with joint constraints. J. Guid. Control Dyn. 13(6), 930–945 (1965)

    MATH  Google Scholar 

  25. Nassar, M.R., et al.: An approximately bayesian delta-rule model explains the dynamics of belief updating in a changing environment. J. Guid. Control Dyn. 30(37), 12366–12378 (2010)

    Google Scholar 

  26. Patchett, C., Jump, M., Fisher, M.: Safety and certification of unmanned air systems. Eng. Technol. Ref. 1(1) (2015)

    Google Scholar 

  27. Pnueli, A.: The temporal logic of programs. In: Providence, pp. 46–57 (1977)

    Google Scholar 

  28. Pontryagin, L.S.: Optimal control processes. Usp. Mat. Nauk 14(3), 3–20 (1959)

    Google Scholar 

  29. Prajna, S., Jadbabaie, A., Pappas, G.J.: A framework for worst-case, stochastic safety verification using barrier certificates. IEEE Trans. Autom. Control 52(8), 1415–1428 (2007)

    Article  MathSciNet  Google Scholar 

  30. Prandini, M., Hu, J.: Stochastic reachability: theory and numerical approximation. J. Guid. Control Dyn. 24, 107–138 (2006)

    MATH  Google Scholar 

  31. Prékopa, A.: Stochastic Programming, vol. 324. Springer, Netherlands (2013)

    MATH  Google Scholar 

  32. Rouff, C., Hinchey, M.: Experience from the DARPA urban challenge. Springer Science & Business Media, London (2011)

    Google Scholar 

  33. Rushby, J.: New challenges in certification for aircraft software. In: EMSOFT, pp. 211–218. ACM (2011)

    Google Scholar 

  34. Terwilliger, B.A., Ison, D.C., Vincenzi, D.A., Liu, D.: Advancement and application of unmanned aerial system Human-Machine-Interface (HMI) technology. In: Yamamoto, S. (ed.) HCI 2014, Part II. LNCS, vol. 8522, pp. 273–283. Springer, Heidelberg (2014)

    Google Scholar 

  35. Van Den Berg, J., Abbeel, P., Goldberg, K.: LQG-MP: optimized path planning for robots with motion uncertainty and imperfect state information. J. Guid. Control Dyn. 30(7), 895–913 (2011)

    Google Scholar 

  36. Vitus, M.: Stochastic Control Via Chance Constrained Optimization and its Application to Unmanned Aerial Vehicles. PhD thesis, Stanford University (2012)

    Google Scholar 

  37. Vitus, M.P., Tomlin, C.J.: Closed-loop belief space planning for linear, Gaussian systems. In: ICRA, pp. 2152–2159. IEEE (2011)

    Google Scholar 

  38. Vitus, M.P., Tomlin, C.J.: On feedback design and risk allocation in chance constrained control. J. Guid. Control Dyn. 2011, 734–739 (2011)

    Google Scholar 

  39. Vitus, M.P., Tomlin, C.J.: A hybrid method for chance constrained control in uncertain environments. In: CDC, pp. 2177–2182, December 2012

    Google Scholar 

  40. Vitus, M.P., Tomlin, C.J.: A probabilistic approach to planning and control in autonomous urban driving. In: CDC, pp. 2459–2464 (2013)

    Google Scholar 

  41. Xu, W., Pan, J., Wei, J., Dolan, J.M.: Motion planning under uncertainty for on-road autonomous driving. In: ICRA, pp. 2507–2512. IEEE (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. United Technology Research Center, Berkeley, USA

    Susmit Jha & Vasumathi Raman

Authors
  1. Susmit Jha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vasumathi Raman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Susmit Jha .

Editor information

Editors and Affiliations

  1. University of Minnesota, Minneapolis, Minnesota, USA

    Sanjai Rayadurgam

  2. NASA Ames Research Center , Moffett Field, California, USA

    Oksana Tkachuk

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Jha, S., Raman, V. (2016). Automated Synthesis of Safe Autonomous Vehicle Control Under Perception Uncertainty. In: Rayadurgam, S., Tkachuk, O. (eds) NASA Formal Methods. NFM 2016. Lecture Notes in Computer Science(), vol 9690. Springer, Cham. https://doi.org/10.1007/978-3-319-40648-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40648-0_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40647-3

  • Online ISBN: 978-3-319-40648-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation