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Journal of Automated Reasoning

, Volume 60, Issue 1, pp 43–62 | Cite as

Safe Autonomy Under Perception Uncertainty Using Chance-Constrained Temporal Logic

  • Susmit Jha
  • Vasumathi Raman
  • Dorsa Sadigh
  • Sanjit A. Seshia
Article

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. C2TL extends temporal logic by including chance constraints as predicates in the formula which allows modeling of perception uncertainty while retaining its ease of reasoning. 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 also present a risk distribution approach that enables synthesis of plans with lower cost without increasing the overall risk. We demonstrate the effectiveness of the proposed approach on a diverse set of illustrative examples.

Keywords

Autonomy Temporal logic Safe Control 

References

  1. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Akametalu, A.K., Fisac, J.F., Gillula, J.H., Kaynama, S., Zeilinger, M.N., Tomlin, C.J.: Reachability-based safe learning with gaussian processes. In: 53rd IEEE Conference on Decision and Control, pp. 1424–1431. IEEE (2014)Google Scholar
  3. 3.
    Andersen, M.S., Dahl, J., Vandenberghe, L.: Cvxopt: A python package for convex optimization, version 1.1. 6. Available at cvxopt. org, (2013)Google Scholar
  4. 4.
    Åström, K.J.: Introduction to Stochastic Control Theory. Courier Corporation, North Chelmsford (2012)zbMATHGoogle Scholar
  5. 5.
    Bailey, T., Durrant-Whyte, Hugh: Simultaneous localization and mapping (slam): Part ii. IEEE Robot. Autom. Mag. 13(3), 108–117 (2006)CrossRefGoogle Scholar
  6. 6.
    Belotti, P., Lee, J., Liberti, L., Margot, F., Wachter, A.: Branching and bounds tightening techniques for non-convex MINLP. Optim. Methods Softw. 24, 597–634 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Berkenkamp, F., Schoellig, A.P.: Safe and robust learning control with gaussian processes. In: Control Conference (ECC), 2015 European, pp. 2496–2501. IEEE, (2015)Google Scholar
  8. 8.
    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
  9. 9.
    Broggi, A., et al.: Autonomous vehicles control in the VisLab intercontinental autonomous challenge. Ann. Rev. Control 36(1), 161–171 (2012)CrossRefGoogle Scholar
  10. 10.
    Cassandras, Christos G., Lygeros, John: Stochastic Hybrid Systems, vol. 24. CRC Press, Boca Raton (2006)zbMATHGoogle Scholar
  11. 11.
    Charnes, A., Cooper, W.W., Symonds, G.H.: Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil. Manag. Sci. 4(3), 235–263 (1958)CrossRefGoogle Scholar
  12. 12.
    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
  13. 13.
    Devroye, Luc, Györfi, László, Lugosi, Gábor: A Probabilistic Theory of Pattern Recognition, vol. 31. Springer, Berlin (2013)zbMATHGoogle Scholar
  14. 14.
    Dietterich, T.G., Horvitz, Eric J.: Rise of concerns about AI: reflections and directions. Commun. ACM 58(10), 38–40 (2015)CrossRefGoogle Scholar
  15. 15.
    Donzé, A., Maler, O.: Robust satisfaction of temporal logic over real-valued signals. In: FORMATS, pp. 92–106, (2010)Google Scholar
  16. 16.
    Fu, J., Topcu, U.: Computational methods for stochastic control with metric interval temporal logic specifications. In: CDC, pp. 7440–7447, (2015)Google Scholar
  17. 17.
    Fu, J., Topcu, U.: Synthesis of joint control and active sensing strategies under temporal logic constraints. IEEE Trans. Autom. Control 61(11), 3464–3476 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Goerzen, C., Kong, Zhaodan, Mettler, Bernard: A survey of motion planning algorithms from the perspective of autonomous uav guidance. J. Intell. Robot. Syst. 57(1–4), 65–100 (2010)CrossRefzbMATHGoogle Scholar
  19. 19.
    Huth, Michael, Ryan, Mark: Logic in Computer Science: Modelling and Reasoning about Systems. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  20. 20.
    Jha, S., Raman, V.: Automated synthesis of safe autonomous vehicle control under perception uncertainty. In: NASA Formal Methods, pp. 117–132 (2016)Google Scholar
  21. 21.
    Koutsoukos, X., Riley, D.: Computational methods for reachability analysis of stochastic hybrid systems. In: HSCC, pp. 377–391. Springer, Berlin (2006)Google Scholar
  22. 22.
    Kwiatkowska, M., Norman, G., Parker, D.: Prism: Probabilistic symbolic model checker. In: Computer Performance Evaluation: Modelling Techniques and Tools, pp. 200–204. Springer, Berlin (2002)Google Scholar
  23. 23.
    Li, P., Arellano-Garcia, H., Wozny, Gnter: Chance constrained programming approach to process optimization under uncertainty. Comput. Chem. Eng. 32(1–2), 25–45 (2008)CrossRefGoogle Scholar
  24. 24.
    Mack, Chris, et al.: Fifty years of moore’s law. IEEE Trans. Semicond. Manuf. 24(2), 202–207 (2011)CrossRefGoogle Scholar
  25. 25.
    Martinet, P., Laugier, C., Nunes, U.: Special issue on perception and navigation for autonomous vehicles. IEEE Robot. Autom. Mag. 21(1), 26–27 (2014)CrossRefGoogle Scholar
  26. 26.
    Mathys, D.C., et al.: Uncertainty in perception and the hierarchical Gaussian filter. Front. Hum. Neurosci. 8, 825 (2014)CrossRefGoogle Scholar
  27. 27.
    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
  28. 28.
    Miller, Bruce L., Wagner, Harvey M.: Chance constrained programming with joint constraints. Oper. Res. 13(6), 930–945 (1965)CrossRefzbMATHGoogle Scholar
  29. 29.
    Mitchell, I., Tomlin, C.J.: Level set methods for computation in hybrid systems. In: International Workshop on Hybrid Systems: Computation and Control, pp. 310–323. Springer, Berlin (2000)Google Scholar
  30. 30.
    Mitchell, Ian M., Bayen, Alexandre M., Tomlin, Claire J.: A time-dependent Hamilton–Jacobi formulation of reachable sets for continuous dynamic games. IEEE Trans. Autom Control 50(7), 947–957 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Patchett, C., Jump, M., Fisher, M.: Safety and certification of unmanned air systems. Eng. Technol. Ref. 1, 1 (2015)Google Scholar
  32. 32.
    Pnueli, A.: The temporal logic of programs. In: Providence, pp. 46–57 (1977)Google Scholar
  33. 33.
    Prajna, Stephen, Jadbabaie, Ali, Pappas, George J: A framework for worst-case and stochastic safety verification using barrier certificates. IEEE Trans. Autom. Control 52(8), 1415–1428 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Prandini, Maria, Jianghai, Hu: Stochastic reachability: theory and numerical approximation. Stoch. Hybrid Syst. Autom. Control Eng. Ser. 24, 107–138 (2006)zbMATHGoogle Scholar
  35. 35.
    Prékopa, András: Stochastic Programming, vol. 324. Springer, Berlin (2013)zbMATHGoogle Scholar
  36. 36.
    Pshikhopov, V.K., Medvedev, M.Y., Gaiduk, A.R., Gurenko, B.V.: Control system design for autonomous underwater vehicle. In: 2013 Latin American Robotics Symposium and Competition (2013)Google Scholar
  37. 37.
    Raman, V., Donzé, A., Maasoumy, M., Murray, R.M., Sangiovanni-Vincentelli, A.L., Seshia, S.A.: Model predictive control with signal temporal logic specifications. In CDC, pp. 81–87 (2014)Google Scholar
  38. 38.
    Raman, V., Donzé, A., Sadigh, D., Murray, R.M., Seshia, S.A.: Reactive synthesis from signal temporal logic specifications. In: HSCC, pp. 239–248 (2015)Google Scholar
  39. 39.
    Rouff, Christopher, Hinchey, Mike: Experience from the DARPA Urban Challenge. Springer, Berlin (2011)Google Scholar
  40. 40.
    Rushby, J.: New challenges in certification for aircraft software. In: EMSOFT, pp. 211–218. ACM (2011)Google Scholar
  41. 41.
    Sadigh, D., Kapoor, A.: Safe control under uncertainty with probabilistic signal temporal logic. In: Robotics: Science and Systems XII, (2016)Google Scholar
  42. 42.
    Summers, S., Kamgarpour, M., Lygeros, J., Tomlin, C.: A stochastic reach-avoid problem with random obstacles. In: Proceedings of the 14th International Conference on Hybrid Systems: Computation and Control, pp. 251–260. ACM (2011)Google Scholar
  43. 43.
    Sun, W., van den Berg, J., Alterovitz, R.: Stochastic Extended LQR: Optimization-Based Motion Planning Under Uncertainty, pp. 609–626. Springer, Cham (2015)Google Scholar
  44. 44.
    Svorenova, M., Kretínský, J., Chmelik, M., Chatterjee, K., Cerná, I., Belta, C.: Temporal Logic Control for Stochastic Linear Systems Using Abstraction Refinement of Probabilistic Games. In: HSCC, pp. 259–268 (2015)Google Scholar
  45. 45.
    Todorov, E., Li, W.: A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems. In: American Control Conference, 2005. Proceedings of the 2005, vol. 1, pp. 300–306. IEEE (2005)Google Scholar
  46. 46.
    Vitus, M.: Stochastic Control Via Chance Constrained Optimization and its Application to Unmanned Aerial Vehicles. PhD thesis, Stanford University, (2012)Google Scholar
  47. 47.
    Vitus, M.P., Tomlin, C.J.: Closed-loop belief space planning for linear, Gaussian systems. In: ICRA, pp. 2152–2159. IEEE (2011)Google Scholar
  48. 48.
    Vitus, M.P., Tomlin, C.J.: A hybrid method for chance constrained control in uncertain environments. In: CDC, pp. 2177–2182 (2012)Google Scholar
  49. 49.
    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
  50. 50.
    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

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.SRI InternationalMenlo ParkUSA
  2. 2.Zoox, Inc.Menlo ParkUSA
  3. 3.UC BerkeleyBerkeleyUSA

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