Skip to main content

The Black-Box Simplex Architecture for Runtime Assurance of Autonomous CPS

  • Conference paper
  • First Online:
NASA Formal Methods (NFM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13260))

Included in the following conference series:

Abstract

The Simplex Architecture is a runtime assurance framework where control authority may switch from an unverified and potentially unsafe advanced controller to a backup baseline controller in order to maintain the safety of an autonomous cyber-physical system. In this work, we show that runtime checks can replace the requirement to statically verify safety of the baseline controller. This is important as there are many powerful control techniques, such as model-predictive control and neural network controllers, that work well in practice but are difficult to statically verify. Since the method does not use internal information about the advanced or baseline controller, we call the approach the Black-Box Simplex Architecture. We prove the architecture is safe and present two case studies where (i) model-predictive control provides safe multi-robot coordination, and (ii) neural networks provably prevent collisions in groups of F-16 aircraft, despite the controllers occasionally outputting unsafe commands.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
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

Similar content being viewed by others

Notes

  1. 1.

    A video of the simulation is available at https://youtu.be/bcVJBkGgnxA.

  2. 2.

    A video of the simulation is available at https://youtu.be/qmk31jS6B2Y.

  3. 3.

    https://arxiv.org/abs/2102.12981.

  4. 4.

    https://youtu.be/Bhn0uqKCj7Q.

References

  1. Alsterda, J.P., Brown, M., Gerdes, J.C.: Contingency model predictive control for automated vehicles. In: 2019 American Control Conference (ACC), pp. 717–722 (2019). https://doi.org/10.23919/ACC.2019.8815260

  2. Althoff, M., Dolan, J.M.: Online verification of automated road vehicles using reachability analysis. IEEE Trans. Robot. 30(4) (2014)

    Google Scholar 

  3. Bak, S., Chivukula, D.K., Adekunle, O., Sun, M., Caccamo, M., Sha, L.: The system-level simplex architecture for improved real-time embedded system safety. In: 2009 15th IEEE Real-Time and Embedded Technology and Applications Symposium, pp. 99–107. IEEE (2009)

    Google Scholar 

  4. Bak, S., Johnson, T.T., Caccamo, M., Sha, L.: Real-time reachability for verified simplex design. In: 35th IEEE Real-Time Systems Symposium (RTSS 2014). IEEE Computer Society, Rome, December 2014

    Google Scholar 

  5. Bak, S., Liu, C., Johnson, T.: The second international verification of neural networks competition (VNN-COMP 2021): summary and results. arXiv preprint arXiv:2109.00498 (2021)

  6. Bak, S., Tran, H.D., Hobbs, K., Johnson, T.T.: Improved geometric path enumeration for verifying Relu neural networks. In: Proceedings of the 32nd International Conference on Computer Aided Verification (2020)

    Google Scholar 

  7. Borrmann, U., Wang, L., Ames, A.D., Egerstedt, M.: Control barrier certificates for safe swarm behavior. In: Egerstedt, M., Wardi, Y. (eds.) ADHS. IFAC-PapersOnLine, vol. 48, pp. 68–73. Elsevier, Amsterdam (2015)

    Google Scholar 

  8. Chen, X., Ábrahám, E., Sankaranarayanan, S.: Flow*: an analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 258–263. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_18

    Chapter  Google Scholar 

  9. Clark, M., et al.: A study on run time assurance for complex cyber physical systems. Technical report, Air Force Research Laboratory, Aerospace Systems Directorate (2013)

    Google Scholar 

  10. Desai, A., Ghosh, S., Seshia, S.A., Shankar, N., Tiwari, A.: SOTER: a runtime assurance framework for programming safe robotics systems. In: 49th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, DSN 2019, Portland, OR, USA, 24–27 June 2019. IEEE (2019)

    Google Scholar 

  11. Girard, A.: Reachability of uncertain linear systems using zonotopes. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 291–305. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31954-2_19

    Chapter  MATH  Google Scholar 

  12. Gurriet, T., Mote, M., Ames, A.D., Feron, E.: An online approach to active set invariance. In: Conference on Decision and Control. IEEE (2018)

    Google Scholar 

  13. Gurriet, T., Mote, M., Singletary, A., Feron, E., Ames, A.D.: A scalable controlled set invariance framework with practical safety guarantees. In: 2019 IEEE 58th Conference on Decision and Control (CDC), pp. 2046–2053. IEEE (2019)

    Google Scholar 

  14. Heidlauf, P., Collins, A., Bolender, M., Bak, S.: Verification challenges in f-16 ground collision avoidance and other automated maneuvers. In: 5th International Workshop on Applied Verification of Continuous and Hybrid Systems. EPiC Series in Computing, EasyChair (2018)

    Google Scholar 

  15. Julian, K.D., Kochenderfer, M.J., Owen, M.P.: Deep neural network compression for aircraft collision avoidance systems. J. Guid. Control. Dyn. 42(3), 598–608 (2019)

    Article  Google Scholar 

  16. Kapinski, J., Deshmukh, J.: Discovering forward invariant sets for nonlinear dynamical systems. In: Cojocaru, M.G., Kotsireas, I.S., Makarov, R.N., Melnik, R.V.N., Shodiev, H. (eds.) Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science. SPMS, vol. 117, pp. 259–264. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-12307-3_37

    Chapter  Google Scholar 

  17. Katz, G., Barrett, C., Dill, D.L., Julian, K., Kochenderfer, M.J.: Reluplex: an efficient SMT solver for verifying deep neural networks. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 97–117. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_5

    Chapter  Google Scholar 

  18. Kaynama, S., Maidens, J., Oishi, M., Mitchell, I.M., Dumont, G.A.: Computing the viability kernel using maximal reachable sets. In: Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control, pp. 55–64 (2012)

    Google Scholar 

  19. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. In: Cox, I.J., Wilfong, G.T. (eds.) Autonomous Robot Vehicles, pp. 396–404. Springer, New York (1986). https://doi.org/10.1007/978-1-4613-8997-2_29

    Chapter  Google Scholar 

  20. Kochenderfer, M.J., Chryssanthacopoulos, J.: Robust airborne collision avoidance through dynamic programming. Project Report ATC-371 130, Lincoln Laboratory, Massachusetts Institute of Technology (2011)

    Google Scholar 

  21. Lin, Q., Chen, X., Khurana, A., Dolan, J.: ReachFlow: an online safety assurance framework for waypoint-following of self-driving cars. In: 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (2020)

    Google Scholar 

  22. Magdici, S., Althoff, M.: Fail-safe motion planning of autonomous vehicles. In: 2016 IEEE 19th International Conference on Intelligent Transportation Systems (ITSC), pp. 452–458. IEEE (2016)

    Google Scholar 

  23. Maidens, J.N., Kaynama, S., Mitchell, I.M., Oishi, M.M., Dumont, G.A.: Lagrangian methods for approximating the viability kernel in high-dimensional systems. Automatica 49(7), 2017–2029 (2013)

    Article  MathSciNet  Google Scholar 

  24. Marston, M., Baca, G.: ACAS-Xu initial self-separation flight tests. Technical report, NASA (2015)

    Google Scholar 

  25. Mashima, D., Chen, B., Zhou, T., Rajendran, R., Sikdar, B.: Securing substations through command authentication using on-the-fly simulation of power system dynamics. In: IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (2018)

    Google Scholar 

  26. Mehmood, U., Bak, S., Smolka, S.A., Stoller, S.D.: Safe cps from unsafe controllers. In: Proceedings of the Workshop on Computation-Aware Algorithmic Design for Cyber-Physical Systems, pp. 26–28 (2021)

    Google Scholar 

  27. Murray, R.M., Li, Z., Sastry, S.S., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)

    Google Scholar 

  28. Lee, R., Jha, S., Mavridou, A., Giannakopoulou, D. (eds.): NFM 2020. LNCS, vol. 12229. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-55754-6

  29. Phan, D.T., Grosu, R., Jansen, N., Paoletti, N., Smolka, S.A., Stoller, S.D.: Neural simplex architecture. In: Lee, R., Jha, S., Mavridou, A., Giannakopoulou, D. (eds.) NFM 2020. LNCS, vol. 12229, pp. 97–114. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-55754-6_6

    Chapter  Google Scholar 

  30. Phan, D., Yang, J., Grosu, R., Smolka, S.A., Stoller, S.D.: Collision avoidance for mobile robots with limited sensing and limited information about moving obstacles. Formal Methods Syst. Des. 51(1), 62–86 (2017). https://doi.org/10.1007/s10703-016-0265-4

    Article  MATH  Google Scholar 

  31. Saint-Pierre, P.: Approximation of the viability kernel. Appl. Math. Optim. 29(2), 187–209 (1994)

    Article  MathSciNet  Google Scholar 

  32. Schierman, J., et al.: Runtime assurance framework development for highly adaptive flight control systems. Report AD1010277, Defense Technical Information Center (2015)

    Google Scholar 

  33. Schouwenaars, T., Valenti, M., Feron, E., How, J.: Implementation and flight test results of MILP-based UAV guidance. In: 2005 IEEE Aerospace Conference, pp. 1–13 (2005)

    Google Scholar 

  34. Schouwenaars, T.: Safe trajectory planning of autonomous vehicles. Ph.D. thesis, Massachusetts Institute of Technology (2006)

    Google Scholar 

  35. Schurmann, B., Klischat, M., Kochdumper, N., Althoff, M.: Formal safety net control using backward reachability analysis. IEEE Trans. Autom. Control (2021)

    Google Scholar 

  36. Seto, D., Krogh, B., Sha, L., Chutinan, A.: The simplex architecture for safe online control system upgrades. In: Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No. 98CH36207), vol. 6. IEEE (1998)

    Google Scholar 

  37. Sha, L.: Using simplicity to control complexity. IEEE Softw. 18(4), 20–28 (2001). https://doi.org/10.1109/MS.2001.936213

    Article  Google Scholar 

  38. Stevens, B.L., Lewis, F.L., Johnson, E.N.: Aircraft Control and Simulation. Wiley, New York (2015)

    Google Scholar 

Download references

Acknowledgement

This material is based upon work supported by National Science Foundation (NSF) under grant numbers OIA-2134840, OIA-2040599, CCF-1918225, CCF-1954837 and CPS-1446832, the Office of Naval Research (ONR) under grants N000142112719 and N000142212156, and the Air Force Office of Scientific Research (AFOSR) under award numbers FA9550-19-1-0288, FA9550-21-1-0121, FA9550-22-1-0450. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF, United States Air Force or the United States Navy. An early version of this work was presented in the CAADCPS 2021 workshop under the title “Safe CPS from Unsafe Controllers” [26].

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sanaz Sheikhi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Mehmood, U., Sheikhi, S., Bak, S., Smolka, S.A., Stoller, S.D. (2022). The Black-Box Simplex Architecture for Runtime Assurance of Autonomous CPS. In: Deshmukh, J.V., Havelund, K., Perez, I. (eds) NASA Formal Methods. NFM 2022. Lecture Notes in Computer Science, vol 13260. Springer, Cham. https://doi.org/10.1007/978-3-031-06773-0_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-06773-0_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-06772-3

  • Online ISBN: 978-3-031-06773-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics