Skip to main content

Exploring Model Quality for ACAS X

  • Conference paper
  • First Online:
FM 2016: Formal Methods (FM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9995))

Included in the following conference series:

Abstract

The next generation airborne collision avoidance system, ACAS X, aims to provide robustness through a probabilistic model that represents sources of uncertainty. From this model, dynamic programming produces a look-up table that is used to give advisories to the pilot in real time. The model is not present in the final system and is therefore not included in the standard certification processes. Rather, the model is checked indirectly, by ensuring that ACAS X performs as well as, or better than, the state-of-the-art, TCAS. We claim that to build confidence in such systems, it is important to target model quality directly. We investigate this issue of model quality as part of our research on informing certification standards for autonomy. Using ACAS X as our driving example, we study the relationship between the probabilistic model and the real world, in an attempt to characterize the quality of the model for the purpose of building ACAS X. This paper presents model conformance metrics, their application to ACAS X, and the results that we obtained from our study.

D. Guck—Author performed this work while employed by SGT, Inc. as an intern at the NASA Ames Research Center.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

    ACAS X handles cases with multiple aircraft but this paper focuses on scenarios involving two aircraft.

  2. 2.

    We use the MDP rather than its corresponding continuous version for aircraft dynamics, because the generation of the LUT is based on the MDP model.

References

  1. Dimjasevic, M., Giannakopoulou, D.: Test-case generation for runtime analysis, vice versa: verification of aircraft separation assurance. In: Proceedings of the 2015 International Symposium on Software Testing and Analysis, ISSTA 2015, Baltimore, 12–17 July 2015, pp. 282–292 (2015)

    Google Scholar 

  2. Galdino, A.L., Muñoz, C., Ayala-Rincón, M.: Formal verification of an optimal air traffic conflict resolution and recovery algorithm. In: Leivant, D., Queiroz, R. (eds.) WoLLIC 2007. LNCS, vol. 4576, pp. 177–188. Springer, Heidelberg (2007). doi:10.1007/978-3-540-73445-1_13

    Chapter  Google Scholar 

  3. Ghorbal, K., Jeannin, J., Zawadzki, E., Platzer, A., Gordon, G.J., Capell, P.: Hybrid theorem proving of aerospace systems: applications and challenges. J. Aerospace Inf. Sys. 11(10), 702–713 (2014)

    Article  Google Scholar 

  4. Giannakopoulou, D., Bushnell, D.H., Schumann, J., Erzberger, H., Heere, K.: Formal testing for separation assurance. Ann. Math. Artif. Intell. 63(1), 5–30 (2011)

    Article  MATH  Google Scholar 

  5. Giannakopoulou, D., Howar, F., Isberner, M., Lauderdale, T., Rakamaric, Z., Raman, V.: Taming test inputs for separation assurance. In: ACM/IEEE International Conference on Automated Software Engineering, ASE 2014, Vasteras, 15–19 September 2014, pp. 373–384 (2014)

    Google Scholar 

  6. Jeannin, J.-B., Ghorbal, K., Kouskoulas, Y., Gardner, R., Schmidt, A., Zawadzki, E., Platzer, A.: A formally verified hybrid system for the next-generation airborne collision avoidance system. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 21–36. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46681-0_2

    Google Scholar 

  7. Kochenderfer, M.J.: Decision Making Under Uncertainty: Theory and Application. MIT Press, Cambridge (2015)

    MATH  Google Scholar 

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

    Google Scholar 

  9. Kuchar, J., Drumm, A.C.: The traffic alert and collision avoidance system. Linc. Lab. J. 16(2), 277 (2007)

    Google Scholar 

  10. Lee, R., Kochenderfer, M.J., Mengshoel, O.J., Brat, G.P., Owen, M.P.: Adaptive stress testing of airborne collision avoidance systems. In: 2015 IEEE/AIAA 34th Digital Avionics Systems Conference (DASC), p. 6C2-1. IEEE (2015)

    Google Scholar 

  11. Loos, S.M., Renshaw, D.W., Platzer, A.: Formal verification of distributed aircraft controllers. In: Proceedings of the 16th International Conference on Hybrid systems: Computation and Control, HSCC 2013, Philadelphia, 8–11 April 2013, pp. 125–130 (2013)

    Google Scholar 

  12. Lygeros, J., Lynch, N.: On the formal verification of the TCAS conflict resolution algorithms. In: 36th IEEE Conference on Decision and Control, pp. 1829–1834 (1997)

    Google Scholar 

  13. Platzer, A., Clarke, E.M.: Formal verification of curved flight collision avoidance maneuvers: a case study. In: Cavalcanti, A., Dams, D.R. (eds.) FM 2009. LNCS, vol. 5850, pp. 547–562. Springer, Heidelberg (2009). doi:10.1007/978-3-642-05089-3_35

    Chapter  Google Scholar 

  14. Tomlin, C., Pappas, G.J., Sastry, S.: Conflict resolution for air traffic management: a study in multiagent hybrid systems. IEEE Trans. Autom. Control 43(4), 509–521 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  15. Essen, C., Giannakopoulou, D.: Analyzing the next generation airborne collision avoidance system. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 620–635. Springer, Heidelberg (2014). doi:10.1007/978-3-642-54862-8_54

    Chapter  Google Scholar 

  16. von Essen, C., Giannakopoulou, D.: Probabilistic verification and synthesis of the next generation airborne collision avoidance system. STTT 18(2), 227–243 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

We thank Ritchie Lee for his help with RLECAS, Ryan Gardner for helping us interpret the MDP, and Ryan Gardner, Mykel Kochenderfer, Ritchie Lee, and Josh Silbermann for useful discussions and for proof-reading the paper. This work was performed under the Safe Autonomous Systems Operations (SASO) project of the NASA AOSP program.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dennis Guck .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Giannakopoulou, D., Guck, D., Schumann, J. (2016). Exploring Model Quality for ACAS X. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds) FM 2016: Formal Methods. FM 2016. Lecture Notes in Computer Science(), vol 9995. Springer, Cham. https://doi.org/10.1007/978-3-319-48989-6_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-48989-6_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48988-9

  • Online ISBN: 978-3-319-48989-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics