Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study

  • André Platzer
  • Edmund M. Clarke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5850)


Aircraft collision avoidance maneuvers are important and complex applications. Curved flight exhibits nontrivial continuous behavior. In combination with the control choices during air traffic maneuvers, this yields hybrid systems with challenging interactions of discrete and continuous dynamics. As a case study illustrating the use of a new proof assistant for a logic for nonlinear hybrid systems, we analyze collision freedom of roundabout maneuvers in air traffic control, where appropriate curved flight, good timing, and compatible maneuvering are crucial for guaranteeing safe spatial separation of aircraft throughout their flight. We show that formal verification of hybrid systems can scale to curved flight maneuvers required in aircraft control applications. We introduce a fully flyable variant of the roundabout collision avoidance maneuver and verify safety properties by compositional verification.


Hybrid System Collision Avoidance Linear Speed Hybrid Automaton Hybrid Program 
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.


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  1. 1.
    Tomlin, C., Pappas, G.J., Sastry, S.: Conflict resolution for air traffic management. IEEE T. Automat. Contr. 43(4), 509–521 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Dowek, G., Muñoz, C., Carreño, V.A.: Provably safe coordinated strategy for distributed conflict resolution. In: AIAA-2005-6047 (2005)Google Scholar
  3. 3.
    Galdino, A.L., Muñoz, C., Ayala-Rincón, M.: Formal verification of an optimal air traffic conflict resolution and recovery algorithm. In: Leivant, D., de Queiroz, R. (eds.) WoLLIC 2007. LNCS, vol. 4576, pp. 177–188. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Hwang, I., Kim, J., Tomlin, C.: Protocol-based conflict resolution for air traffic control. Air Traffic Control Quarterly 15(1), 1–34 (2007)Google Scholar
  5. 5.
    Henzinger, T.A.: The theory of hybrid automata. In: LICS, pp. 278–292. IEEE, Los Alamitos (1996)Google Scholar
  6. 6.
    Košecká, J., Tomlin, C., Pappas, G., Sastry, S.: 2-1/2D conflict resolution maneuvers for ATMS. In: CDC, Tampa, FL, USA, vol. 3, pp. 2650–2655 (1998)Google Scholar
  7. 7.
    Bicchi, A., Pallottino, L.: On optimal cooperative conflict resolution for air traffic management systems. IEEE Trans. ITS 1(4), 221–231 (2000)Google Scholar
  8. 8.
    Hu, J., Prandini, M., Sastry, S.: Probabilistic safety analysis in three-dimensional aircraft flight. In: CDC, vol. 5, pp. 5335–5340 (2003)Google Scholar
  9. 9.
    Hu, J., Prandini, M., Sastry, S.: Optimal coordinated motions of multiple agents moving on a plane. SIAM Journal on Control and Optimization 42, 637–668 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Umeno, S., Lynch, N.A.: Proving safety properties of an aircraft landing protocol using I/O automata and the PVS theorem prover. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 64–80. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Umeno, S., Lynch, N.A.: Safety verification of an aircraft landing protocol: A refinement approach. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 557–572. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Massink, M., Francesco, N.D.: Modelling free flight with collision avoidance. In: Andler, S.F., Offutt, J. (eds.) ICECCS, pp. 270–280. IEEE, Los Alamitos (2001)Google Scholar
  13. 13.
    Platzer, A., Clarke, E.M.: Formal verification of curved flight collision avoidance maneuvers: A case study. Technical Report CMU-CS-09-147, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA (2009)Google Scholar
  14. 14.
    Platzer, A., Clarke, E.M.: Computing differential invariants of hybrid systems as fixedpoints. Form. Methods Syst. Des. (2009); In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 176–189. Springer, Heidelberg (2008)Google Scholar
  15. 15.
    Damm, W., Pinto, G., Ratschan, S.: Guaranteed termination in the verification of LTL properties of non-linear robust discrete time hybrid systems. In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 99–113. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Platzer, A.: Differential dynamic logic for hybrid systems. J. Autom. Reasoning 41(2), 143–189 (2008)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Lafferriere, G., Pappas, G.J., Yovine, S.: A new class of decidable hybrid systems. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 137–151. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  18. 18.
    Pallottino, L., Scordio, V.G., Frazzoli, E., Bicchi, A.: Decentralized cooperative policy for conflict resolution in multi-vehicle systems. IEEE Trans. on Robotics 23(6), 1170–1183 (2007)CrossRefGoogle Scholar
  19. 19.
    Muñoz, C., Carreño, V., Dowek, G., Butler, R.W.: Formal verification of conflict detection algorithms. STTT 4(3), 371–380 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • André Platzer
    • 1
  • Edmund M. Clarke
    • 1
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityPittsburgh

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