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2017 | OriginalPaper | Buchkapitel

Linking Discrete and Continuous Models, Applied to Traffic Manoeuvrers

verfasst von : Ernst-Rüdiger Olderog, Anders P. Ravn, Rafael Wisniewski

Erschienen in: Provably Correct Systems

Verlag: Springer International Publishing

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Abstract

The interplay between discrete and continuous dynamical models is discussed, and a systematic approach to developing and combining these models together is outlined. The combination is done with linking predicates that define refinement relations between the models. As a case study, we build an abstract, discr spatial model and a concrete, continuous dynamic model for traffic manoeuvrers of multiple vehicles on highways. In the discrete model we show the safety (collision freedom) of distance keeping and lane-change manoeuvrers using events and actions to specify state transitions. By linking the discrete and continuous model via suitable predicates that express the discrete events and actions as distances and set-points in the continuous model, the safety carries over to the concrete model.

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Literatur
1.
Zurück zum Zitat Althoff, M., Stursberg, O., Buss, M.: Safety assessment of autonomous cars using verification techniques. In: American Control Conference (ACC) 2007, pp. 4154–4159. IEEE (2007) Althoff, M., Stursberg, O., Buss, M.: Safety assessment of autonomous cars using verification techniques. In: American Control Conference (ACC) 2007, pp. 4154–4159. IEEE (2007)
2.
Zurück zum Zitat Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theor. Comput. Sci. 138(1), 3–34 (1995)MathSciNetCrossRefMATH Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theor. Comput. Sci. 138(1), 3–34 (1995)MathSciNetCrossRefMATH
4.
Zurück zum Zitat Ames, A.D., Cousineau, E.A., Powell, M.J.: Dynamically stable bipedal robotic walking with nao via human-inspired hybrid zero dynamics. In: HSCC 2012, pp. 135–144. ACM (2012) Ames, A.D., Cousineau, E.A., Powell, M.J.: Dynamically stable bipedal robotic walking with nao via human-inspired hybrid zero dynamics. In: HSCC 2012, pp. 135–144. ACM (2012)
5.
Zurück zum Zitat Arechiga, N., Loos, S.M., Platzer, A., Krogh, B.H.: Using theorem provers to guarantee closed-loop system properties. In: American Control Conference (ACC) 2012, pp. 3573–3580. IEEE (2012) Arechiga, N., Loos, S.M., Platzer, A., Krogh, B.H.: Using theorem provers to guarantee closed-loop system properties. In: American Control Conference (ACC) 2012, pp. 3573–3580. IEEE (2012)
6.
Zurück zum Zitat Damm, W., Ihlemann, C., Sofroni-Stokkermans, V.: PTIME parametric verification of safety properties for reasonable linear hybrid systems. Math. Comput. Sci. 5(4), 469–497 (2011)MathSciNetCrossRefMATH Damm, W., Ihlemann, C., Sofroni-Stokkermans, V.: PTIME parametric verification of safety properties for reasonable linear hybrid systems. Math. Comput. Sci. 5(4), 469–497 (2011)MathSciNetCrossRefMATH
7.
Zurück zum Zitat Damm, W., Möhlmann, E., Rakow, A.: Component based design of hybrid systems: a case study on concurrency and coupling. In: HSCC 2014, pp. 145–150. ACM (2014) Damm, W., Möhlmann, E., Rakow, A.: Component based design of hybrid systems: a case study on concurrency and coupling. In: HSCC 2014, pp. 145–150. ACM (2014)
8.
Zurück zum Zitat de Roever, W.-P., Engelhardt, K.: Data Refinement: Model-Oriented Proof Methods and their Comparison. Cambridge University Press, New York (1998)CrossRefMATH de Roever, W.-P., Engelhardt, K.: Data Refinement: Model-Oriented Proof Methods and their Comparison. Cambridge University Press, New York (1998)CrossRefMATH
9.
Zurück zum Zitat Derrick, J., Boiten, E.A.: Refinement in Z and Object-Z: Foundations and Advanced Applications. Springer, London (2014) Derrick, J., Boiten, E.A.: Refinement in Z and Object-Z: Foundations and Advanced Applications. Springer, London (2014)
10.
Zurück zum Zitat Eggers, A., Fränzle, M., Herde, C.: SAT modulo ODE: a direct SAT approach to hybrid systems. In: Cha, S.D., Choi, J., Kim, M., Lee, I., Viswanathan, M. (eds.) ATVA 2008. LNCS, vol. 5311, pp. 171–185. Springer, Heidelberg (2008) Eggers, A., Fränzle, M., Herde, C.: SAT modulo ODE: a direct SAT approach to hybrid systems. In: Cha, S.D., Choi, J., Kim, M., Lee, I., Viswanathan, M. (eds.) ATVA 2008. LNCS, vol. 5311, pp. 171–185. Springer, Heidelberg (2008)
11.
Zurück zum Zitat Fränzle, M., Herde, C.: HySAT: an efficient proof engine for bounded model checking of hybrid systems. Form. Methods Syst. Des. 30(3), 179–198 (2007)CrossRefMATH Fränzle, M., Herde, C.: HySAT: an efficient proof engine for bounded model checking of hybrid systems. Form. Methods Syst. Des. 30(3), 179–198 (2007)CrossRefMATH
13.
Zurück zum Zitat Frehse, G., Guernic, C., Donzé, A., Cotton, S., Dang, T., Maler, O.: SpaceEx: scalable verification of hybrid systems. CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011) Frehse, G., Guernic, C., Donzé, A., Cotton, S., Dang, T., Maler, O.: SpaceEx: scalable verification of hybrid systems. CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011)
14.
15.
Zurück zum Zitat Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds).: Hybrid Systems. LNCS, vol. 736, Springer, Heidelberg (1993) Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds).: Hybrid Systems. LNCS, vol. 736, Springer, Heidelberg (1993)
16.
Zurück zum Zitat Grumberg, O.: Abstraction and reduction in model checking. In: Schwichtenberg, H., Steinbrüggen, R. (eds.) Proof and System-Reliabilty. Nato Science Series II. Math., Physics and Chemistry, vol. 62, pp. 213–260. Kluwer Academic Publishers, Boston (2002) Grumberg, O.: Abstraction and reduction in model checking. In: Schwichtenberg, H., Steinbrüggen, R. (eds.) Proof and System-Reliabilty. Nato Science Series II. Math., Physics and Chemistry, vol. 62, pp. 213–260. Kluwer Academic Publishers, Boston (2002)
17.
Zurück zum Zitat Habets, L., Collins, P., van Schuppen, J.: Reachability and control synthesis for piecewise-affine hybrid systems on simplices. IEEE Trans. Autom. Control 51(6), 938–948 (2006)MathSciNetCrossRef Habets, L., Collins, P., van Schuppen, J.: Reachability and control synthesis for piecewise-affine hybrid systems on simplices. IEEE Trans. Autom. Control 51(6), 938–948 (2006)MathSciNetCrossRef
18.
Zurück zum Zitat Henzinger, T.A.: The theory of hybrid automata. In: LICS 1996, pp. 278–292. IEEE (1996) Henzinger, T.A.: The theory of hybrid automata. In: LICS 1996, pp. 278–292. IEEE (1996)
19.
Zurück zum Zitat Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: HyTech: a model checker for hybrid systems. STTT 1(1–2), 110–122 (1997)CrossRefMATH Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: HyTech: a model checker for hybrid systems. STTT 1(1–2), 110–122 (1997)CrossRefMATH
20.
Zurück zum Zitat Hereid, A., Kolathaya, S., Jones, M.S., Van Why, J., Hurst, J.W., Ames, A.D.: Dynamic Multi-domain Bipedal Walking with Atrias Through Slip Based Human-Inspired Control. HSCC 2014. pp. 263–272, ACM (2014) Hereid, A., Kolathaya, S., Jones, M.S., Van Why, J., Hurst, J.W., Ames, A.D.: Dynamic Multi-domain Bipedal Walking with Atrias Through Slip Based Human-Inspired Control. HSCC 2014. pp. 263–272, ACM (2014)
21.
Zurück zum Zitat Hilscher, M., Linker, S., Olderog, E.-R.: Proving safety of traffic manoeuvres on country roads. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) Theories of Programming and Formal Methods. LNCS, vol. 8051, pp. 196–212. Springer, Heidelberg (2013) Hilscher, M., Linker, S., Olderog, E.-R.: Proving safety of traffic manoeuvres on country roads. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) Theories of Programming and Formal Methods. LNCS, vol. 8051, pp. 196–212. Springer, Heidelberg (2013)
22.
Zurück zum Zitat Hilscher, M., Linker, S., Olderog, E.-R., Ravn, A.P.: An abstract model for proving safety of multi-lane traffic manoeuvres. In: Qin, S., Qiu, Z. (eds.) ICFEM 2011. LNCS, vol. 6991, pp. 404–419. Springer, Heidelberg (2011) Hilscher, M., Linker, S., Olderog, E.-R., Ravn, A.P.: An abstract model for proving safety of multi-lane traffic manoeuvres. In: Qin, S., Qiu, Z. (eds.) ICFEM 2011. LNCS, vol. 6991, pp. 404–419. Springer, Heidelberg (2011)
23.
Zurück zum Zitat Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice Hall, London (1998) Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice Hall, London (1998)
24.
Zurück zum Zitat Lee, E.A., Zheng, H.: Operational semantics of hybrid systems. HSCC 2005, 25–53 (2005) Lee, E.A., Zheng, H.: Operational semantics of hybrid systems. HSCC 2005, 25–53 (2005)
25.
Zurück zum Zitat Linker, S.: Proofs for traffic safety: combining diagrams and logic. Ph.D thesis, Dept. of. Comp. Sci, Univ. of Oldenburg (2015) Linker, S.: Proofs for traffic safety: combining diagrams and logic. Ph.D thesis, Dept. of. Comp. Sci, Univ. of Oldenburg (2015)
27.
Zurück zum Zitat Loos, S.M., Platzer, A., Nistor, L.: Adaptive cruise control: hybrid, distributed, and now formally verified. In: Butler, M.J., Schulte, W. (eds.) FM 2011. LNCS, vol. 6664, pp. 42–56. Springer, Heidelberg (2011) Loos, S.M., Platzer, A., Nistor, L.: Adaptive cruise control: hybrid, distributed, and now formally verified. In: Butler, M.J., Schulte, W. (eds.) FM 2011. LNCS, vol. 6664, pp. 42–56. Springer, Heidelberg (2011)
28.
Zurück zum Zitat Lygeros, J., Godbole, D.N., Sastry, S.S.: Verified hybrid controllers for automated vehicles. IEEE Trans. Autom. Control 43(4), 522–539 (1998)MathSciNetCrossRefMATH Lygeros, J., Godbole, D.N., Sastry, S.S.: Verified hybrid controllers for automated vehicles. IEEE Trans. Autom. Control 43(4), 522–539 (1998)MathSciNetCrossRefMATH
29.
Zurück zum Zitat Lynch, N.A., Segala, R., Vaandrager, F.W.: Hybrid I/O automata revisited. HSCC 2001, 403–417 (2001) Lynch, N.A., Segala, R., Vaandrager, F.W.: Hybrid I/O automata revisited. HSCC 2001, 403–417 (2001)
30.
31.
Zurück zum Zitat Moor, T., Raisch, J., Davoren, J.: Admissiblity criteria for a hierarchical design of hybrid systems. In: Proceedings IFAD Conference on Analysis and Design of Hybrid Systems, pp. 389–394. St. Malo, France (2003) Moor, T., Raisch, J., Davoren, J.: Admissiblity criteria for a hierarchical design of hybrid systems. In: Proceedings IFAD Conference on Analysis and Design of Hybrid Systems, pp. 389–394. St. Malo, France (2003)
32.
Zurück zum Zitat Moor, T., Raisch, J., O’Young, S.: Discrete supervisory control of hybrid systems based on l-complete approximations. Discret. Event Dyn. Syst. 12, 83–107 (2002)MathSciNetCrossRefMATH Moor, T., Raisch, J., O’Young, S.: Discrete supervisory control of hybrid systems based on l-complete approximations. Discret. Event Dyn. Syst. 12, 83–107 (2002)MathSciNetCrossRefMATH
33.
Zurück zum Zitat Moszkowski, B.: A temporal logic for multilevel reasoning about hardware. Computer 18(2), 10–19 (1985)CrossRef Moszkowski, B.: A temporal logic for multilevel reasoning about hardware. Computer 18(2), 10–19 (1985)CrossRef
34.
Zurück zum Zitat Nadjm-Tehrani, S., Strömberg, J.: From physical modelling to compositional models of hybrid systems. In: Langmaack, H., de Roever, W.P., Vytopil, J. (eds.) Formal Techniques in Real-Time and Fault-Tolerant Systems, Third International Symposium Organized Jointly with the Working Group Provably Correct Systems – ProCoS, vol. 863 of LNCS, pp. 583–604. Springer (1994) Nadjm-Tehrani, S., Strömberg, J.: From physical modelling to compositional models of hybrid systems. In: Langmaack, H., de Roever, W.P., Vytopil, J. (eds.) Formal Techniques in Real-Time and Fault-Tolerant Systems, Third International Symposium Organized Jointly with the Working Group Provably Correct Systems – ProCoS, vol. 863 of LNCS, pp. 583–604. Springer (1994)
35.
Zurück zum Zitat Olderog, E.-R., Ravn, A., Wisniewski, R.: Linking spatial and dynamic models for traffic maneuvers. In: 54th IEEE Conference on Decision and Control (CDC), 8 pp. IEEE (2015) Olderog, E.-R., Ravn, A., Wisniewski, R.: Linking spatial and dynamic models for traffic maneuvers. In: 54th IEEE Conference on Decision and Control (CDC), 8 pp. IEEE (2015)
36.
Zurück zum Zitat Platzer, A.: Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics. Spinger, Heidelberg (2010)CrossRefMATH Platzer, A.: Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics. Spinger, Heidelberg (2010)CrossRefMATH
37.
Zurück zum Zitat Rajamani, R.: Vehicle Dynamics and Control. Mechanical engineering series. Springer Science, New York (2006)MATH Rajamani, R.: Vehicle Dynamics and Control. Mechanical engineering series. Springer Science, New York (2006)MATH
38.
Zurück zum Zitat Rajhans, A., Krogh, B.H.: Compositional heterogeneous abstraction. In: HSCC 2013, pp. 253–262. ACM (2013) Rajhans, A., Krogh, B.H.: Compositional heterogeneous abstraction. In: HSCC 2013, pp. 253–262. ACM (2013)
39.
Zurück zum Zitat Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Proceedings 3rd International Conference Knowledge Representation and Reasoning (1992) Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Proceedings 3rd International Conference Knowledge Representation and Reasoning (1992)
40.
Zurück zum Zitat Schäfer, A.: A calculus for shapes in time and space. In: Liu, Z., Araki, K. (eds.) ICTAC 2004. LNCS, vol. 3407, pp. 463–478. Springer, Heidelberg (2005) Schäfer, A.: A calculus for shapes in time and space. In: Liu, Z., Araki, K. (eds.) ICTAC 2004. LNCS, vol. 3407, pp. 463–478. Springer, Heidelberg (2005)
41.
Zurück zum Zitat Shao, Z., Liu, J.: Spatio-temporal hybrid automata for cyber-physical systems. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) ICTAC 2013. LNCS, vol. 8049, pp. 337–354. Springer, Heidelberg (2005) Shao, Z., Liu, J.: Spatio-temporal hybrid automata for cyber-physical systems. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) ICTAC 2013. LNCS, vol. 8049, pp. 337–354. Springer, Heidelberg (2005)
42.
Zurück zum Zitat Sreenath, K., Hill Jr., C.R., Kumar, V.: A partially observable hybrid system model for bipedal locomotion for adapting to terrain variations. In: HSCC 2013, pp. 137–142. ACM (2013) Sreenath, K., Hill Jr., C.R., Kumar, V.: A partially observable hybrid system model for bipedal locomotion for adapting to terrain variations. In: HSCC 2013, pp. 137–142. ACM (2013)
43.
Zurück zum Zitat van Benthem, J., Bezhanishvili, G.: Modal logics of space. In: Aiello, M., Pratt-Hartmann, I., Benthem, J. (eds.) Handbook of Spatial Logics, pp. 217–298. Springer, Netherlands (2007)CrossRef van Benthem, J., Bezhanishvili, G.: Modal logics of space. In: Aiello, M., Pratt-Hartmann, I., Benthem, J. (eds.) Handbook of Spatial Logics, pp. 217–298. Springer, Netherlands (2007)CrossRef
44.
Zurück zum Zitat Varaija, P.: Smart cars on smart roads: problems of control. IEEE Trans. Autom. Control AC 38(2), 195–207 (1993)MathSciNetCrossRef Varaija, P.: Smart cars on smart roads: problems of control. IEEE Trans. Autom. Control AC 38(2), 195–207 (1993)MathSciNetCrossRef
45.
Zurück zum Zitat Werling, M., Gindele, T., Jagszent, D., Gröll, L.: A robust algorithm for handling traffic in urban scenarios. In: Proceedings of IEEE Intelligent Vehicles Symposium, pp. 168–173. Eindhoven, NL (2008) Werling, M., Gindele, T., Jagszent, D., Gröll, L.: A robust algorithm for handling traffic in urban scenarios. In: Proceedings of IEEE Intelligent Vehicles Symposium, pp. 168–173. Eindhoven, NL (2008)
46.
Zurück zum Zitat Woodcock, J., Davies, J.: Using Z – Specification, Refinement, and Proof. Prentice Hall, New Jersey (1996)MATH Woodcock, J., Davies, J.: Using Z – Specification, Refinement, and Proof. Prentice Hall, New Jersey (1996)MATH
48.
Zurück zum Zitat Zabczyk, J.: Mathematical Control Theory – An Introduction. Birkhäuser (2008) Zabczyk, J.: Mathematical Control Theory – An Introduction. Birkhäuser (2008)
49.
Zurück zum Zitat Zhan, N., Wang, S., Zhao, H.: Formal modelling, analysis and verification of hybrid systems. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) Unifying Theories of Programming and Formal Engineering Methods. LNCS, vol. 8050, pp. 207–281. Springer, Heidelberg (2013) Zhan, N., Wang, S., Zhao, H.: Formal modelling, analysis and verification of hybrid systems. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) Unifying Theories of Programming and Formal Engineering Methods. LNCS, vol. 8050, pp. 207–281. Springer, Heidelberg (2013)
51.
Zurück zum Zitat Ziegler, J., Bender, P., Dang, T., Stiller, C.: Trajectory planning for bertha – A local, continuous method. In: 2014 IEEE Intelligent Vehicles Symposium Proceedings, Dearborn, MI, USA, June 8-11, 2014, pp. 450–457 (2014) Ziegler, J., Bender, P., Dang, T., Stiller, C.: Trajectory planning for bertha – A local, continuous method. In: 2014 IEEE Intelligent Vehicles Symposium Proceedings, Dearborn, MI, USA, June 8-11, 2014, pp. 450–457 (2014)
Metadaten
Titel
Linking Discrete and Continuous Models, Applied to Traffic Manoeuvrers
verfasst von
Ernst-Rüdiger Olderog
Anders P. Ravn
Rafael Wisniewski
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-48628-4_5