Skip to main content
Log in

Coverage-guided test generation for continuous and hybrid systems

  • Published:
Formal Methods in System Design Aims and scope Submit manuscript

Abstract

In this paper, we describe a formal framework for conformance testing of continuous and hybrid systems, using the international standard ‘Formal Methods in Conformance Testing’ FMCT. We propose a novel test coverage measure for these systems, which is defined using the star discrepancy notion. This coverage measure is used to quantify the validation ‘completeness’. It is also used to guide input stimulus generation by identifying the portions of the system behaviors that are not adequately examined. We then propose a test generation method, which is based on a robotic motion planning algorithm and is guided by the coverage measure. This method was implemented in a prototype tool that can handle high dimensional systems (up to 100 dimensions).

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alur R, Courcoubetis C, Halbwachs N, Henzinger TA, Ho P-H, Nicollin X, Olivero A, Sifakis J, Yovine S (1995) The algorithmic analysis of hybrid systems. Theor Comput Sci 138:3–34

    Article  MATH  Google Scholar 

  2. Alur R, Dang T, Esposito J, Hur Y, Ivancic F, Kumar V, Lee I, Mishra P, Pappas G, Sokolsky O (2002) Hierarchical modeling and analysis of embedded systems. In: Proceedings of the IEEE, October 2002

  3. Beck J, Chen WWL (1988) Irregularities of distribution. Cambridge Univ Press, Cambridge

    Google Scholar 

  4. Branicky MS, Curtiss MM, Levine J Morgan S (2005) Sampling-based reachability algorithms for control and verification of complex systems. In: Proc thirteenth Yale workshop on Adaptive and Learning Systems, New Haven, CT

  5. Cheng P, LaValle S (2002) Resolution complete rapidly-exploring random trees. In: Proc IEEE International Conference on Robotics and Automation, pp 267–272

  6. Dang T, Nahhal T (2006) Randomized simulation of hybrid systems. Technical report, Verimag, May 2006

  7. Dobkin D, Eppstein D (1993) Computing the discrepancy. In: Proceedings of the Ninth Annual Symposium on Computational Geometry, pp 47–52

  8. Esposito JM, Kim J, Kumar V (2004) Adaptive RRTs for validating hybrid robotic control systems. In: Int workshop on the Algorithmic Foundations of Robotics

  9. Bhatia A, Frazzoli E (2004) Incremental search methods for reachability analysis of continuous and hybrid systems. In: Hybrid Systems: Computation and Control HSCC. LNCS, vol 2993. Springer, Berlin, pp 142–156

    Google Scholar 

  10. Julius AA, Fainekos GE, Anand M, Lee I, Pappas GJ (2007) Robust test generation and coverage for hybrid systems. In: Hybrid Systems: Computation and Control HSCC. LNCS. Springer, Berlin, pp 329–342

    Chapter  Google Scholar 

  11. Kim J, Esposito JM, Kumar V (2006) Sampling-based algorithm for testing and validating robot controllers. Int J Rob Res 25(12):1257–1272

    Article  Google Scholar 

  12. LaValle SM, Branicky MS, Lindemann SR (2004) On the relationship between classical grid search and probabilistic roadmaps. Int J Rob Res 23(7–8):673–692

    Article  Google Scholar 

  13. Faure H (1978) Discrépance de suites associees à un système de numération. General theory of distribution modulo 1. In: Irregularities of distribution

  14. Kuffner J, LaValle S (2000) RRT-connect: An efficient approach to single-query path planning. In Proc IEEE Int’l Conf on Robotics and Automation (ICRA’2000), San Francisco, CA, April 2000

  15. LaValle SM, Kuffner JJ (2001) Rapidly-exploring Random Trees: progress and prospects. In: Algorithmic and computational robotics: new directions. AK Peters, Wellesley, pp 293–308

    Google Scholar 

  16. Lee D, Yannakakis M (1996) Principles and methods of testing finite state machines—A survey. In: Proceedings of the IEEE, vol 84, pp 1090–1123

  17. Lindemann SR, LaValle SM (2004) Incrementally reducing dispersion by increasing voronoi bias in RRTs. In: Proceedings IEEE International Conference on Robotics and Automation

  18. Mitchell I, Tomlin C (2000) Level set methods for computation in hybrid Systems. In: Hybrid Systems: Control and Computation HSCC. LNCS, vol 1790. Springer, Berlin

    Chapter  Google Scholar 

  19. Moore A (1991) A tutorial on kd-trees. Computer laboratory technical report no 209, University of Cambridge, http://www.cs.cmu.edu/~awm/papers.html

  20. Nahhal T, Dang T (2007) Guided randomized simulation. In: Hybrid Systems: Control and Computation. LNCS, vol 4416. Springer, Berlin, pp 731–735

    Chapter  Google Scholar 

  21. Nahhal T (2007) Model-based testing of hybrid systems. PhD thesis, Joseph Fourier University, October 2007

  22. Plaku E, Kavraki LE, Vardi MY (2007) Hybrid systems: From verification to falsification. In: Damm W, Hermanns H (eds) International Conference on Computer Aided Verification (CAV). LNCS, vol 4590. Springer, Berlin, pp 468–481

    Chapter  Google Scholar 

  23. Tan L, Kim J, Sokolsky O, Lee I (2004) Model-based testing and monitoring for hybrid embedded systems. In: IRI, pp 487–492

  24. Thiémard E (2001) An algorithm to compute bounds for the star discrepancy. J Complex 17(4):850

    Article  MATH  Google Scholar 

  25. Tretmans J (1999) Testing concurrent systems: a formal approach. In: Int Conference on Concurrency Theory CONCUR. LNCS, vol 1664. Springer, Berlin

    Chapter  Google Scholar 

  26. Tretmans J (1994) A formal approach to conformance testing. In: Proceedings of the IFIP TC6/WG6.1 sixth international workshop on Protocol Test Systems VI. North-Holland, Amsterdam, pp 257–276

    Google Scholar 

  27. Yershova A, Jaillet L, Simeon T, LaValle SM (2005) Dynamic-domain RRTs: efficient exploration by controlling the sampling domain. In: Proc IEEE International Conference on Robotics and Automation

  28. Wang X, Hickernell F (2000) Randomized Halton sequences. Math Comput Model 32:887–899

    Article  MATH  MathSciNet  Google Scholar 

  29. Zhu H, Hall PAV, May JHR (1997) Software unit test coverage and adequacy. In: ACM Computing Surveys, 29, 4 Dec 1997

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thao Dang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dang, T., Nahhal, T. Coverage-guided test generation for continuous and hybrid systems. Form Methods Syst Des 34, 183–213 (2009). https://doi.org/10.1007/s10703-009-0066-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10703-009-0066-0

Keywords

Navigation