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A Case Study on Numerical Analysis of a Path Computation Algorithm

Grégoire Boussu, Nikolai Kosmatov, Franck Védrine

TL;DR

A case study on numerical analysis of an industrial implementation of the fast marching algorithm, a popular path computation algorithm frequently used for trajectory computation, is presented.

Abstract

Lack of numerical precision in control software -- in particular, related to trajectory computation -- can lead to incorrect results with costly or even catastrophic consequences. Various tools have been proposed to analyze the precision of program computations. This paper presents a case study on numerical analysis of an industrial implementation of the fast marching algorithm, a popular path computation algorithm frequently used for trajectory computation. We briefly describe the selected tools, present the applied methodology, highlight some attention points, summarize the results and outline future work directions.

A Case Study on Numerical Analysis of a Path Computation Algorithm

TL;DR

A case study on numerical analysis of an industrial implementation of the fast marching algorithm, a popular path computation algorithm frequently used for trajectory computation, is presented.

Abstract

Lack of numerical precision in control software -- in particular, related to trajectory computation -- can lead to incorrect results with costly or even catastrophic consequences. Various tools have been proposed to analyze the precision of program computations. This paper presents a case study on numerical analysis of an industrial implementation of the fast marching algorithm, a popular path computation algorithm frequently used for trajectory computation. We briefly describe the selected tools, present the applied methodology, highlight some attention points, summarize the results and outline future work directions.

Paper Structure

This paper contains 15 sections, 3 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Outline.
  4. The Verification Target: the Fast Marching Algorithm
  5. First Step: Solving the Eikonal Equation
  6. Second Step: Finding an Optimal Path by a Backward Propagation
  7. Applications of These Algorithms
  8. The Verification Approach and Results
  9. A Common Instrumentation Mechanism for Different Verifications
  10. Results of the Approach based on Dynamic Analyses
  11. Evaluating the Impact of Perturbations on the Control Flow and the Resulting Path
  12. Ongoing Work on Formal Verification for Thin Numerical Scenarios
  13. Conclusion
  14. Future Work.
  15. Acknowledgment.

Figures (11)

  • Figure 1: Neighbors selected for calculation of $T_c(M)$
  • Figure 2: Propagation of the wave front
  • Figure 3: Calculation of pseudo-gradient on a segment
  • Figure 4: Result of calculation of a path avoiding turbulence areas
  • Figure 5: (Simplified) trace of the execution with Cadna (in green), where the cost of the path is evaluated by three values $v_1,$$v_2,$$v_3$.
  • ...and 6 more figures