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Convergence Analysis of Spatial-Sampling-Based Algorithms for Time-Optimal Smooth Velocity Planning

Author

Listed:
  • Luca Consolini

    (Università degli Studi di Parma)

  • Mattia Laurini

    (Università degli Studi di Parma)

  • Marco Locatelli

    (Università degli Studi di Parma)

  • Federico Cabassi

    (Università degli Studi di Parma)

Abstract

For a vehicle on an assigned path, we consider the problem of finding the time-optimal speed law that satisfies kinematic and dynamic constraints, related to maximum speed and maximum tangential and transversal acceleration. We show that the problem can be solved with an arbitrarily high precision by performing a finite element lengthwise path discretization and using a quadratic spline for interpolation. In particular, we show that an $$\epsilon $$ϵ-optimal solution can be found in a time which is a polynomial function of $$\epsilon ^{-1}$$ϵ-1, more precisely its eighth power.

Suggested Citation

  • Luca Consolini & Mattia Laurini & Marco Locatelli & Federico Cabassi, 2020. "Convergence Analysis of Spatial-Sampling-Based Algorithms for Time-Optimal Smooth Velocity Planning," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1083-1108, March.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:3:d:10.1007_s10957-019-01626-4
    DOI: 10.1007/s10957-019-01626-4
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    References listed on IDEAS

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    1. Federico Cabassi & Luca Consolini & Marco Locatelli, 2018. "Time-optimal velocity planning by a bound-tightening technique," Computational Optimization and Applications, Springer, vol. 70(1), pages 61-90, May.
    2. E. Velenis & P. Tsiotras, 2008. "Minimum-Time Travel for a Vehicle with Acceleration Limits: Theoretical Analysis and Receding-Horizon Implementation," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 275-296, August.
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