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Time-optimal velocity planning by a bound-tightening technique

Author

Listed:
  • Federico Cabassi

    (Università di Parma)

  • Luca Consolini

    (Università di Parma)

  • Marco Locatelli

    (Università di Parma)

Abstract

Range reduction techniques often considerably enhance the performance of algorithmic approaches for the solution of nonconvex problems. In this paper we propose a range reduction technique for a class of optimization problems with some special structured constraints. The procedure explores and updates the values associated to the nodes of a suitably defined graph. Convergence of the procedure and some efficiency issues, in particular related to the order into which the nodes of the graph are explored. The proposed technique is applied to solve problems arising from a relevant practical application, namely velocity planning along a given trajectory. The computational experiments show the efficiency of the procedure and its ability of returning solutions within times much lower than those of nonlinear solvers and compatible with real-time applications.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:70:y:2018:i:1:d:10.1007_s10589-017-9978-6
    DOI: 10.1007/s10589-017-9978-6
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    References listed on IDEAS

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    1. 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.
    2. Peiping Shen & Yuan Ma & Yongqiang Chen, 2011. "Global optimization for the generalized polynomial sum of ratios problem," Journal of Global Optimization, Springer, vol. 50(3), pages 439-455, July.
    3. Alberto Caprara & Marco Locatelli & Michele Monaci, 2016. "Theoretical and computational results about optimality-based domain reductions," Computational Optimization and Applications, Springer, vol. 64(2), pages 513-533, June.
    4. H. P. Benson, 2010. "Simplicial Branch-and-Reduce Algorithm for Convex Programs with a Multiplicative Constraint," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 213-233, May.
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    Cited by:

    1. 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.
    2. Luca Consolini & Mattia Laurini & Marco Locatelli, 2019. "Graph-based algorithms for the efficient solution of optimization problems involving monotone functions," Computational Optimization and Applications, Springer, vol. 73(1), pages 101-128, May.

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