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

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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 \(\epsilon \)-optimal solution can be found in a time which is a polynomial function of \(\epsilon ^{-1}\), more precisely its eighth power.

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Notes

  1. A function \(f:\mathbb R\rightarrow \mathbb R\) is Lipschitz, if there exists a real positive constant L such that

    \((\forall x,y \in \mathbb R)\ |f(x)-f(y)| \le L |x-y|\).

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Acknowledgements

This research has financially been supported by the Programme “FIL-Quota Incentivante” of University of Parma and co-sponsored by Fondazione Cariparma. The authors are grateful to the Associate Editor and the anonymous Reviewers for the careful reading and the many suggestions which allowed to improve this work.

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Authors and Affiliations

  1. Dipartimento di Ingegneria e Architettura, Università degli Studi di Parma, Parco Area delle Scienze, 181/A, 43124, Parma, Italy

    Luca Consolini, Mattia Laurini, Marco Locatelli & Federico Cabassi

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  1. Luca Consolini
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  2. Mattia Laurini
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  3. Marco Locatelli
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  4. Federico Cabassi
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Correspondence to Luca Consolini.

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Communicated by Felix L. Chernousko.

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Consolini, L., Laurini, M., Locatelli, M. et al. Convergence Analysis of Spatial-Sampling-Based Algorithms for Time-Optimal Smooth Velocity Planning. J Optim Theory Appl 184, 1083–1108 (2020). https://doi.org/10.1007/s10957-019-01626-4

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