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arXiv · 2503.09424

Hidden convexity property of a speed planning problem

Stefano Ardizzoni·Luca Consolini·Mattia Laurini·Marco Locatelli
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Abstract

In this paper we address the speed planning problem for a vehicle along a predefined path. A weighted average of two (conflicting) terms, energy consumption and travel time, is minimized. After deriving a non-convex mathematical model of the problem, we introduce a convex relaxation of the model and show that, after the application of a suitable feasibility-based bound tightening procedure, the convex relaxation shares the same optimal value and solution of the non-convex problem. We also establish that the feasible region of the non-convex problem is a lattice and, through that, a necessary and sufficient condition for the non-emptiness of the feasible region.

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Stefano Ardizzoni, Luca Consolini, Mattia Laurini, Marco Locatelli. 2025-03-12. Hidden convexity property of a speed planning problem. https://arxiv.org/abs/2503.09424

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