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

Luca Consolini (), Mattia Laurini (), Marco Locatelli () and Federico Cabassi ()
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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

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 3, No 17, 1083-1108

Abstract: 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.

Keywords: Convergence analysis; Velocity planning; Convex optimization; 49M25; 90C25; 65K05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-019-01626-4

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