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

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 b...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 184; no. 3; pp. 1083 - 1108
Main Authors: Consolini, Luca, Laurini, Mattia, Locatelli, Marco, Cabassi, Federico
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2020
Springer Nature B.V
Subjects:
Acceleration
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Interpolation
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Theory of Computation
Velocity planning
65K05
49M25
Convex optimization
90C25
Convergence analysis
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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 ϵ -optimal solution can be found in a time which is a polynomial function of ϵ - 1 , more precisely its eighth power.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-019-01626-4