Title : Solving some optimal path planning problems using an approach based on measure theory ( Solving some optimal path planning problems using an approach based on measure theory )
Authors: - - , Ali Vahidian Kamyad , Mohammad Hadi Farahi , - - ,
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Abstract
Abstract In this paper we solve a collection of optimal path planning problems using a method based on measure theory. First we consider the problem as an optimization problem and then we convert it to an optimal control problem by defining some artificial control functions. Then we perform a metamorphosis in the space of problem. In fact we define an injection between the set of admissible pairs, containing the control vector function and a collision-free path defined on free space and the space of positive Radon measures. By properties of this kind of measures we obtain a linear programming problem that its solution gives rise to constructing approximate optimal trajectory of the original problem. Some numerical examples are proposed. 2005 Elsevier Inc. All rights reserved.
Keywords
Keywords: Optimal path planning; Optimal control; Approximation theory; Measure theory; Linear programming
@article{paperid:202986,
author = { -, - and Vahidian Kamyad, Ali and Farahi, Mohammad Hadi and -, -},
title = {Solving some optimal path planning problems using an approach based on measure theory},
journal = {Applied Mathematics and Computation},
year = {2005},
volume = {170},
month = {September},
issn = {0096-3003},
pages = {1418--1435},
numpages = {17},
keywords = {Keywords: Optimal path planning; Optimal control; Approximation theory; Measure theory;
Linear programming},
}
%0 Journal Article
%T Solving some optimal path planning problems using an approach based on measure theory
%A -, -
%A Vahidian Kamyad, Ali
%A Farahi, Mohammad Hadi
%A -, -
%J Applied Mathematics and Computation
%@ 0096-3003
%D 2005
