A Path Planning Algorithm for a Dynamic Environment Based on Proper Generalized Decomposition

Antonio Falcó, Lucía Hilario, Nicolás Montés, Marta C. Mora and Enrique Nadal
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Antonio Falcó: ESI International Chair@CEU-UCH, Departamento de Matemáticas, Física y Ciencias Tecnológicas, Universidad Cardenal Herrera-CEU, CEU Universities, San Bartolomé 55, 46115 Alfara del Patriarca, Spain
Lucía Hilario: ESI International Chair@CEU-UCH, Departamento de Matemáticas, Física y Ciencias Tecnológicas, Universidad Cardenal Herrera-CEU, CEU Universities, San Bartolomé 55, 46115 Alfara del Patriarca, Spain
Nicolás Montés: ESI International Chair@CEU-UCH, Departamento de Matemáticas, Física y Ciencias Tecnológicas, Universidad Cardenal Herrera-CEU, CEU Universities, San Bartolomé 55, 46115 Alfara del Patriarca, Spain
Marta C. Mora: Departamento de Ingeniería Mecánica y Construcción, Universitat Jaume I, Avd. Vicent Sos Baynat s/n, 12071 Castellón, Spain
Enrique Nadal: Departamento de Ingeniería Mecánica y de Materiales, Universitat Politècnica de València Camino de Vera, s/n, 46022 Valencia, Spain

Mathematics, 2020, vol. 8, issue 12, 1-11

Abstract: A necessity in the design of a path planning algorithm is to account for the environment. If the movement of the mobile robot is through a dynamic environment, the algorithm needs to include the main constraint: real-time collision avoidance. This kind of problem has been studied by different researchers suggesting different techniques to solve the problem of how to design a trajectory of a mobile robot avoiding collisions with dynamic obstacles. One of these algorithms is the artificial potential field (APF), proposed by O. Khatib in 1986, where a set of an artificial potential field is generated to attract the mobile robot to the goal and to repel the obstacles. This is one of the best options to obtain the trajectory of a mobile robot in real-time (RT). However, the main disadvantage is the presence of deadlocks. The mobile robot can be trapped in one of the local minima. In 1988, J.F. Canny suggested an alternative solution using harmonic functions satisfying the Laplace partial differential equation. When this article appeared, it was nearly impossible to apply this algorithm to RT applications. Years later a novel technique called proper generalized decomposition (PGD) appeared to solve partial differential equations, including parameters, the main appeal being that the solution is obtained once in life, including all the possible parameters. Our previous work, published in 2018, was the first approach to study the possibility of applying the PGD to designing a path planning alternative to the algorithms that nowadays exist. The target of this work is to improve our first approach while including dynamic obstacles as extra parameters.

Keywords: proper generalized decomposition; motion planning; artificial potential fields; harmonic functions; Laplace equation; dynamic environment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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