Real-Time Path Planning Based on Harmonic Functions under a Proper Generalized Decomposition-Based Framework
| Autor: | Marta C. Mora, Nicolás Montés, Francisco Chinesta, Lucia Hilario, Nuria Rosillo, Enrique Nadal, Antonio Falcó |
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| Přispěvatelé: | Universidad Cardenal Herrera-CEU (CEU-UCH), Laboratoire Procédés et Ingénierie en Mécanique et Matériaux (PIMM), Conservatoire National des Arts et Métiers [CNAM] (CNAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), Universitat Jaume I, Department of Electronic Engineering [Universitat Politecnica de Valencia], Universitat Politècnica de València (UPV), UCH. Departamento de Matemáticas, Física y Ciencias Tecnológicas, Producción Científica UCH 2021 |
| Rok vydání: | 2021 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization Harmonic functions Computer science Robótica TP1-1185 02 engineering and technology Sciences de l'ingénieur Poisson equation Biochemistry Article potential fields Analytical Chemistry Decomposition (Mathematics) Computer Science::Robotics [SPI]Engineering Sciences [physics] 020901 industrial engineering & automation Autómatas matemáticos Teoria de Atomic and Molecular Physics 0502 economics and business Machine theory Motion planning Electrical and Electronic Engineering Instrumentation path planning Path planning Descomposición (Matemáticas) 050210 logistics & transportation Social robot Chemical technology 05 social sciences Ecuaciones en derivadas parciales Mobile robot Potential fields Differential equations Partial Atomic and Molecular Physics and Optics Proper Generalized Decomposition Variable (computer science) Harmonic function Funciones armónicas Robotics Benchmark (computing) Robot Poisson's equation and Optics harmonic functions |
| Zdroj: | Repositori Universitat Jaume I Universitat Jaume I Sensors (Basel, Switzerland) Sensors Sensors, MDPI, 2021, 21 (12), pp.3943. ⟨10.3390/s21123943⟩ Volume 21 Issue 12 Sensors, Vol 21, Iss 3943, p 3943 (2021) CEU Repositorio Institucional Fundación Universitaria San Pablo CEU (FUSPCEU) |
| ISSN: | 1424-8220 |
| Popis: | Este artículo se encuentra disponible en la siguiente URL: https://www.mdpi.com/1424-8220/21/12/3943 Este artículo de investigación pertenece al número especial "Autonomous Navigation in Robotics: A New Challenge towards Social Robots". This paper presents a real-time global path planning method for mobile robots using harmonic functions, such as the Poisson equation, based on the Proper Generalized Decomposition (PGD) of these functions. The main property of the proposed technique is that the computational cost is negligible in real-time, even if the robot is disturbed or the goal is changed. The main idea of the method is the off-line generation, for a given environment, of the whole set of paths from any start and goal configurations of a mobile robot, namely the computational vademecum, derived from a harmonic potential field in order to use it on-line for decision-making purposes. Up until now, the resolution of the Laplace or Poisson equations has been based on traditional numerical techniques unfeasible for real-time calculation. This drawback has prevented the extensive use of harmonic functions in autonomous navigation, despite their powerful properties. The numerical technique that reverses this situation is the Proper Generalized Decomposition. To demonstrate and validate the properties of the PGD-vademecum in a potential-guided path planning framework, both real and simulated implementations have been developed. Simulated scenarios, such as an L-Shaped corridor and a benchmark bug trap, are used, and a real navigation of a LEGO®MINDSTORMS robot running in static environments with variable start and goal configurations is shown. This device has been selected due to its computational and memory-restricted capabilities, and it is a good example of how its properties could help the development of social robots. |
| Databáze: | OpenAIRE |
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