Real-Time Path Planning Based on Harmonic Functions under a Proper Generalized Decomposition-Based Framework
TypeArticles dans des revues avec comité de lecture
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.
Showing items related by title, author, creator and subject.
HUERTA, Antonio; NADAL, Enrique; CHINESTA, Francisco (John Wiley and Sons Ltd, 2018)Domain decomposition strategies and proper generalized decomposition are efficiently combined to obtain a fast evaluation of the solution approximation in parameterized elliptic problems with complex geometries. The classical ...
NADAL, Enrique; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elias; CHINESTA, Francisco (Elsevier, 2018)Even if the diffusion equation has been widely used in physics and engineering, and its physical content is well understood, some variants of it escape fully physical understanding. In particular, anormal diffusion appears ...
On the multi‑scale description of electrical conducting suspensions involving perfectly dispersed rods PEREZ, Marta; ABISSET-CHAVANNE, Emmanuelle; BARASINSKI, Anais; CHINESTA, Francisco; AMMAR, Amine; KEUNINGS, Roland (Springer, 2015)Nanocomposites allow for a significant enhancement of functional properties, in particular electrical conduction. In order to optimize materials and parts, predictive models are required to evaluate particle distribution ...
From dilute to entangled fibre suspensions involved in the flow of reinforced polymers: A unified framework PEREZ, Marta; GUEVELOU, S; ABISSET-CHAVANNE, Emmanuelle; CHINESTA, Francisco; KEUNINGS, Roland (Elsevier, 2017)Most suspension descriptions nowadays employed are based on Jeffery model and some of its phenomenological adaptations that do not take into account the possible existence of a relative velocity between the fibres and the ...
PEREZ, Marta; SCHEUER, Adrien; ABISSET-CHAVANNE, Emmanuelle; AMMAR, Amine; CHINESTA, Francisco; KEUNINGS, Roland (Springer, 2019)When addressing the flow of concentrated suspensions composed of rods, dense clusters are observed. Thus, the adequate modelling and simulation of such a flow requires addressing the kinematics of these dense clusters and ...