Authors:
Thanh Phong Tran
1
;
Laetitia Perez
2
;
Laurent Autrique
2
;
Edouard Leclercq
1
;
Syrine Bouazza
1
and
Dimitri Lefevbre
1
Affiliations:
1
GREAH, Université Le Havre Normandie, 25 Street Philippe Lebon, Le Havre, France
;
2
LARIS, University of Angers, 62 Av. Notre Dame du Lac, Angers, France
Keyword(s):
Inverse Problem, Moving Heat Source, Optimal Assignment Problem, Partial Differential Equation, Parametric Identification.
Abstract:
Previous studies have investigated inverse problems in physical systems described by partial differential equations, particularly for identifying unknown parameters of mobile heat sources. An iterative minimization of a quadratic cost function, based on the conjugate gradient method, has shown reliable results in identifying heat densities and trajectories both offline and online. Although fixed sensor arrays can be effective, covering the full operating range of a moving heat source requires a large number of sensors, leading to inefficiencies and waste. A more efficient approach uses fewer mobile sensors mounted on autonomous robots. However, this introduces challenges in robot control, ensuring optimal positioning, coordination, and collision avoidance. To address this, we propose a method that combines sensitivity-based sensor placement with robot assignment algorithms such as the Hungarian Algorithm and Multi-Agent Path Finding. This enables effective tracking of the heat source
’s trajectory while optimizing sensor deployment. The approach not only increases overall sensitivity of the sensor network but also improves identification performance with reduced latency and higher accuracy.
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