Project start: 1.10.2025.

The development of new solvers for partial differential equations for the HEDAC method in ergodic control, as well as the application of the developed control, are the project's primary goals. Current implementations use direct solvers for linear systems in finite difference and finite element methods; however, existing approaches are not sufficiently efficient for 3D domains and the computational performance required for real-time control. As a solution, developing an iterative solver based on a uniform rectangular grid for 2D and 3D continua is proposed, along with applying techniques such as Adaptive Mesh Refinement and MultiGrid, which would significantly improve computational performance.

The project also focuses on the development of techniques for accurate robot localization in unknown environments, including managing sensor uncertainties, such as LiDAR, and probabilistically correcting the robot's location and obstacles. The developed systems will use various mobile robots and sensor equipment to collect data, considering issues related to insufficient data quality and redundancy.

The main objectives of the project include autonomous 2D and 3D mapping and exploration of unknown spaces, inspection of external and network structures, aerial surveillance, and monitoring of marine pollution. Additionally, the project focuses on the development of computer vision and machine learning techniques for detecting objects, people, damage, and pipeline leaks based on images from RGB, RGB-D, and thermal cameras, as well as data fusion. A significant focus will be on the implementation of algorithms on real robotic systems and experimental testing. The research team, composed of experts from various fields, is already actively collaborating on scientific projects, and the project has the potential for significant social and economic impact in the development of digital tools for civil and public infrastructure.

The project contributes to open science policies and innovations in higher education, with numerous events planned for the popularization of science. From a social perspective, the project provides solutions for faster and safer responses in crises, while from an economic perspective, it opens opportunities for applying developed technologies in industry, ecology, and civil protection.