Fast Algorithm for Centralized Multi-Agent Maze Exploration

Abstract

Recent advances in robotics have paved the way for robots to replace humans in perilous situations, such as searching for victims in burning buildings, in earthquake-damaged structures, in uncharted caves, traversing minefields or patrolling crime-ridden streets. These challenges can be generalized as problems where agents have to explore unknown mazes. We propose a cooperative multi-agent system of automated mobile agents for exploring unknown mazes and localizing stationary targets. The Heat Equation-Driven Area Coverage (HEDAC) algorithm for maze exploration employs a potential field to guide the exploration of the maze and integrates cooperative behaviors of the agents such as collision avoidance, coverage coordination, and path planning. In contrast to previous applications for continuous static domains, we adapt the HEDAC method for mazes on expanding rectilinear grids. The proposed algorithm guarantees the exploration of the entire maze and can ensure the avoidance of collisions and deadlocks. Moreover, this is the first application of the HEDAC algorithm to domains that expand over time. To cope with the dynamically changing domain, a red–black successive over-relaxation (SOR) iterative linear solver has been adapted and implemented, which significantly reduced the computational complexity of the presented algorithm when compared to a dense direct solver and to matrix-free BiCGSTAB and GMRES solvers applied to the same linear system. The results highlight significant improvements and show the applicability of the algorithm in different mazes. They confirm its robustness, adaptability, scalability and simplicity, which enables centralized parallel computation to control multiple agents in the maze.

The authors' abstract, as published at the source. Mathematics, 2026 · DOI ↗