Fast algorithm for centralized multi-agent maze exploration

Recent advancements in robotics have paved the way for robots to replace humans in perilous situations, such as searching for victims in blazing buildings, earthquake-damaged structures, uncharted caves, traversing minefields, or patrolling crime-ridden streets. These challenges can be generalized as problems where agents need to explore unknown mazes. Although various algorithms for single-agent maze exploration exist, extending them to multi-agent systems poses complexities. We propose a solution: a cooperative multi-agent system of automated mobile agents for exploring unknown mazes and locating stationary targets. Our algorithm employs a potential field governing maze exploration, integrating cooperative agent behaviors like collision avoidance, coverage coordination, and path planning. This approach builds upon the Heat Equation Driven Area Coverage (HEDAC) method by Ivi\'c, Crnkovi\'c, and Mezi\'c. Unlike previous continuous domain applications, we adapt HEDAC for discrete domains, specifically mazes divided into nodes. Our algorithm is versatile, easily modified for anti-collision requirements, and adaptable to expanding mazes and numerical meshes over time. Comparative evaluations against alternative maze-solving methods illustrate our algorithm's superiority. The results highlight significant enhancements, showcasing its applicability across diverse mazes. Numerical simulations affirm its robustness, adaptability, scalability, and simplicity, enabling centralized parallel computation in autonomous systems of basic agents/robots.