Fast algorithm for centralized multi-agent maze exploration

TL;DR

This work introduces a centralized HEDAC-based framework for cooperative exploration of unknown, expanding mazes by multiple agents. It formulates a discrete, time-stepped maze problem driven by a heat-equation-derived potential field $u$, updated via a fast BR SOR solver, with source term $s(oldsymbol{x},t)=\max(0,1-c(oldsymbol{x},t))$ and agent dynamics $rac{doldsymbol{z}_p}{dt}=v_a\frac{\nabla u}{\|\nabla u\|}$. Empirical results across diverse maze sizes and densities demonstrate rapid mapping, favorable comparisons to direct solvers and alternative multi-agent methods (especially in sparse mazes), and robustness to collision-avoidance settings. The approach is shown to be robust, scalable, and computationally efficient for centralized control of multi-robot exploration in unknown environments, with potential extensions to graph search and optimized solver parameters.

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, succesive over-relaxation (SOR) iterative linear solver has been adapted and implemented, which significantly reduced the computational complexity of the presented algorithm when compared to standard direct and iterative linear solvers. 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/robots in the maze.

Figures (11)

• Figure 1: An example of a maze, represented as a numerical grid. Maze walls are represented by a red line, and a possible location in the maze where an agent can stand is represented by black nodes. The edges between these nodes are only used to provide information about whether the two nodes are adjacent or not. A solid black line represents a real connection between two nodes, and a dotted black line represents an obstacle between two nodes.
• Figure 2: Examples of the maze nodes $x_{i,j}$ neighborhood depending on the arrangement of the maze walls. Maze walls are shown with red lines, while the nodes and the connections between them are shown in black.
• Figure 3: Examples of $50 \times 50$ mazes with different wall densities: a perfect maze with 49% (A), 40% (B) and 30% (C).
• Figure 4: Example of a simulation of $20 \times 20$ maze exploration by three agents. (A), (B) and (C) show agent trajectories and potential in known nodes after 20, 100 and 229 steps, respectively. Grey colored nodes are not known by the algorithm at given step.
• Figure 5: Example of a simulation of $20 \times 20$ maze exploration by three agents: Computational times, coverage, and number of iterations for SOR solver are displayed in for each step of the exploration.

Theorems & Definitions (2)

• Theorem 3.1
• proof