Design for One, Deploy for Many: Navigating Tree Mazes with Multiple Agents

TL;DR

This work addresses coordinating many agents in maze-like, tree-structured environments with limited communication. It introduces the MAMT framework, where a head runs a single-agent maze solver and leadership is dynamically transferred to followers to maintain a connected traversal toward the undisclosed goal $g$, ensuring eventual convergence under two-hop communication constraints. Across simulations with up to $n$ agents and real-robot tests, MAMT reduces makespan and, with increasing $n$, drives the average sum-of-fuel toward the shortest-path length, with DFS generally delivering the best empirical performance. The results demonstrate scalable, distributed coordination that approaches full-knowledge performance in large-agent regimes, offering practical applicability in subterranean or densely structured settings.

Abstract

Maze-like environments, such as cave and pipe networks, pose unique challenges for multiple robots to coordinate, including communication constraints and congestion. To address these challenges, we propose a distributed multi-agent maze traversal algorithm for environments that can be represented by acyclic graphs. It uses a leader-switching mechanism where one agent, assuming a head role, employs any single-agent maze solver while the other agents each choose an agent to follow. The head role gets transferred to neighboring agents where necessary, ensuring it follows the same path as a single agent would. The multi-agent maze traversal algorithm is evaluated in simulations with groups of up to 300 agents, various maze sizes, and multiple single-agent maze solvers. It is compared against strategies that are naïve, or assume either global communication or full knowledge of the environment. The algorithm outperforms the naïve strategy in terms of makespan and sum-of-fuel. It is superior to the global-communication strategy in terms of makespan but is inferior to it in terms of sum-of-fuel. The findings suggest it is asymptotically equivalent to the full-knowledge strategy with respect to either metric. Moreover, real-world experiments with up to 20 Pi-puck robots confirm the feasibility of the approach.

Figures (7)

• Figure 1: The multi-agent maze traversal problem. (a) Example maze represented as a connected, acyclic graph with start node $s$ and goal node $g$ (orange). Agents navigate the maze, with one agent, assuming the head role (light green), running a single-agent maze solver while all other agents (dark green) choose an agent to follow. The head role can transfer dynamically between neighboring agents. (b) Communication network between agents. (c) Tree graph representing the follower associations.
• Figure 2: Illustration of the NodeTowards$_i(j)$ function from the perspective of agent $i=3$ at start node $s$. Purple arrows indicate the nodes from which agent 3 receives messages sent by neighboring agents $j$.
• Figure 3: Example illustrating how the agents move and transfer the head role. (a) All agents initialize at the start node, and one agent becomes the head agent (light green). (b) The head moves to an adjacent node according to the single-agent maze solver, other agents (dark green) select agent 1 as their leader. (c) The head explores the maze further. (d) Agent 2 moves to follow the head, while the head role is transferred to agent 2. (e) Two agents following the same leader compete for the same node. (f) The followers resolve the conflict by selecting the smallest ID as the follower. The other agent updates its leader pointer.
• Figure 4: Snapshots of 50 agents exploring a 10$\times$10 maze using the DFS algorithm. The numbers on the left and right sides of the maze indicate the number of agents in the start and goal nodes, respectively. The head agent (light green) explores the maze, while the other agents (dark green) maintain a directed network to the head agent.
• Figure 5: Makespan (top row) and average sum-of-fuel (bottom row) per agent for different maze sizes and numbers of agents using DFS, BFS, and random walk solvers. Dashed lines indicate the median value for each maze size if agents followed the optimal path. Each configuration was tested for 20 trials.