Elastic Formation Control for Robot Swarms Using Dynamic Boundary-Based Potential Fields

Autonomous navigation in complex environments requires robots to plan safe and robust paths, and potential field techniques based on Boundary Value Problems (BVP) have shown promise for this task. However, when applied to robot swarms, many existing approaches fail to maintain group cohesion in cluttered environments, often allowing the swarm to split unintentionally. In this work, we propose a novel strategy that dynamically computes elastic swarm formations using BVP-based potential fields with local distortions, while coordinating velocity to preserve formation integrity. Our method enables the swarm to expand or contract according to environmental constraints, ensuring uniform progress toward the goal without leaving individual robots behind. Experimental results in both simulated and real-world settings demonstrate that our approach allows the swarm to navigate safely and effectively through complex spaces, consistently reaching the goal as a single, cohesive group. In addition, comparative analysis with recent swarm navigation methods shows that our approach achieves favorable results, particularly in terms of consistent inter-robot spacing and stable formation behavior.