Relaxing Constraints in Anonymous Multi Agent Path Finding for Large Agents

The study addressed the problem of Anonymous Multi-Agent Path-finding (AMAPF). Unlike the classical formulation, where the assignment of agents to goals is fixed, in the anonymous MAPF setting it is irrelevant which agent reaches specific goal, provided that all goals are occupied. Most existing multi-agent pathfinding algorithms rely on a discrete representation of the environment (e.g., square grids) and do not account for the sizes of agents. This limits their applicability in real-world scenarios, such as trajectory planning for mobile robots in warehouses. Conversely, methods operating in continuous space typically impose substantial restrictions on the input data, such as constraints on the distances between initial and goal positions or between start/goal positions and obstacles. In this work, we considered one of the AMAPF algorithms designed for continuous space, where agents are modeled as disks of equal size. The algorithm requires a strict minimum separation of $4$ agent radii between any start/goal positions. Proposed a modification aimed at relaxing the constraints and reduce this limit from $4$ to $2\sqrt{3}$. We theoretically demonstrated that the proposed enhancements preserve original theoretical properties, including the guarantee that all agents will eventually achieve their goals safely and without collisions.