A Reinforcement Learning-Based Hierarchical Probabilistic Shape Formation Framework for Large-Scale Robotic Swarms

This study develops a hierarchical framework for large-scale robotic swarm shape formation. At the upper level, reinforcement-learning-based probabilistic swarm guidance (RLPSG) uses proximal policy optimization (PPO) to learn target-specific transition probabilities from density feedback. A receiving rule directs robots toward deficient target bins while allowing transit through zero-target bins. Current Hellinger distance (HD) selects terminal allocation below 0.05 and ordinary probabilistic allocation otherwise. Terminal allocation clears zero-target bins while retaining PPO redistribution between neighboring positive-target bins. Relative-position adjustment favors nearby destinations. At the lower level, a safety-filtered Voronoi-based artificial potential field (SFVOAPF) planner converts assignments into motion with velocity lag and actuator limits. Tests with 2000 robots and 64 concentrated initial conditions per target yield median first-hit times of 12, 11, and 14 allocation steps for the ring, letter A, and separated blocks, respectively. All 192 trials finish with HD below 0.05 and zero background occupancy. Terminal allocation reduces cumulative bin changes by 14.17%, 18.08%, and 2.90% relative to probabilistic allocation throughout. Population-change tests finish below the HD threshold in 383 of 384 trials. Six planar closed-loop trials with static obstacles achieve formation with zero contacts under reference and composite-disturbance conditions, including bounded sensing errors and delayed, lossy measurement uploads.