Robot swarms can exhibit coherent collective behaviors through local perception, limited communication and decentralized decision-making, yet modeling and controlling such emergence remains challenging when behaviors unfold over multiple phases. Here we introduce PhySwarm, a physics-informed micro--macro framework that represents multi-stage swarm emergence as physically constrained density-field evolution coupled to executable robot motion. At the macroscopic level, a multi-phase advection--diffusion--reaction model (Macro-ADR) describes phase-dependent swarm-density evolution through directed transport, diffusion-based spatial regulation and behavioral phase transitions. At the microscopic level, an equivalent deterministic motion model (Micro-EDM) realizes these mechanisms through potential-field advection, density-gradient compensation and rate- or event-gated phase switching. A neural-physics controller (NPC) maps local observations and temporal memory to bounded physical parameters, and is trained with a reinforcement learning--PINN objective that combines task rewards with macro-scale density residuals and micro-scale motion-consistency constraints. In several proof-of-concept swarm missions -- including trail-guided foraging, formation-reconfigurable navigation and role-adaptive search and rescue -- we demonstrate that PhySwarm can generate distinct multi-stage emergent behaviors within a unified physics-informed modeling framework. The learned density fields and physical parameters provide interpretable evidence of how advection, diffusion and reaction jointly regulate multi-stage swarm organization. These results establish a physics-informed route for learning, interpreting and controlling emergent behaviors in robot swarms.

翻译：机器人集群可通过局部感知、有限通信和去中心化决策展现协调的集体行为，但当行为在多个阶段展开时，对此类涌现行为的建模与控制仍面临挑战。本文提出PhySwarm——一种物理信息启发的微观-宏观双尺度框架，将多阶段集群涌现表示为受物理约束的密度场演化过程，该过程与可执行的机器人运动相耦合。在宏观层面，多相平流-扩散-反应模型（Macro-ADR）通过定向传输、基于扩散的空间调节和相变行为描述阶段依赖的集群密度演化。在微观层面，等效确定性运动模型（Micro-EDM）通过势场平流、密度梯度补偿以及速率触发或事件触发的相位切换实现上述机制。神经物理控制器（NPC）将局部观测与时序记忆映射为有界物理参数，并通过结合任务奖励、宏观密度残差与微观运动一致性约束的强化学习-物理信息神经网络联合目标进行训练。在多项概念验证集群任务（包括路径引导觅食、形态重构导航和角色自适应搜救）中，我们证明PhySwarm能在统一的物理信息建模框架下生成显著的多阶段涌现行为。学习得到的密度场与物理参数提供了平流、扩散和反应如何协同调控多阶段集群组织的可解释性证据。这些结果确立了机器人集群涌现行为学习、解释与控制的物理信息驱动路径。