Probabilistic Energy Modeling Unifies Versatile Swarm Control

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.

Decentralized multi-agent swarm coordination on resource-constrained edge platforms remains fundamentally bottlenecked by the exponential scaling of joint action spaces and high-latency communication overhead. This paper introduces the Swarm Policy Interference Network (SPIN) framework, an architectural paradigm that bypasses these limitations by modeling swarm topologies as a compressed tensor network. We factorize the joint policy tensors of local multi-agent cliques into Matrix Product State (MPS) chains, reducing the computational complexity of evaluation from an exponential $O(n^m)$ wall to a strictly linear $O(m \cdot n \cdot χ^2)$ constraint. To bridge local continuous spatial geometry with this discrete algebraic backend without requiring power-intensive online training loops, we introduce a decoupled, hybrid neuro-symbolic control pipeline. Local multi-layered neural networks operate as structural coordination encoders, pre-trained offline to nonlinearly map hand-engineered geometric descriptors into abstract environmental target measures. At runtime, edge agents execute instantaneous behavioral adaptations by applying the Radon-Nikodým derivative directly as a zero-shot importance-reweighting filter. We validate the framework within a discrete-time multi-agent simulation sandbox spanning tracking, decentralized dispersion/area coverage, and multi-goal coordination regimes. Qualitative telemetry demonstrates that the integrated pipeline achieves stable target-directed motion, anti-collapse spatial spreading under decentralized constraints, and structured subgroup formation across multiple targets, providing a mathematically grounded route to tractable, low-power edge swarm intelligence.

Robot swarms utilize many independent limited-sensing agents to produce complex emergent behaviors without requiring centralized control. However, little research explores how agents can infer swarm-level behavior from purely local perception, a capability critical for detecting faults and behavior changes. In this paper, we introduce Synchronized Swarm Behavior Classification (SyncSBC), which combines improvements in machine learning and distributed consensus to classify collective swarm behavior and synchronize swarm decision-making in an entirely decentralized manner. We show that SyncSBC achieves high classification accuracy and low synchronization delay, making it suitable for real-world deployment. Finally, we use SyncSBC to demonstrate two promising swarm applications on real robots where we show that swarms utilizing SyncSBC can accurately identify anomalies in robot behavior and autonomously coordinate collective changes in swarm behavior. Videos, code and supplemental experiments are available at https://sites.google.com/view/sync-sbc/home.