Smoothed Particle Hydrodynamics with Differential Interaction Potentials for Multi-Swarm Segregation and Coordination

In this paper, we present a distributed framework for coordinated motion among multiple robotic swarms. The proposed approach is built upon the Smoothed Particle Hydrodynamics (SPH) paradigm, in which each robot is modeled as a particle and computes its control input based on the relative positions of neighboring robots within a finite communication range. Inspired by the immiscibility phenomenon observed in water-oil mixtures, we incorporate a differential interaction mechanism into the SPH framework to encode heterogeneous inter-group behaviors. As a result, in scenarios involving multiple robot groups with distinct affiliations, the swarm can spontaneously evolve from random initial configurations into multiple well-segregated and uniformly organized formations. Simulation results validate the effectiveness of the proposed method.