Dual-Trail Stigmergic Coordination Enables Robust Three-Dimensional Underwater Swarm Coverage

Swarm coverage by unmanned underwater vehicles (UUVs) is essential for inspection, environmental monitoring, and search operations, but remains challenging in three-dimensional domains under limited sensing and communication. Pheromone-based stigmergic coordination provides a low-bandwidth alternative to explicit communication, yet conventional single-field models are susceptible to depth-dependent sensing inconsistencies and multi-source signal interference. This paper introduces a dual-trail stigmergic coordination framework in which a virtual pheromone field encodes short-term motion cues while an auxiliary coverage trail records the accumulated exploration effort. UUV motion is guided by the combined gradients of these two fields, enabling more consistent behavior across depth layers and mitigating ambiguities caused by overlapping pheromone sources. At the macroscopic level, swarm evolution is modeled by a coupled system of partial differential equations (PDEs) describing vehicle density, pheromone concentration, and coverage trail. A Lyapunov functional is constructed to derive sufficient conditions under which perturbations around the uniform coverage equilibrium decay exponentially. Numerical simulations in three-dimensional underwater domains demonstrate that the proposed framework reduces coverage holes, limits redundant overlap, and improves robustness with respect to a single-pheromone baseline and a potential-field-based controller. These results indicate that dual-field stigmergic control is a promising and scalable approach for UUV coverage in constrained underwater environments.