A CM-GAPSO optimization framework for cooperative path planning of UUV formations in polar under-ice observation missions

Path planning for unmanned underwater vehicle (UUV) formations in polar under-ice environments is fundamentally challenged by GNSS signal occlusion, severely degraded acoustic communication, dynamic ice obstacles, and the inherent tension between individual obstacle avoidance and formation integrity. While existing methods address either single-UUV path optimization or formation control under idealized assumptions, few existing methods can simultaneously address the coupled requirements of kinematic feasibility, ice-zone threat avoidance, and adaptive formation maintenance within a unified framework. To address this gap, this paper presents CM-GAPSO, a hybrid cooperative multi-population genetic algorithm and Safe Particle Swarm Optimization framework designed for polar under-ice UUV formation coverage observation missions. The method employs the spherical vector encoding used in SPSO, in which path segment length, azimuth angle, and pitch angle parameterize the trajectory and intrinsically ensure kinematic feasibility. Genetic crossover and mutation mechanisms are embedded within a three-subpopulation cooperative evolution strategy comprising superior, hybrid, and inferior subpopulations with distinct update rules to sustain population diversity and resist premature convergence. A multi-objective cost function is constructed, integrating path length, proximity to ice-related threat zones, depth stability, turning smoothness, and a flexible formation configuration penalty with threat-dependent weight adaptation and narrow-region scaling. Extensive simulations under realistic Arctic sea ice conditions demonstrate that CM-GAPSO achieves a mean total path cost of 3753.75 with a 100% success rate. Ablation experiments reveal that the removal of the narrow-region adaptive scaling strategy increases total cost by 157.9%, while the exclusion of genetic operators raises cost by 103.6%, confirming the indispensable contribution of each core component. Comparative evaluations further show that CM-GAPSO consistently outperforms standard PSO, GWO, and conventional GA in terms of path quality, convergence speed, and formation coordination stability.