Nomenclature.

To address the complex challenges associated with multiple unmanned aerial vehicles (multi-UAVs) cooperative inspection in offshore wind farms, including limited sensing and communication ranges, constrained battery capacity, and round-trip mission requirements, this paper introduces an optimal coordinated trajectory method for multi-UAV based on a distributed differential game (DDG) framework. The approach explicitly accounts for energy consumption, incorporating round-trip requirements into a game-theoretic objective function to facilitate energy-aware trajectory planning. Each UAV operates based solely on local information from neighboring UAVs, enabling distributed decision-making that ensures collision-free coordination while optimizing global inspection time and overall energy efficiency. The convergence of the proposed strategy to a global Nash equilibrium (G-NE), as confirmed by theoretical analysis, ensures system-level coordination optimality subject to round-trip and energy constraints. Simulation results demonstrate that the method significantly enhances inspection efficiency and reduces task completion time by up to compared to conventional approaches, while guaranteeing the safe return of all UAVs.