Grid-based mobile robot path planning often requires a trade-off between path efficiency and maneuver regularity when obstacle force detours and trigger heading changes. This paper proposes a multi-objective grey wolf optimizer for grid-based path planning with turn-aware optimization. The path length and maneuver burden are optimized simultaneously using an 8-connected motion model with Euclidean-consistent costs and a strict no-corner-cutting feasibility rule. The experimental analysis is organized in three levels: A basic benchmark specification with 9-map environments, a structured 60-map benchmark covering five grid sizes, four obstacle-density levels, and three obstacle morphologies, and sequential qualitative visualization of dynamic obstacle avoidance and multi-robot coordination. The proposed method consistently achieves the lowest mean path length and the lowest mean turn count among the compared methods. Statistical comparison further shows significant gains in path length and turning burden on the majority of benchmark environments. The results indicate that the proposed method preserves favorable path-quality trade-offs across increasing grid size, obstacle density, and structural complexity, while also exhibiting coherent behavior in dynamic avoidance and coordination scenarios.