To address the challenges of high-precision pose alignment, dynamic path smoothness, and efficient multi-objective optimization in three-dimensional UAV path planning under complex environments, this study proposes the Lie Group-based Griffon Vulture Grey Wolf Hybrid Optimizer (L-VGWO) framework. First, the framework employs the rotation-vector representation of the Lie group \(\text{SO}(3)\) to parameterize the path. Through the use of exponential and logarithmic mappings, the proposed model inherently preserves geometric continuity and avoids singularities in rotational motion. Second, to overcome the difficulty of efficient optimization in the high-dimensional Lie algebra space, we design the core solver of L-VGWO, which integrates the local refinement capability of the Grey Wolf Optimizer (GWO) with the global exploration ability of the Griffon Vulture Optimizer (GVOA). This cooperative mechanism substantially improves the balance between exploration and exploitation when optimizing the multi-objective cost function. Under a comprehensive objective formulation that includes obstacle avoidance, pose accuracy terms, and angular and linear velocity smoothness constraints, L-VGWO is validated through multi-scenario simulations and statistical analyses.
