Opacity-Informed UAV Navigation with 3D Gaussian Splatting and Model Predictive Control

This paper presents an integrated UAV navigation system that combines 3D Gaussian Splatting (3DGS) for environment mapping, A* algorithm for global path planning, and Model Predictive Control (MPC) for trajectory tracking with obstacle avoidance. The 3DGS-generated Gaussian sphere map provides rich geometric information including opacity and scale parameters, which are utilized to construct a collision cost function embedded into the MPC optimization framework. Experimental results demonstrate that the proposed system achieves significant improvements in both path planning and trajectory tracking performance. The A* algorithm with Gaussian opacity-aware cost function reduces the integrated occupancy probability by 26.7% compared to traditional grid-based methods. The MPC controller with collision cost achieves a position RMSE of 0.030m, representing a 66.3% improvement over the baseline MPC without collision cost. The integrated system operates at an effective control frequency of 75Hz with an average single-step computation time of 13.3ms, meeting real-time requirements for UAV navigation in GNSS-denied environments.