Obstacle avoidance is essential for safe navigation and motion planning. Recent radiance field reconstruction methods enable object detection and modeling with high fidelity, but remain too memory- and compute-intensive for on-board perception-based path planning. To address these limitations, we propose PolyMerge to convert a large, photorealistic 3D Gaussian Splatting (3DGS) model of a scene into a lightweight representation of convex polytopes whose union provably over-approximates all obstacles in the original 3DGS model. PolyMerge tunes the polytope count to trade off conservativeness and compute cost, and integrates with control barrier functions (CBFs) to plan collision-free paths. We showcase PolyMerge in simulation and hardware experiments on a Crazyflie drone, which uses PolyMerge to compute and follow safe trajectories in real time under severe onboard compute constraints, outperforming baselines in speed while guaranteeing safety. For our code and videos, visit https://athlon76.github.io/PolyMerge-website/.

翻译：障碍规避对于安全导航和运动规划至关重要。最近的辐射场重建方法能够以高保真度实现物体检测与建模，但在机载感知路径规划中仍因内存和计算开销过大而受限。为解决这些问题，我们提出PolyMerge方法，将场景的大型照片级真实3D高斯溅射（3DGS）模型转换为轻量化的凸多面体表示，其并集可被证明对原始3DGS模型中所有障碍物形成过逼近。PolyMerge通过调整多面体数量来权衡保守性与计算成本，并与控制障碍函数（CBFs）集成以规划无碰撞路径。我们在Crazyflie无人机上通过仿真和硬件实验展示了PolyMerge：该无人机在严苛的机载计算资源约束下，利用PolyMerge实时计算并跟踪安全轨迹，在保障安全性的同时其速度优于基线方法。代码和视频请访问https://athlon76.github.io/PolyMerge-website/。