用高斯点直接优化机器人轨迹，实现快速精准避障。
FOCI: Trajectory Optimization on Gaussian Splats
- 以高斯点表示环境与机器人，基于重叠积分计算碰撞
- 在数万高斯点环境下，几秒内生成任意形状机器人无碰撞路径
- 适合腿式机器人在狭窄空间的定向运动规划
3D Gaussian Splatting（3DGS）作为一种比神经辐射场（NeRFs）更快的3D重建与视图合成方法，近年来受到广泛关注。本文提出FOCI（Field Overlap Collision Integral），一种直接在高斯点上进行轨迹优化的算法。该方法利用高斯点间的重叠积分构建可解释的碰撞判别机制。与传统使用保守包围盒低估通行性的方法不同，本工作将环境和机器人均建模为高斯点云，不仅具备良好的计算特性，还支持方向感知规划，使机器人能够通过极窄通道。我们在合成与真实高斯点云数据上进行了广泛测试，结果表明：即使在包含数十万高斯点的环境中，也能在数秒内为ANYmal腿式机器人生成无碰撞轨迹。项目主页与代码已公开于https://rffr.leggedrobotics.com/works/foci/
原文摘要 · Abstract (English)
3D Gaussian Splatting (3DGS) has recently gained popularity as a faster alternative to Neural Radiance Fields (NeRFs) in 3D reconstruction and view synthesis methods. Leveraging the spatial information encoded in 3DGS, this work proposes FOCI (Field Overlap Collision Integral), an algorithm that is able to optimize trajectories directly on the Gaussians themselves. FOCI leverages a novel and interpretable collision formulation for 3DGS using the notion of the overlap integral between Gaussians. Contrary to other approaches, which represent the robot with conservative bounding boxes that underestimate the traversability of the environment, we propose to represent the environment and the robot as Gaussian Splats. This not only has desirable computational properties, but also allows for orientation-aware planning, allowing the robot to pass through very tight and narrow spaces. We extensively test our algorithm in both synthetic and real Gaussian Splats, showcasing that collision-free trajectories for the ANYmal legged robot that can be computed in a few seconds, even with hundreds of thousands of Gaussians making up the environment. The project page and code are available at https://rffr.leggedrobotics.com/works/foci/
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