Neural Radiance Fields and Gaussian Splatting have transformed the field of computer vision by enabling photo-realistic representation of complex scenes. Despite this success, they have seen only limited use in real-world robotics tasks such as trajectory optimization. Two key factors have contributed to this limited success. First, it is challenging to reason about collisions in radiance models. Second, it is difficult to perform inference of radiance models fast enough for real-time trajectory synthesis. This paper addresses these challenges by proposing SPLANNING, a risk-aware trajectory optimizer that operates in a Gaussian Splatting model. This paper first derives a method for rigorously upper-bounding the probability of collision between a robot and a radiance field. Second, this paper introduces a normalized reformulation of Gaussian Splatting that enables the efficient computation of the collision bound in a Gaussian Splat. Third, a method is presented to optimize trajectories while avoiding collisions with a scene represented by a Gaussian Splat. Experiments demonstrate that SPLANNING outperforms state-of-the-art methods in generating collision-free trajectories in highly cluttered environments. The proposed system is also tested on a real-world robot manipulator.
神经辐射场（Neural Radiance Fields）和高斯分布（Gaussian Splatting）通过实现复杂场景的逼真表示，已经改变了计算机视觉领域的面貌。然而，尽管取得了显著成功，它们在诸如轨迹优化等实际机器人任务中的应用仍然有限。这种局限性主要归因于两个关键因素。首先，在辐射场模型中推理碰撞具有挑战性。其次，难以在辐射模型中以足够快的速度进行推理，以实现实时轨迹合成。本文通过提出SPLANNING（一种在高斯分布模型下运行的风险感知轨迹优化器）来应对这些挑战。本文首先推导了一种严格上界机器人与辐射场碰撞概率的方法。其次，提出了一种标准化的高斯分布重新表述，使得在高斯分布中高效计算碰撞界成为可能。第三，本文提出了一种优化轨迹的方法，能够在避免与由高斯分布表示的场景发生碰撞的同时进行优化。实验表明，SPLANNING 在生成无碰撞轨迹的高密度环境中表现优于现有的最先进方法。该系统还在实际的机器人机械臂上进行了测试。