SAFER-Splat: A Control Barrier Function for Safe Navigation with Online Gaussian Splatting Maps

TL;DR

SAFER-Splat tackles safe robotic navigation in online GSplat maps by introducing a control barrier function (CBF) that operates on ellipsoidal primitives. The CBF is embedded in a quadratic program with constraint pruning to scale to hundreds of thousands of Gaussians, enabling real-time operation. The approach is complemented by SplatBridge for real-time GSplat training, and experiments show substantial speedups and safer behavior compared to NeRF-based controllers in simulation, plus successful onboard-perception drone tests. The work highlights the practicality of combining interpretable, geometric GSplat maps with principled safety guarantees for autonomous navigation.

Abstract

SAFER-Splat (Simultaneous Action Filtering and Environment Reconstruction) is a real-time, scalable, and minimally invasive action filter, based on control barrier functions, for safe robotic navigation in a detailed map constructed at runtime using Gaussian Splatting (GSplat). We propose a novel Control Barrier Function (CBF) that not only induces safety with respect to all Gaussian primitives in the scene, but when synthesized into a controller, is capable of processing hundreds of thousands of Gaussians while maintaining a minimal memory footprint and operating at 15 Hz during online Splat training. Of the total compute time, a small fraction of it consumes GPU resources, enabling uninterrupted training. The safety layer is minimally invasive, correcting robot actions only when they are unsafe. To showcase the safety filter, we also introduce SplatBridge, an open-source software package built with ROS for real-time GSplat mapping for robots. We demonstrate the safety and robustness of our pipeline first in simulation, where our method is 20-50x faster, safer, and less conservative than competing methods based on neural radiance fields. Further, we demonstrate simultaneous GSplat mapping and safety filtering on a drone hardware platform using only on-board perception. We verify that under teleoperation a human pilot cannot invoke a collision. Our videos and codebase can be found at https://chengine.github.io/safer-splat.

Figures (5)

• Figure 1: SAFER-Splat is a safety layer for online robotic GSplat mapping.
• Figure 2: The CBF is posed as an optimization problem, minimizing the distance between the robot $\mathbf{p}$ and some point $y^*$ on the ellipsoid. We solve the robot-ellipsoid distance program through a bisection search, and return both its gradient and Hessian.
• Figure 3: Computation time (lower is better), minimum distance to collision (above zero is safe), magnitude of control effort correction (lower is better), and progress to goal (higher is better) for five different scenes indicated by the icons. SAFER-Splat (ours, green), is compared with our CBF on a conservative bounding sphere of each ellipsoid (blue), our CBF on the GSplat means (yellow), and NeRF-CBF tong2023enforcing (red). Each trajectory is visualized as a translucent dot in the minimum distance and the wedge indicates the mean.
• Figure 4: Top row: Overlaid color and depth renders from the GSplats produced using SAFER-Splat in the real-world experiments. Bottom row: Overlaid corresponding keyframe color image and sparse point cloud.
• Figure 5: We showcase SAFER-Splat across three real-world scenes. A snapshot of the drone trajectory is shown on the left panel for each of the three scenes, annotated with the approximate desired and filtered control directions. In each of these trajectories, the operator attempted to directly hit the obstacle. On the right, we show the full flight trajectory, showing robustness with repeated collision avoidance. The pictured portion of each trajectory is highlighted in grey.

Theorems & Definitions (6)

• Proposition 1
• proof
• Theorem 1
• proof
• Corollary 1
• proof