  We present Splat-Nav, a real-time navigation pipeline designed to work with
environment representations generated by Gaussian Splatting (GSplat), a popular
emerging 3D scene representation from computer vision. Splat-Nav consists of
two components: 1) Splat-Plan, a safe planning module, and 2) Splat-Loc, a
robust pose estimation module. Splat-Plan builds a safe-by-construction
polytope corridor through the map based on mathematically rigorous collision
constraints and then constructs a B\'ezier curve trajectory through this
corridor. Splat-Loc provides a robust state estimation module, leveraging the
point-cloud representation inherent in GSplat scenes for global pose
initialization, in the absence of prior knowledge, and recursive real-time pose
localization, given only RGB images. The most compute-intensive procedures in
our navigation pipeline, such as the computation of the B\'ezier trajectories
and the pose optimization problem run primarily on the CPU, freeing up GPU
resources for GPU-intensive tasks, such as online training of Gaussian Splats.
We demonstrate the safety and robustness of our pipeline in both simulation and
hardware experiments, where we show online re-planning at 5 Hz and pose
estimation at about 25 Hz, an order of magnitude faster than Neural Radiance
Field (NeRF)-based navigation methods, thereby enabling real-time navigation.
