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We present Splat-Nav, a real-time robot navigation pipeline for Gaussian splatting (GSplat) scenes, a powerful new 3-D scene representation. Splat-Nav consists of two components: first, Splat-Plan, a safe planning module, and second, Splat-Loc, a robust vision-based 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 Bézier curve trajectory through this corridor. Splat-Loc provides real-time recursive state estimates given only an RGB feed from an on-board camera, leveraging the point-cloud representation inherent in GSplat scenes. Working together, these modules give robots the ability to recursively replan smooth and safe trajectories to goal locations. Goals can be specified with position coordinates, or with language commands by using a semantic GSplat. We demonstrate improved safety compared to point cloud-based methods in extensive simulation experiments. In a total of 126 hardware flights, we demonstrate equivalent safety and speed compared to motion capture and visual odometry, but without a manual frame alignment required by those methods. We show online replanning at more than 2 Hz and pose estimation at about 25 Hz, an order of magnitude faster than neural radiance field-based navigation methods, thereby enabling real-time navigation. 

In this work, we propose a novel method to supervise 3D Gaussian Splatting (3DGS) scenes using optical tactile sensors. Optical tactile sensors have become widespread in their use in robotics for manipulation and object representation; however, raw optical tactile sensor data is unsuitable to directly supervise a 3DGS scene. Our representation leverages a Gaussian Process Implicit Surface to implicitly represent the object, combining many touches into a unified representation with uncertainty. We merge this model with a monocular depth estimation network, which is aligned in a two stage process, coarsely aligning with a depth camera and then finely adjusting to match our touch data. For every training image, our method produces a corresponding fused depth and uncertainty map. Utilizing this additional information, we propose a new loss function, variance weighted depth supervised loss, for training the 3DGS scene model. We leverage the DenseTact optical tactile sensor and RealSense RGB-D camera to show that combining touch and vision in this manner leads to quantitatively and qualitatively better results than vision or touch alone in a few-view scene syntheses on opaque as well as on reflective and transparent objects. Please see our project page at armlabstanford.github.io/touch-gs