Splat-Nav: Safe Real-Time Robot Navigation in Gaussian Splatting Maps

We present Splat-Nav, a navigation pipeline that consists of a real-time safe planning module and a robust state estimation module designed to operate in the Gaussian Splatting (GSplat) environment representation, a popular emerging 3D scene representation from computer vision. We formulate rigorous collision constraints that can be computed quickly to build a guaranteed-safe polytope corridor through the map. We then optimize a B-spline trajectory through this corridor. We also develop a real-time, robust state estimation module by interpreting the GSplat representation as a point cloud. The module enables the robot to localize its global pose with zero prior knowledge from RGB-D images using point cloud alignment, and then track its own pose as it moves through the scene from RGB images using image-to-point cloud localization. We also incorporate semantics into the GSplat in order to obtain better images for localization. All of these modules operate mainly on CPU, freeing up GPU resources for tasks like real-time scene reconstruction. We demonstrate the safety and robustness of our pipeline in both simulation and hardware, where we show re-planning at 5 Hz and pose estimation at 20 Hz, an order of magnitude faster than Neural Radiance Field (NeRF)-based navigation methods, thereby enabling real-time navigation.

CATNIPS: Collision Avoidance Through Neural Implicit Probabilistic Scenes

We formalize a novel interpretation of Neural Radiance Fields (NeRFs) as giving rise to a Poisson Point Process (PPP). This PPP interpretation allows for rigorous quantification of uncertainty in NeRFs, in particular, for computing collision probabilities for a robot navigating through a NeRF environment model. The PPP is a generalization of a probabilistic occupancy grid to the continuous volume and is fundamental to the volumetric ray-tracing model underlying radiance fields. Building upon this PPP model, we present a chance-constrained trajectory optimization method for safe robot navigation in NeRFs. Our method relies on a voxel representation called the Probabilistic Unsafe Robot Region (PURR) that spatially fuses the chance constraint with the NeRF model to facilitate fast trajectory optimization. We then combine a graph-based search with a spline-based trajectory optimization to yield robot trajectories through the NeRF that are guaranteed to satisfy a user-specific collision probability. We validate our chance constrained planning method through simulations, showing superior performance compared with two other methods for trajectory planning in NeRF environment models.

Vision-Only Robot Navigation in a Neural Radiance World

Neural Radiance Fields (NeRFs) have recently emerged as a powerful paradigm for the representation of natural, complex 3D scenes. NeRFs represent continuous volumetric density and RGB values in a neural network, and generate photo-realistic images from unseen camera viewpoints through ray tracing. We propose an algorithm for navigating a robot through a 3D environment represented as a NeRF using only an on-board RGB camera for localization. We assume the NeRF for the scene has been pre-trained offline, and the robot's objective is to navigate through unoccupied space in the NeRF to reach a goal pose. We introduce a trajectory optimization algorithm that avoids collisions with high-density regions in the NeRF based on a discrete time version of differential flatness that is amenable to constraining the robot's full pose and control inputs. We also introduce an optimization based filtering method to estimate 6DoF pose and velocities for the robot in the NeRF given only an onboard RGB camera. We combine the trajectory planner with the pose filter in an online replanning loop to give a vision-based robot navigation pipeline. We present simulation results with a quadrotor robot navigating through a jungle gym environment, the inside of a church, and Stonehenge using only an RGB camera. We also demonstrate an omnidirectional ground robot navigating through the church, requiring it to reorient to fit through the narrow gap. Videos of this work can be found at https://mikh3x4.github.io/nerf-navigation/ .