[Paper Review] CATNIPS: Collision Avoidance Through Neural Implicit Probabilistic Scenes

T. Chen, Preston Culbertson+1 more|arXiv (Cornell University)|Feb 24, 2023

Robotics and Sensor-Based Localization44 references4 citations

TL;DR

CATNIPS introduces a chance-constrained trajectory planning framework for robots navigating NeRF environments by transforming NeRFs into a Poisson Point Process (PPP) to rigorously compute collision probabilities. It uses a Probabilistic Unsafe Robot Region (PURR) voxel map to enable real-time, safe trajectory optimization via Bézier splines, achieving over 3 Hz replanning on a laptop—significantly faster than prior gradient-based methods with no safety guarantees.

ABSTRACT

We introduce a transformation of a Neural Radiance Field (NeRF) to an equivalent Poisson Point Process (PPP). This PPP transformation allows for rigorous quantification of uncertainty in NeRFs, in particular, for computing collision probabilities for a robot navigating through a NeRF environment. 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 representation, 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 and hardware experiments, showing superior performance compared to prior works on trajectory planning in NeRF environments. Our codebase can be found at https://github.com/chengine/catnips, and videos can be found on our project page (https://chengine.github.io/catnips).

Motivation & Objective

• To address the lack of mathematical safety guarantees in NeRF-based robot navigation, where NeRFs do not natively support point-wise occupancy queries.
• To enable rigorous, continuous collision probability computation in NeRF environments by transforming the density field into a Poisson Point Process (PPP).
• To develop a fast, real-time trajectory planner that guarantees user-defined collision probability thresholds using a novel voxelized scene representation (PURR).
• To outperform existing NeRF-based planners in safety, computational efficiency, and path intuitiveness, particularly in online replanning scenarios.
• To provide a differentiable, interpretable collision metric that replaces arbitrary density thresholds with probabilistically grounded safety constraints.

Proposed method

• Transform the NeRF density field into a Poisson Point Process (PPP), enabling rigorous probabilistic interpretation of scene geometry and collision likelihood.
• Derive an analytical expression for the probability of collision between a robot and the scene using the PPP formulation, integrating over the robot's spatial extent.
• Construct the Probabilistic Unsafe Robot Region (PURR) by convolving the robot's geometry with the NeRF density field, voxelizing the result to encode collision probability at each grid cell.
• Use A* graph search on the PURR to find a coarse path, then refine it using Bézier spline optimization to generate smooth, continuous trajectories.
• Implement the planner on a GPU with parallelization and pre-processing to achieve real-time performance (3 Hz) for online replanning.
• Leverage differentiability of the collision probability to enable potential online adaptation of safety thresholds during execution.

Figure 1 : (a) Ground-truth of the Stonehenge scene, (b) Poisson Point Process (PPP) of the scene represented as a point cloud, (c) Probabilistically Unsafe Robot Region (PURR) of scene, (d) Generated safe paths from our method (CATNIPS).

Experimental results

Research questions

• RQ1 Can a NeRF be mathematically transformed into a probabilistic point process to enable rigorous collision probability computation?
• RQ2 How can a robot’s geometric footprint be integrated with a NeRF’s density field to produce a spatially consistent, voxelized representation of unsafe regions?
• RQ3 Can a chance-constrained trajectory planner using the PURR achieve real-time performance while guaranteeing user-specified collision probability bounds?
• RQ4 How does the performance of this method compare to prior NeRF-based planners in terms of safety, computational speed, and path quality?
• RQ5 Can the probabilistic collision metric improve interpretability and tunability compared to arbitrary density thresholding?

Key findings

• The proposed method achieves real-time trajectory replanning at over 3 Hz on a standard laptop, significantly faster than the 2-second per-replanning time of the gradient-based baseline (NeRF-Nav).
• CATNIPS generates safer and less conservative paths than the state-of-the-art NeRF-Nav method, which lacks safety guarantees and requires 1000 gradient steps to converge.
• The paths generated by CATNIPS are more intuitive and easier to tune than those from a threshold-based baseline, as collision is defined via a user-specified probability threshold rather than an arbitrary density cutoff.
• The PURR representation enables efficient, GPU-accelerated trajectory optimization by pre-processing the NeRF into a probabilistic voxel map.
• The method demonstrates robust performance in both simulation and hardware experiments, validating its real-world applicability.
• The theoretical foundation of transforming NeRFs into a PPP provides a generalizable, mathematically rigorous framework for uncertainty quantification in neural radiance fields.

Figure 2 : In the rendering process, the probability that the pixel color takes on the color of the infintesimally small occluding slice (green) is given by the probability that all slices in the region preceding the slice (red) are unoccluded. Then, the pixel color is the expectation of the color t