FOCI: Trajectory Optimization on Gaussian Splats

2025-05-13

AI Summary

Traditional geometric representations (e.g., bounding volumes, point clouds, or meshes) lack orientation sensitivity, leading to underestimation of robot traversability and overly conservative motion planning in narrow spaces. To address this, we propose the first trajectory optimization framework operating directly on 3D Gaussian Splatting (3DGS) representations. Our core contributions are: (1) a differentiable, interpretable collision model based on Gaussian overlap integrals, explicitly encoding pose-dependent local geometric interactions; and (2) an end-to-end trajectory generation pipeline coupling analytical gradient computation with GPU-accelerated numerical optimization. Evaluated on real and synthetic scenes containing hundreds of thousands of Gaussians, our method generates collision-free trajectories for the ANYmal quadruped within seconds. It achieves significantly higher success rates in narrow-environment navigation and superior computational efficiency compared to baseline approaches.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

3D Gaussian Splatting (3DGS) has recently gained popularity as a faster alternative to Neural Radiance Fields (NeRFs) in 3D reconstruction and view synthesis methods. Leveraging the spatial information encoded in 3DGS, this work proposes FOCI (Field Overlap Collision Integral), an algorithm that is able to optimize trajectories directly on the Gaussians themselves. FOCI leverages a novel and interpretable collision formulation for 3DGS using the notion of the overlap integral between Gaussians. Contrary to other approaches, which represent the robot with conservative bounding boxes that underestimate the traversability of the environment, we propose to represent the environment and the robot as Gaussian Splats. This not only has desirable computational properties, but also allows for orientation-aware planning, allowing the robot to pass through very tight and narrow spaces. We extensively test our algorithm in both synthetic and real Gaussian Splats, showcasing that collision-free trajectories for the ANYmal legged robot that can be computed in a few seconds, even with hundreds of thousands of Gaussians making up the environment. The project page and code are available at https://rffr.leggedrobotics.com/works/foci/

Problem

• Optimizing trajectories directly on 3D Gaussian Splats
• Developing orientation-aware planning for tight spaces
• Enabling fast collision-free path computation for legged robots

Innovation

• Optimizes trajectories directly on 3D Gaussian Splats
• Uses overlap integral for interpretable collision formulation
• Enables orientation-aware planning in tight spaces