IEEE/RSJ International Conference on Intelligent Robots and Systems - IROS 2025, Hangzhou (China). 19-25 October 2025
Summary:
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/
Spanish layman's summary:
Este artículo presenta FOCI, un método rápido de optimización de trayectorias usando 3D Gaussian Splatting (3DGS). Al modelar tanto el robot como el entorno como Gaussianas, FOCI permite una planificación precisa y consciente de la orientación en espacios reducidos. Calcula trayectorias libres de colisiones en segundos mediante una novedosa formulación de colisiones basada en la superposición de Gaussianas.
English layman's summary:
The paper introduces FOCI, a fast trajectory optimization method using 3D Gaussian Splatting (3DGS). By modeling both the robot and environment as Gaussians, FOCI enables accurate, orientation-aware planning through tight spaces. It computes collision-free paths in seconds using a novel Gaussian overlap-based collision formulation.
Keywords: Three-dimensional displays , Simultaneous localization and mapping , Trajectory planning , Robot kinematics , Robot sensing systems , Neural radiance field , Planning , Collision avoidance , Robots , Trajectory optimization
DOI: 
https://doi.org/10.1109/IROS60139.2025.11245845
Published in: IROS 2025: Conference proceedings, pp: 1884-1891, ISBN: 979-8-3315-4394-5
Publication date: 27-Nov-2025.
Citation:
M. Gomez Andreu, M. Wilder-Smith, V. Klemm, V. Patil, J. Tordesillas Torres, M. Hutter, "FOCI: Trajectory Optimization on Gaussian Splats", presented at IEEE/RSJ International Conference on Intelligent Robots and Systems - IROS 2025, Hangzhou, China, 19-25 October 2025. In: IROS 2025: Conference proceedings, pp. 1884-1891, doi: 10.1109/IROS60139.2025.11245845
IIT-25-214C
