PolyMerge: Compressing 3D Gaussian Splats with Polytope Coverings for Provably Safe Resource-Constrained Navigation

2026-06-15

AI Summary

This work addresses the challenge of enabling real-time onboard obstacle avoidance with high-fidelity 3D Gaussian Splatting models, which are typically hindered by substantial computational and memory demands. To overcome this limitation, the authors propose compressing the splatting representation into a convex polytopic cover that strictly envelopes the original obstacles. This compact geometric abstraction is seamlessly integrated with Control Barrier Functions (CBFs) to enable provably safe, real-time trajectory planning. As the first method to construct a lightweight yet safety-preserving geometric surrogate for 3D Gaussian Splatting, the approach significantly improves computational efficiency on resource-constrained platforms—such as Crazyflie drones—while outperforming existing baselines in simultaneously satisfying real-time performance and rigorous safety guarantees.

Abstract

Obstacle avoidance is essential for safe navigation and motion planning. Recent radiance field reconstruction methods enable object detection and modeling with high fidelity, but remain too memory- and compute-intensive for on-board perception-based path planning. To address these limitations, we propose PolyMerge to convert a large, photorealistic 3D Gaussian Splatting (3DGS) model of a scene into a lightweight representation of convex polytopes whose union provably over-approximates all obstacles in the original 3DGS model. PolyMerge tunes the polytope count to trade off conservativeness and compute cost, and integrates with control barrier functions (CBFs) to plan collision-free paths. We showcase PolyMerge in simulation and hardware experiments on a Crazyflie drone, which uses PolyMerge to compute and follow safe trajectories in real time under severe onboard compute constraints, outperforming baselines in speed while guaranteeing safety. For our code and videos, visit https://athlon76.github.io/PolyMerge-website/.

Problem

• obstacle avoidance
• 3D Gaussian Splatting
• resource-constrained navigation
• real-time perception
• safe motion planning

Innovation

• 3D Gaussian Splatting
• convex polytopes
• control barrier functions
• resource-constrained navigation
• obstacle over-approximation