CollisionSplatting: Collision-Aware Motion Planning in 3DGS Scenes with Image-Conditioned Objectives and Adjustable Conservatism

R. Khorrambakht; Joaquim Ortiz-Haro; Stephan Weiss; Ludovic Righetti

cs.ROSep 28, 2026

CollisionSplatting: Collision-Aware Motion Planning in 3DGS Scenes with Image-Conditioned Objectives and Adjustable Conservatism

Authors: R. Khorrambakht, Joaquim Ortiz-Haro, Stephan Weiss, Ludovic Righetti

Organizations: Machines in Motion Lab, Tandon School of Engineering, New York University · Department of Smart Systems Technologies, University of Klagenfurt, Austria. · Artificial and Natural Intelligence Toulouse Institute (ANITI)

Abstract

Incorporating dense visual information into motion planning remains challenging, as geometric planners rely on abstracted scene representations that discard visual richness, while learned visual models often lack geometric interpretability and computational efficiency. This paper introduces CollisionSplatting, a simple, modular, GPU-accelerated, probability-inspired distance metric with tunable conservatism that operates directly on standard 3D Gaussian Splatting (3DGS) scenes. When combined with learned image-conditioned reward functions, this metric enables joint geometric and visual planning by unifying collision-aware costs with image-space objectives. We integrate the metric into GPU-accelerated Model Predictive Path Integral (MPPI) and Rapidly-Exploring Random Tree (RRT) planners, and show on-par or better collision-classification performance compared to representative baselines while achieving substantially higher collision-checking throughput and significantly lower VRAM usage. Finally, we demonstrate the effectiveness of our metric in real-world vision-guided navigation and manipulation tasks, highlighting 3DGS as a practical bridge between rich perception and real-time motion planning.

Figures & tables

Fig. 1: Precision-recall curves for CollisionSplatting distance metric and representative baselines.

Method	Throughput (GPU) ( $\delimiter 52568952$ )	Throughput (CPU) ( $\delimiter 52568952$ )	Acceleration ( $\delimiter 52568952$ )	VRAM Utilization ( $\delimiter 52573049$ )	Batch Size
Method	Checks/s (mean $\mathchar 8710$ STD)	Checks/s (mean $\mathchar 8710$ STD)	$\mathbf{\delimiter 67273472\mathchar 29038_{\text{GPU}}\delimiter 68408078\mathchar 29038_{\text{CPU}}\delimiter 84054785}$	(GB)	Batch Size
SplatNav [ 3 ]	$\mathchar 28721\mathchar 28726\mathchar 28722\mathchar 314\mathchar 28721\mathchar 8710\mathchar 28721\mathchar 314\mathchar 28726$	$\mathchar 28722\mathchar 28723\mathchar 314\mathchar 28727\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28725$	$\mathchar 28726\mathchar 314\mathchar 28728\mathchar 28724\mathchar 8706$	$\mathchar 28720\mathchar 314\mathchar 28722\mathchar 28722$	1
SAFER-SPLAT [ 4 ]	$\mathchar 28722\mathchar 28721\mathchar 28727\mathchar 314\mathchar 28725\mathchar 8710\mathchar 28723\mathchar 314\mathchar 28724$	$\mathchar 28723\mathchar 28724\mathchar 314\mathchar 28724\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28725$	$\mathchar 28726\mathchar 314\mathchar 28723\mathchar 28723\mathchar 8706$	$\mathchar 28720\mathchar 314\mathchar 28723\mathchar 28728$	1
ATLASNav † [ 5 ]	$\mathchar 28721\mathchar 28726\mathchar 24891\mathchar 28723\mathchar 28721\mathchar 28728\mathchar 314\mathchar 28727\mathchar 8710\mathchar 28723\mathchar 28728\mathchar 28721\mathchar 314\mathchar 28720$	$\mathchar 28722\mathchar 28726\mathchar 28722\mathchar 314\mathchar 28722\mathchar 8710\mathchar 28721\mathchar 28727\mathchar 314\mathchar 28723$	$\mathchar 28726\mathchar 28722\mathchar 314\mathchar 28722\mathchar 28723\mathchar 8706$	$\mathchar 28725\mathchar 28725\mathchar 314\mathchar 28720$	$\mathchar 28724\mathchar 24891\mathchar 28720\mathchar 28729\mathchar 28726$
SPLANNING [ 6 ]	$\mathchar 28721\mathchar 28725\mathchar 28727\mathchar 24891\mathchar 28725\mathchar 28723\mathchar 28728\mathchar 314\mathchar 28725\mathchar 8710\mathchar 28726\mathchar 28720\mathchar 28723\mathchar 314\mathchar 28726$	$\mathchar 28722\mathchar 24891\mathchar 28724\mathchar 28720\mathchar 28729\mathchar 314\mathchar 28724\mathchar 8710\mathchar 28721\mathchar 28728\mathchar 314\mathchar 28723$	$\mathchar 28726\mathchar 28725\mathchar 314\mathchar 28723\mathchar 28728\mathchar 8706$	$\mathchar 28721\mathchar 28724\mathchar 314\mathchar 28725\mathchar 28720$	$\mathchar 28724\mathchar 24891\mathchar 28720\mathchar 28729\mathchar 28726$
CollisionSplatting (Ours)	$\mathchar 28722\mathchar 28721\mathchar 28725\mathchar 24891\mathchar 28725\mathchar 28727\mathchar 28728\mathchar 314\mathchar 28729\mathchar 8710\mathchar 28727\mathchar 24891\mathchar 28726\mathchar 28726\mathchar 28720\mathchar 314\mathchar 28722$	$\mathchar 28721\mathchar 28723\mathchar 24891\mathchar 28726\mathchar 28725\mathchar 28723\mathchar 314\mathchar 28723\mathchar 8710\mathchar 28724\mathchar 28724\mathchar 28720\mathchar 314\mathchar 28724$	$\mathchar 28721\mathchar 28725\mathchar 314\mathchar 28727\mathchar 8706$	0.16	$\mathchar 28724\mathchar 24891\mathchar 28720\mathchar 28729\mathchar 28726$

TABLE I: Collision Detection Throughput and VRAM Utilization Comparison

Panel of Figure 3 — Fig. 2: Effect of the conservatism factor $\mathchar 29038_{\mathchar 28955}$ on the paths discovered by the RRT planner. Increasing $\mathchar 29038_{\mathchar 28955}$ yields more conservative trajectories that avoid tight passages.

$\mathchar 29038_{\mathchar 28955}$ (conservatism)	Path Length ( $\delimiter 52573049$ ) (RRT)	Path Length ( $\delimiter 52573049$ ) (RRT+Refinement)	$\mathchar 29028_{\mathchar 29037\mathchar 29033\mathchar 29038}$ ( $\delimiter 52568952$ ) (RRT)	$\mathchar 29028_{\mathchar 29037\mathchar 29033\mathchar 29038}$ ( $\delimiter 52568952$ ) (RRT+Refinement)	Smoothness ( $\delimiter 52573049$ ) (RRT)	Smoothness ( $\delimiter 52573049$ ) (RRT+Refinement)
0.00	$\mathchar 28720\mathchar 314\mathchar 28726\mathchar 28720\mathchar 28721\mathchar 28727\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28728\mathchar 28724\mathchar 28721$	$\mathchar 28720\mathchar 314\mathchar 28725\mathchar 28727\mathchar 28724\mathchar 28728\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28727\mathchar 28727\mathchar 28728$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28722\mathchar 28723\mathchar 28726\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28721\mathchar 28724$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28723\mathchar 28720\mathchar 28720\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28723\mathchar 28725$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28722\mathchar 28724\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28725\mathchar 28721$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28723\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28723$
0.25	$\mathchar 28720\mathchar 314\mathchar 28725\mathchar 28728\mathchar 28721\mathchar 28728\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28727\mathchar 28722\mathchar 28723$	$\mathchar 28720\mathchar 314\mathchar 28725\mathchar 28724\mathchar 28727\mathchar 28727\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28725\mathchar 28729\mathchar 28729$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28722\mathchar 28725\mathchar 28722\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28722\mathchar 28721$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28723\mathchar 28724\mathchar 28725\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28721\mathchar 28728$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28723\mathchar 28723\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28724\mathchar 28729$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28723\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28722$
0.50	$\mathchar 28720\mathchar 314\mathchar 28725\mathchar 28726\mathchar 28728\mathchar 28725\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28725\mathchar 28728\mathchar 28720$	$\mathchar 28720\mathchar 314\mathchar 28725\mathchar 28724\mathchar 28724\mathchar 28721\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28724\mathchar 28726\mathchar 28725$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28722\mathchar 28722\mathchar 28725\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28728\mathchar 28726$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28723\mathchar 28721\mathchar 28721\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28721\mathchar 28725$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28723\mathchar 28726\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28725\mathchar 28728$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28724\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28723$
0.75	$\mathchar 28720\mathchar 314\mathchar 28726\mathchar 28723\mathchar 28729\mathchar 28720\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28721\mathchar 28727\mathchar 28727\mathchar 28723$	$\mathchar 28720\mathchar 314\mathchar 28725\mathchar 28728\mathchar 28727\mathchar 28725\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28721\mathchar 28722\mathchar 28729\mathchar 28728$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28722\mathchar 28726\mathchar 28727\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28721\mathchar 28722$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28723\mathchar 28724\mathchar 28725\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28723\mathchar 28723$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28723\mathchar 28724\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28724\mathchar 28727$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28723\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28723$
1.00	$\mathchar 28720\mathchar 314\mathchar 28726\mathchar 28720\mathchar 28724\mathchar 28728\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28728\mathchar 28720\mathchar 28726$	$\mathchar 28720\mathchar 314\mathchar 28725\mathchar 28725\mathchar 28729\mathchar 28720\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28726\mathchar 28723\mathchar 28726$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28723\mathchar 28720\mathchar 28721\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28722\mathchar 28722$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28723\mathchar 28726\mathchar 28720\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28724\mathchar 28721$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28725\mathchar 28721\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28725\mathchar 28728$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28723\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28723$
1.25	$\mathchar 28720\mathchar 314\mathchar 28726\mathchar 28726\mathchar 28724\mathchar 28723\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28721\mathchar 28726\mathchar 28722\mathchar 28726$	$\mathchar 28720\mathchar 314\mathchar 28726\mathchar 28720\mathchar 28728\mathchar 28724\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28721\mathchar 28721\mathchar 28726\mathchar 28720$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28722\mathchar 28728\mathchar 28726\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28721\mathchar 28722$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28723\mathchar 28723\mathchar 28724\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28726\mathchar 28725$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28725\mathchar 28728\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28727\mathchar 28724$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28723\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28720\mathchar 28723$

TABLE II: Global RRT planning and local MPPI refinement vs various conservatism factors.

Scene	Path Length ( $\delimiter 52573049$ )	Closest Distance ( $\delimiter 52568952$ )
$\mathchar 29005_{\mathchar 28721}$ (Smallest Gaussians)	$\mathchar 28720\mathchar 314\mathchar 28726\mathchar 28720\mathchar 28724\mathchar 28728\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28728\mathchar 28720\mathchar 28726$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28723\mathchar 28720\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28722$
$\mathchar 29005_{\mathchar 28722}$	$\mathchar 28720\mathchar 314\mathchar 28726\mathchar 28727\mathchar 28724\mathchar 28727\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28721\mathchar 28727\mathchar 28722\mathchar 28721$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28723\mathchar 28721\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28724$
$\mathchar 29005_{\mathchar 28723}$ (Largest Gaussians)	$\mathchar 28720\mathchar 314\mathchar 28727\mathchar 28725\mathchar 28723\mathchar 28721\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28722\mathchar 28728\mathchar 28721\mathchar 28722$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28723\mathchar 28725\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28723$

TABLE III: Planning conservatism vs scenes with increasingly larger Gaussian primitives.

Fig. 3: Computed collision distance along a linear path crossing reconstructed scenes with different Gaussian scales. As the distribution of large Gaussians increases, the metric yields smaller (more conservative) distance values, especially at sections of the path that traverse across obstacles.

Panel of Figure 7 — Fig. 4: CollisionSplatting deployed to real-world locomotion and manipulation for collision-aware visual reaching and object navigation tasks.

† A negative distance indicates physical collision with the environment.
Configuration	Distance to	Translation Error	Rotation Error
	Closest Splat (m $\delimiter 52568952$ )	(m $\delimiter 52573049$ )	(degrees $\delimiter 52573049$ )
Without Collision Cost	$\mathchar 8704\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28722\mathchar 28721\mathchar 28722\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28722\mathchar 28729^{\mathchar 8825}$	$\mathbf{\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28724\mathchar 28727\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28725\mathchar 28727}$	$\mathbf{\mathchar 28723\mathchar 314\mathchar 28724\mathchar 28728\mathchar 28720\mathchar 28726\mathchar 8710\mathchar 28721\mathchar 314\mathchar 28720\mathchar 28726\mathchar 28722\mathchar 28727}$
With Collision Cost	$\mathbf{\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28727\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28720\mathchar 28728}$	$\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28723\mathchar 28721\mathchar 8710\mathchar 28720\mathchar 314\mathchar 28720\mathchar 28721\mathchar 28724$	$\mathchar 28725\mathchar 314\mathchar 28726\mathchar 28729\mathchar 28723\mathchar 8710\mathchar 28721\mathchar 314\mathchar 28725\mathchar 28720\mathchar 28723$

TABLE IV: Visual target reaching performance with or without collision cost.

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Jun 15, 2026, cs.ROJ/K move · Enter open · S save

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

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1Georgia Institute of Technology.

Polytopes 3D Generation Object Detection

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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/.

Abstract

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