Low-Latency Mapless ESDF Queries for MAV Reactive Collision Avoidance

Leonard Freißmuth; Cedric Le Gentil; Helen Oleynikova; Stefan Leutenegger

cs.ROOct 9, 2026

Low-Latency Mapless ESDF Queries for MAV Reactive Collision Avoidance

Authors: Leonard Freißmuth, Cedric Le Gentil, Helen Oleynikova, Stefan Leutenegger

Organizations: Mobile Robotics Lab, ETH Zurich

Abstract

Reactive collision avoidance in unknown, cluttered environments must perceive obstacles and correct motion within milliseconds. Existing methods rely on maps for high-rate collision queries, but their acceleration structures require pre- processing. That cost is amortized in long-horizon planning, where a map serves millions of queries; reactive planning, however, is a near-field, short-horizon problem with potentially only hundreds of queries per measurement, where building a map may not pay off. We propose a mapless, Graphics Processing Unit (GPU)-accelerated Euclidean Signed Distance Field (ESDF) query with negligible pre-processing that operates directly on posed depth images, with resolution set by pooling the image rather than by a voxel size. On an embedded GPU it is simultaneously more accurate and lower in total latency than every voxel-grid configuration we measured between 2 cm and 20 cm, at one to two orders of magnitude less memory at matched resolution. With our query integrated into a Model Predictive Controller (MPC), simulated runs in laser-scanned forests at up to 9 m/s collide in 0.4 % through dense branches, against 5.9 % with the best voxel grid and 5.5 % with the best mapless baseline at our resolution, whose failures we attribute to voxel resolution and total latency respectively. We deploy the system onboard at two forest sites and fly at commanded speeds of up to 4 m/s.

Figures & tables

Fig. 1 : We represent the environment as a set of posed depth images $\mathcal{I}_{t}$ and compute distances and gradients for a query in every image in parallel before merging them. The dense field in the background is illustrative only, since we evaluate the field at query points alone, and all algorithms work in 3D although we draw in 2D.

Fig. 2 : The robot’s surroundings divide into known free space

\mathcal{F}

, the observed surface

\mathcal{O}

, and unknown space

\mathcal{U}

, and our representation lives in the image space of camera frame

\mathtt{C}_{t}

Panel of Figure 3 — Fig. 3 : Single-frame query and merging. (a) The truncation sphere of radius $r_{\text{max}}$ around $\mathbf{q}$ projects to a box of pixels, and only the blocks it covers are searched. (b) Of these, a block is active when its stored depth range intersects $[\,q_{z}-r_{\text{max}},\,q_{z}+r_{\text{max}}\,]$ , and all other blocks are skipped. (c) Occlusion boundaries as ray segments from a pixel’s depth to that of its neighbor nearest to $\mathbf{q}$ , searched within $d^{\,\text{opti}}(\mathbf{q})$ for $d^{\,\text{cons}}(\mathbf{q})$ . (d) Max-pooling of $\phi_{t}(\mathbf{q})$ across views in the three cases of Sec. III-D , with only $\mathcal{U}$ views at $\mathbf{q}^{1}$ , mixed views at $\mathbf{q}^{2}$ , and only $\mathcal{F}$ views at $\mathbf{q}^{3}$ .

Fig. 4 : Benchmarks on the Orin NX with

N=1

frame in (a) and

N=5

in (b) and (c). (a) Median absolute distance error against a full-resolution reference, over voxel size for the grids and as dashed lines for our pooling levels

p

, whose coarse settings match the finest grid. (b) Total latency of

400

queries from the start of the last integration to the last answer, where every pooling level of ours lies below the fastest grid. (c) Total latency over the number of queries at each method’s finest setting (solid) and at

10\text{\,}\mathrm{cm}

or the matching pooling level (dashed). (d) Map memory over the integrated frames. ∗ FIESTA runs at

5\text{\,}\mathrm{cm}

at its finest setting, all other voxel grids at

2\text{\,}\mathrm{cm}

Panel of Figure 5 — Fig. 5 : (a) Collision rate over commanded speed (lockstep- onboard ) at each method’s finest flyable setting (solid, NVBlox at $5\text{\,}\mathrm{cm}$ ) and at about $10\text{\,}\mathrm{cm}$ (dashed), blue for conservative and red for optimistic methods, ours at most $2\text{\,}\mathrm{\%}$ . (b) Branches and (c) trunks of a laser-scanned forest.

Fig. 8 : Our

p=1

query blocked for

\ell

after each measurement (lockstep- delayed ). Stops rise from

50\text{\,}\mathrm{ms}

on.

Panel of Figure 8 — Fig. 9 : (a) Collision rate on noisy D455 depth over odometry noise of $k$ $\mathrm{cm}$ and $0.1k$ $\mathrm{\SIUnitSymbolDegree}$ RMS, with and without the margin. The band spans the speeds. (b) The queried ESDF around 3D-printed letters, without (top) and with margin (bottom).

Panel of Figure 9 — Fig. 10 : (a) Five trajectories per site, colored by speed, with the reference in blue and the onboard point cloud in gray. Line and point width encode height above ground. The MAV at several instants of a run through (b) the branches and (c) the trunks, with an approximate reference in blue.

Fig. 11 : Onboard latency from measurement to released plan over the $1240$ planning loops of the ten flights, with $N=5$ and $p=4$ . Boxes span the quartiles, whiskers the 5th to 95th percentile, and stacked bars the median per stage.

Collision Avoidance

Collision avoidance develops methods for predicting and preventing unsafe encounters among autonomous agents, vehicles, robots, and obstacles.

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GPU-Accelerated Polygonal Signed Distance Functions for Real-Time Collision Avoidance

Taekwon Ga, Jongeun Choi

School of Mechanical Engineering, Yonsei University, Seoul 03722, South Korea

Signed Distance Functions GPU Acceleration Model Predictive Control Robot Collision Avoidance

Open paper AskPDF arXiv

Optimization-based local planning and control require high-rate evaluation of collision-avoidance constraints over a prediction horizon. Accurately accounting for robot and obstacle geometry in these evaluations can be computationally expensive. The resulting bottleneck motivates collision-avoidance constraints that combine computational efficiency with geometric fidelity. The proposed polygonal signed distance function (PSDF) returns the minimum of exact signed distances between a convex polygonal robot footprint and convex obstacle components represented by their boundary edges. It is implemented as a training-free, branch-free tensorized geometric pipeline enabling batched GPU execution and automatic differentiation. The PSDF is embedded in model predictive control by locally linearizing the PSDF-based safety constraint within a sequential quadratic programming--based real-time iteration scheme, yielding the PSDF-embedded model predictive controller (PSDF-MPC). The design separates CPU/GPU computation so that the GPU evaluates batched PSDF values and gradients while the CPU solves a sparse quadratic program whose size and sparsity are determined by system dimensions and horizon length rather than obstacle and edge counts. Microbenchmarks show that PSDF scales favorably relative to geometric and learned collision-field baselines. Closed-loop comparisons in simulation, together with real-world navigation experiments, demonstrate that PSDF-MPC operates in real time and achieves collision-free navigation in dense polygonal environments.

Abstract

Collision Avoidance

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