A robot-based study has tested a way to describe vegetation by how it bends and pushes back, rather than by whether a particular machine can get through it. In experiments with a woody twig and an artificial grass bush, the researchers found that a detailed profile of bending stiffness stayed consistent across the contact heights they tested, while a simpler single-number stiffness measure changed with the geometry of the interaction.
The distinction matters for field robots, which may encounter flexible obstacles from different positions. The study presents the detailed profile as a potentially reusable mechanical description, while treating the simpler measure as a practical option for fixed-height, small-deflection interactions. Those proposed uses remain to be tested across other robots, sensors and vegetation.
Two ways to describe a bending stem
The framework produces two model outputs. The first is a distributed flexural-rigidity profile, written as EI(s), that describes how resistance to bending varies along a stem. It uses the stem’s observed shape together with the force applied during contact. The second is a lumped rotational stiffness, kθ, which compresses the interaction into a single measure derived from contact force alone.
A stationary Zed2i RGB-D camera supplied observations, while SAM2 segmentation, morphological skeletonization and Dijkstra shortest-path extraction supplied the stem centerline for the shape-based estimate. The direct estimator then recovered the profile from bending moment and local curvature without assuming a preset functional form.
The mechanical model makes strong assumptions. It treats the stem as a planar Kirchhoff rod under quasi-static loading: the stem does not stretch, behaves as a linearly elastic material, has one contact point, and is clamped at its base with a free tip. The direct estimate also becomes ill-conditioned where curvature approaches zero, so the authors fitted a taper formula after identifying that problem.
A narrow physical test
The evaluation involved two specimens: an artificial grass bush measuring 0.47 metres and a woody twig measuring 0.80 metres. A wire force sensor mounted on a UR10 robot arm pushed each specimen from first contact through full traversal at a constant height and at several contact heights. For the grass, the initial contact heights were 9, 11 and 14 centimetres; for the twig, they were 45, 55 and 65 centimetres.
This was a methods demonstration, not a broad survey of vegetation. Only the two specimens were tested, and the supplied analysis does not report replicate counts for each condition. The grass specimen was artificial rather than a living rooted plant, and the experiments did not include a separate control group.
The fitted profiles differed sharply
The fitted taper parameters separated the two specimens. For the twig, the taper exponent p was 0.43 and the base flexural rigidity EI0 was 2.63 newton-metres squared, with a taper-fit R² of 0.87. For the grass, p was 1.60, EI0 was 0.112 newton-metres squared, and the fit R² was 0.96. The fit statistics describe how closely the chosen taper form matched the estimated profiles; no confidence intervals were reported.
When the fitted taper was used for forward simulation, the median shape error was 14.3 millimetres for the twig and 3.9 millimetres for the grass. The median force error was 0.47 newtons for the twig and 0.85 newtons for the grass. The reported reference lengths and peak forces were 0.80 metres and 5.3 newtons for the twig, and 0.47 metres and 4.1 newtons for the grass.
The simpler lumped stiffness told a different story as contact height changed. Its fitted value fell from 0.31 to 0.14 newton-metres per radian for the grass, and from 1.60 to 0.98 newton-metres per radian for the twig. In other words, the single-number description depended on the interaction geometry, even though the pooled EI(s) profile remained consistent across the tested heights.
Where the simpler model stops working
The lumped model also failed to follow the full force response once the interaction moved beyond the initial linear region. Measured force reached a plateau, but the constant-kθ torque balance continued to rise with bending angle. The authors therefore limit this simplified model to fixed-height, limited-deflection interactions and note that it cannot represent yielding or complete plant behaviour.
The results do not show improved robot navigation, crop protection or environmental monitoring, and they do not establish performance across broad vegetation classes or living rooted plants. Experimental transfer to other robot platforms and sensing systems was not reported. The model’s planar, quasi-static and small-deflection assumptions also leave open how the framework will perform when those conditions change.
The authors identify broader vegetation validation as a next step, along with a dataset linking visual observations to mechanically identified properties. The paper presents that dataset as future work rather than as an outcome of the current evaluation.
The manuscript is a version-one preprint on arXiv, dated 26 August 2026. The work reports funding from the French National Research Agency Junior Research Chair program and the International Research Center “Innovation Transportation and Production Systems” of the I-SITE CAP 20-25.
Paper data and sources
Original title: When Obstacles Bend: Modeling Vegetation Deformation in the context of Field Robotics
Authors: Muhammad Hsaeeb Zaar Khizar, Tom Montagnon, Roland Lenain et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
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