A mechanical profile that describes how stiffness is distributed along a stem stayed stable as a robot pushed an artificial grass bush and a woody twig at different heights, while a simpler single-number stiffness changed, according to an arXiv preprint. The authors present the distributed profile as more reusable when a robot's contact point moves, but the evidence covers only those two specimens.
A stiffness map, not just a single number
The paper proposes characterizing vegetation through intrinsic mechanical properties measured as a robot interacts with it. Its main output is distributed flexural rigidity, a measure of how much resistance to bending is present along different parts of a stem. It also calculates lumped rotational stiffness, a single value that summarizes the turning resistance seen at a contact point. The two are presented as complementary ways to describe the same interaction.
How the robot measured bending
To estimate the distributed profile, the researchers represented a stem as a planar flexible rod and combined contact-force readings with the stem's observed shape during ordinary robot traversal. In the model, bending moment is related to local flexural rigidity and curvature, the amount by which the stem turns away from a straight line. A wire force sensor on a UR10 arm pushed each specimen from first contact to full traversal at a fixed height, while an RGB-D camera recorded shape.
The grass bush was tested at contact heights of 9, 11 and 14 cm, while the twig was tested at 45, 55 and 65 cm. The researchers fit a taper law, a compact description of how stiffness changes along the specimen, using measurements pooled across the tested heights. They then checked it against force and centerline measurements excluded from fitting. Shape error was the root-mean-square distance between predicted and measured centerlines over up to 200 resampled points below the contact point.
The profile stayed steadier
At the fitted taper, the base flexural rigidity was 2.63 N m2 for the twig and 0.112 N m2 for the grass. In plain terms, the model assigned the twig a much higher base resistance to bending. The taper exponents, which describe how quickly that rigidity changed along each specimen, were 0.43 for the twig and 1.60 for the grass. The reported fit scores were 0.87 and 0.96, respectively. No confidence or uncertainty interval was reported for these fitted values.
Across the tested contact heights, the distributed profile remained stable. The lumped stiffness did not: it decreased from 0.31 to 0.14 N m/rad for the grass and from 1.60 to 0.98 N m/rad for the twig. On this basis, the authors report that the rod model can predict force or deflection at a new contact height without a new fit for every height, although that generalization was demonstrated only within the tested specimens and setup.
The held-out predictions were not exact. For the twig, the median centerline shape error was 14.3 mm and the median force error was 0.47 N. For the grass, the corresponding figures were 3.9 mm and 0.85 N. Peak measured forces were 5.3 N for the twig and 4.1 N for the grass. The comparison was mixed: the grass had the smaller shape error, while the twig had the smaller force error.
Where the shortcut breaks down
The single-number model also failed to follow the full response once the interaction moved beyond the initial linear region. Measured force reached a plateau as the vegetation bent below the interaction point, but the constant-stiffness torque model continued to rise with angle. It therefore did not represent the complete plant response once the small-deflection approximation no longer matched the motion.
That leaves the two models with different practical roles. The lumped version requires only robot pose and force measurements, so the authors present it as a simpler real-time option when contact geometry is fixed and deflections remain within the modeled elastic regime. The spatial profile uses shape information during fitting but offers greater transferability across contact heights, and the authors say it can be reused across robots and sensing configurations.
A narrow test of a broader idea
The study's evidence is narrow. It used one artificial grass bush and one woody twig in laboratory push-through trials, with usable contact heights constrained by the force sensor's range. The result is a comparison within that setup, not a demonstration across a broad range of vegetation or field conditions.
The test also combined force and shape measurements. Its vision branch segmented RGB-D images, traced a stem centerline and converted depth data into metric arc length before fitting a smooth curve. The experiment does not show that a robot can infer these mechanical properties from visual observations alone or replace force measurements in deployment.
Taken together, the preprint presents a way to carry a richer description of stem mechanics from one tested contact height to another, while retaining a simpler model for fixed, small-deflection interactions. It remains a two-specimen laboratory demonstration, not evidence that either model is ready for general field use.
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
Original paper · Full text