From Observed Response to Material laws
*Corresponding author: stepa@berkeley.edu
Video
Narrated through on-screen captions; the video has no audio track.
Different materials respond differently to the same action. We observe how the material moves during one interaction. Our method, FORM, identifies a material law. We use the identified law to plan new actions for new geometries.
First, we record the material as it deforms. With RGB-D, we reconstruct the shape assuming symmetry around the pressing axis. We keep the volume fixed, so the material spreads sideways as it flattens. We infer the flow inside from the surface motion, assuming no slip at contacts. Then we follow particles through this flow to recover their 3D paths. With stereo, we track the same texture in two views to recover surface motion. From the surface motion, we estimate how the interior moves. The motion and measured contact forces then go into material identification.
Which material law explains the motion we just observed? We weight Newton’s law and integrate over space and time. Our test fields cancel the pressure term, leaving only deviatoric stress. We express stress using known responses and unknown coefficients. Linear least squares gives us the coefficients of the material law. Keeping the law fixed, we plan new robot actions in simulation. Finally, we execute that plan on the real material.
From bending and force, we identify each material’s stiffness. Our task is rod insertion: a new action and geometry. Matched ID uses the rod’s identified law; swapped ID uses the other material’s law.
We reuse the material laws identified from bending. We plan forward-stroke duration and aim angle to stop the ball on target. Matched plans succeed; swapped plans miss.
From pressing, we identify stiffness and yield stress for each material. Keeping those laws fixed, we plan six pinches to shape a larger block into an X. Both matched plans give lower surface error.
For each material, one press identifies stiffness and yield stress. We use those laws to predict a separate, lower-force press. Next, we plan four pinches to shape fresh specimens into an X. Here, the robot executes the plan on a fresh Play-Doh specimen. The identified laws stay fixed throughout planning and execution. After rigid alignment, footprint overlap is 72 to 78 percent.
We identify an effective viscosity from a single glycerol pour. We keep it fixed and plan the cup’s tilt for each of six target volumes. Across all six targets, the largest mean error is 3.8 milliliters. Water overpours when we use the same commands planned for glycerol.
FORM identifies a material law from one robot interaction. We identify material laws without backpropagation. We use the law in MPM to predict motion and plan actions. We reuse the identified material law for new actions and geometries.
Every unfamiliar deformable material presents a robot with unknown physical properties and an unknown response to force and motion, making rapid online identification essential for reliable manipulation. We present FORM (From Observed Response to Material laws), which identifies material behavior from a single robot interaction and reuses the recovered model to plan manipulation under new actions and geometries. We convert observed material motion and contact forces into linear equations via weak-form momentum balance with material parameters as unknowns, and assemble them in the same MPM discretization used for forward prediction, reducing identification to a single least-squares solve whose solution is used directly by the simulator without refitting or conversion. Across four material classes, this reduces identification time from roughly 10–25 minutes for iterative baselines to 2–5 seconds, while retaining competitive accuracy on new motions, initial conditions, and geometries. We demonstrate the approach on elastic rod insertion, golf putting with an elastic club, elastoplastic shaping, and target-volume pouring, where models identified from one interaction are reused to plan different motions or manipulate different geometries. The method estimates elastic properties within 3.4% and elastoplastic properties within 2%, achieves 72.4–77.8% IoU in hardware shaping, and limits the largest mean pouring error to 3.8 mL over 60–160 mL targets.
Method
FORM holds the observed motion fixed and asks which material law explains it. Weighted momentum balance turns that question into a linear system in the material coefficients, assembled in the same MPM discretization the robot later uses to predict new actions.
Weighting momentum balance with a smooth test field ψj and integrating by parts moves derivatives from stress onto the weight. Divergence-free fields, ∇·ψj = 0, remove the unknown pressure for every pressure field and leave the deviatoric stress to identify.
![Integral of tau(theta) double-dot D[psi_j], minus the integral of p times the divergence of psi_j, which is zero when psi_j is divergence-free, equals the integral of rho (g minus a) dot psi_j.](assets/math/weak.svg)
Accelerations estimated from tracked motion are imprecise at high deformation rates. Space–time weights that vanish at both ends of each window let integration by parts replace acceleration with the known rate of change of the weight along each track.
Stress is a combination of candidate responses, either analytic laws or pretrained function-encoder bases. Each may depend nonlinearly on deformation, but only linearly on the coefficients θ, so every test field adds one linear equation and one least-squares solve returns θ.
With the MPM quadratic B-splines as test fields, each weighted balance is the simulator’s internal-force assembly under particle quadrature. The identified coefficients go straight into MPM, without refitting or conversion.
![psi_(i,d)(x) = N_i(x) e_d; the integral of sigma double-dot D[psi_(i,d)] is approximately the sum over particles of V_p e_d-transpose sigma_p grad N_i(x_p), which equals minus e_d-transpose times the MPM internal force at node i.](assets/math/basis.svg)
With θ̂ held fixed, MPM predicts the outcome of candidate motions, and the planner searches a small set of motion parameters for the lowest task cost. Plans run open loop: measurements during execution never update the model.
Results
Every task identifies the law from a single probe and keeps it fixed. Matched ID plans with the material’s own law; swapped ID plans with the other material’s law.
A bending probe identifies Young’s modulus from tracked surface texture and pusher force: 80.61 kPa for material A (true 80 kPa) and 248.11 kPa for B (true 240 kPa). The same laws then plan two tasks with new actions and geometry.
Materials A and B share their stiffness, but B’s yield threshold is ten times higher. A flat-plate press on a 30 × 30 × 25 mm specimen identifies both parameters, and six planned pinches then shape a larger block into an X.
| Material | E (kPa) | Y (kPa) |
|---|---|---|
| A | 80.795 / 80 | 1.015 / 1 |
| B | 81.396 / 80 | 10.184 / 10 |
Identified / true values; every error is below 2%. Hencky elasticity with von Mises plasticity.
| Plan | A | B |
|---|---|---|
| Matched ID | 0.883 mm | 1.256 mm |
| Swapped ID | 1.226 mm | 1.739 mm |
Mean closest-point distance to the target surface, 1 s after the fingers withdraw.
One press of a 45 mm sphere, reconstructed from two RealSense D435 cameras under constant volume, identifies stiffness and yield stress for red Play-Doh, yellow butter slime, and gray plasticine. With those laws fixed, MPM predicts a separate press, and the planner chooses four pinches that shape fresh 60 × 60 × 25 mm blocks into an X, executed open loop.
Play-Doh75.7%
Butter slime72.4%
Plasticine77.8%A single 60° exploratory pour of glycerol gives an effective Newtonian viscosity of 3.44 Pa·s from a reduced weak-form balance at the spout, using the receiver volume tracked on video and the cup motion from the robot’s joint trajectory. With that viscosity and an effective wall-contact coefficient (calibrated in MPM from the same pour) held fixed, MPM selects the final tilt angle for six targets from 60 to 160 mL. The commands are frozen before five hardware repeats per target.
Benchmark
Identification accuracy and solve time on the NCLaw dataset and setup: four materials, one trajectory each. Mean loss is averaged over three generalization tests: extended time, unseen initial conditions, and a new geometry.
| Method | Jell-O | Sand | Plasticine | Water | ||||
|---|---|---|---|---|---|---|---|---|
| Mean loss | Time (s) | Mean loss | Time (s) | Mean loss | Time (s) | Mean loss | Time (s) | |
| NCLawNeural constitutive law | 5.2×10−4 | 1513.2 | 1.6×10−4 | 1305.6 | 1.2×10−4 | 1300.2 | 5.7×10−4 | 1306.8 |
| Diff. Sys-IdOracle: exact law given | 1.2×10−8 | 715.8 | 6.3×10−13 | 1132.8 | 1.6×10−10 | 1028.4 | 4.0×10−9 | 556.2 |
| FORM (Fn Enc.)Pretrained bases by material type | 3.5×10−4 | 5.2 | 3.3×10−8 | 0.1 | 2.9×10−6 | 5.3 | 2.3×10−6 | 4.8 |
| FORM (Full)Full information | 5.1×10−6 | 4.4 | 1.4×10−8 | 2.4 | 5.2×10−7 | 4.7 | 2.3×10−6 | 2.2 |
| FORM (No stress)Observations without stress | 5.1×10−6 | 3.5 | 2.0×10−8 | 6.0 | 5.2×10−7 | 6.5 | 2.3×10−6 | 1.6 |
| FORM (Pos. only)Positions only | 1.3×10−5 | 3.5 | 1.0×10−5 | 12.8 | 4.6×10−6 | 21.8 | 1.0×10−2 | 4.6 |
Code
The repository contains the weak-form identification, a GPU MPM solver in NVIDIA Warp with the added constitutive models, the pipelines for rod insertion, golf putting, shaping, and pouring, a reproduction runner that recomputes the paper’s material estimates and checks saved results, and the renderer for the video and slides.
Recordings and saved simulation data will be released separately.
The MPM solver builds on warp-mpm by Zong et al.; see AUTHORS.md for attribution.
git clone https://github.com/form-robots/FORM.git
cd FORM
uv venv --python 3.12
uv pip install --python .venv/bin/python -r requirements-lock.txt
uv pip install --python .venv/bin/python --no-deps -e '.[paper,dev]'
source .venv/bin/activateCitation
@misc{tretiakov2026form,
title = {{FORM}: Robot Manipulation through Direct Material Law Identification},
author = {Tretiakov, Stepan and Zhao, Ruihan and Hsiao, Cheng-Hsi and Li, Xingjian and
Thorpe, Adam and Iqbal, Hassan and Chinchali, Sandeep and Topcu, Ufuk and Kumar, Krishna},
year = {2026},
url = {https://form-robots.github.io/}
}