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FORM: Robot Manipulation through Direct Material Law Identification

Stepan Tretiakov, Ruihan Zhao, Cheng-Hsi Hsiao, Xingjian Li, Adam Thorpe, Hassan Iqbal, Sandeep Chinchali, Ufuk Topcu, Krishna Kumar

arXiv:2609.38105v1cs.RO

TL;DR

Robots need material models to predict how unfamiliar deformable materials will respond to new actions. FORM identifies material properties from one interaction using weak-form momentum balance and reuses the model for planning. It reports accurate estimates and manipulation outcomes across elastic, elastoplastic, and fluid tasks.

  • Problem

    Unfamiliar deformable materials respond differently to the same forces and motions, so a robot needs a model that predicts responses to actions not yet executed.

    Source: §I · p. 1

  • Method

    FORM uses observed motion and, when needed, contact forces in weak-form momentum balance to solve linearly for material coefficients in the simulator’s MPM discretization.

    Source: §I · pp. 1–2

  • Results

    Elastic properties are recovered within 3.4%, elastoplastic properties within 2%, hardware shaping reaches 72.4–77.8% IoU, and pouring reaches at most 3.8 mL mean error.

    Source: §I · p. 2

  • Takeaways & Limitations

    Models identified from one interaction are reused without refitting to plan under new actions and geometries across elastic, elastoplastic, and fluid materials.

    Source: §I · p. 2, §VI · p. 7

Abstract

from arXiv · show

When interacting with an unfamiliar deformable material, a robot lacks prior knowledge of its physical properties and how it will respond to applied forces and motion. Rapid online identification is therefore essential for reliable manipulation. We present FORM (From Observed Response to Material laws), which identifies material properties from a single robot interaction and reuses the recovered model to plan manipulation under new actions and geometries. We use weak-form momentum balance to convert observed material motion and contact forces into linear equations in the unknown material parameters. These equations are assembled using the same material point method discretization as the forward simulator, so identification reduces to linear least-squares solves whose solutions can be used directly for prediction without refitting or conversion. Across four material classes, FORM reduces identification time from roughly 10--25 minutes for iterative baselines to 2--5 seconds, while maintaining competitive accuracy on new motions, initial conditions, and geometries. We demonstrate our approach in simulation and on hardware across four manipulation tasks: elastic rod insertion, golf putting with an elastic club, elastoplastic shaping, and target-volume pouring. In each task, the model identified from a single interaction is reused to plan new motions or manipulate a different geometry. FORM estimates elastic properties within 3.4% and elastoplastic properties within 2%, achieves 72.4--77.8% IoU in dough shaping, and keeps mean pouring error at 3.8 mL across target volumes of 60--160 mL.

I. INTRODUCTION

FORM identifies material properties from a robot interaction and reuses the recovered model to predict and plan under new actions and geometries. The paper reports accurate property estimates and manipulation results across several material types and tasks.

I. INTRODUCTION

  • A constitutive law relates deformation and deformation rate to internal stress, providing a model for predicting responses to actions not yet executed.The need arises because unfamiliar materials can respond differently to the same force or motion.Source: §I · p. 1
  • Prior approaches either leave constitutive behavior implicit, require repeated simulation and differentiation, or target prepared specimens rather than partial, time-varying robot observations.Weak-form identification enforces momentum balance on measured motion and loads without repeated rollout matching.Source: §I · p. 1
  • FORM tracks material motion and, when needed, contact force, then uses momentum balance to form a linear system for material coefficients.The system uses the same MPM discretization as forward prediction, so recovered coefficients can be used directly for planning without refitting or conversion.Source: §I · pp. 1–2
  • Elastic properties are recovered within 3.4%, elastoplastic properties within 2%, hardware shaping reaches 72.4–77.8% IoU, and pouring reaches at most 3.8 mL mean error.The identified models are held fixed during deployment, without refitting from execution measurements.Source: §I · p. 2

II. RELATED WORK

Prior work offers learned, differentiable, and weak-form approaches to material modeling, but each has limitations for robot interaction data. FORM reconstructs motion and uses weak momentum balance to identify material laws from that motion.

II. RELATED WORK

  • Prior approaches learn implicit dynamics or optimize explicit parameters, while weak-form methods avoid repeated simulation but often require full-field measurements and quasi-static solid settings.The cited approaches also note that simulation-based optimization can be computationally expensive and unstable over long horizons.Source: §II · p. 2

III. IDENTIFYING THE MATERIAL FROM MOTION

  • FORM holds observed motion fixed, represents stress as a linear combination of candidate responses, and uses momentum balance to solve for coefficients without repeated trial simulations.The simulator then holds those coefficients fixed as it evaluates the law during prediction.Source: §III · p. 2
  • Visual observations provide surface motion, while geometric and kinematic assumptions extend reconstruction inside the material; spatial derivatives yield deformation and velocity gradients.Elastic laws use the deformation gradient, while viscous laws use the stretching and shearing rate.Source: §III · p. 2
  • Unobserved stress must produce the measured motion through momentum balance, which separates isotropic pressure stress from deviatoric stress.The isotropic part resists volume change, and the deviatoric part resists shape change.Source: §III · p. 3

A. Removing pressure to identify viscosity

For a Newtonian fluid, FORM identifies viscosity by weighting momentum balance with smooth fields chosen to cancel pressure. Each field supplies a linear equation for the same viscosity.

A. Removing pressure to identify viscosity

  • A smooth vector field that vanishes near the body boundary lets integration by parts move derivatives from stress onto the weight and remove the boundary term.The resulting weak formulation is used to identify viscosity.Source: A. Removing pressure to identify… · p. 3
  • Choosing a divergence-free test field makes the pressure contribution vanish, leaving a linear equation in viscosity for each weight function.The method avoids reconstructing the unobserved pressure field.Source: A. Removing pressure to identify… · p. 3
  • A weight function can be formed as the curl of a smooth vector potential supported inside the body, ensuring zero divergence even when the material compresses.The shared viscosity is identifiable if at least one resulting coefficient A_j is nonzero.Source: A. Removing pressure to identify… · p. 3

B. The same spatial basis for observations and MPM

FORM chooses spatial weight functions to match the forward MPM solver’s stress assembly, so the weak balance recovers the same internal-force assembly used in prediction.

B. The same spatial basis for observations and MPM

C. Representing a range of constitutive laws

FORM represents stress as a linear combination of candidate constitutive responses, allowing nonlinear dependence on material state while keeping identification linear in the coefficients. The method extends to learned bases, full-stress terms, and a reduced liquid model.

C. Representing a range of constitutive laws

  • The stress response is represented by basis functions T_k weighted by material coefficients θ_k; linearity is required only in the coefficients.Each basis may depend nonlinearly on deformation, and candidate functions can come from existing constitutive models.Source: C. Representing a range of… · p. 4
  • Learned function-encoder bases can replace unknown constitutive laws while retaining a single least-squares solve for online identification.The bases are trained offline on generated constitutive laws and can span plausible responses for a material type.Source: C. Representing a range of… · p. 4
  • Full-stress identification adds volumetric responses, while the known pressure contribution must be available independently of fitted coefficients.For sand, pressure is computed from observed volume change using the equation of state and supplied as fixed data.Source: C. Representing a range of… · p. 4
  • Separable test-function weights vanish at both window endpoints, allowing integration by parts to replace imprecise acceleration estimates.The derivative of the known weight along each particle track replaces acceleration in the balance.Source: C. Representing a range of… · p. 4
  • Each test function contributes an equation, and measured contact force supplies terms at boundaries with prescribed velocity before coefficients are fit by least squares.Equations are combined across samples and time windows; fixed-boundary test functions eliminate unknown reaction forces.Source: C. Representing a range of… · p. 4
  • For pouring, receiver-volume increments fit inverse viscosity through a time-integrated cup-lip balance without reconstructing interior motion.The liquid head is inferred from receiver volume, recorded cup motion, known geometry, and initial fill, assuming a horizontal free surface.Source: C. Representing a range of… · p. 4
  • Table II compares learned-basis, full-information, no-stress, and position-only variants; bold marks a lowest-loss non-oracle result and its solve time.Source: Table II · p. 5, C. Representing a range of… · p. 5

D. Numerical Validation and Comparison

Across four representative materials, FORM is evaluated against NCLaw and an oracle identification scheme using one inference trajectory per material. The reported comparison finds competitive approximation accuracy with a fraction of the baselines’ solve time.

D. Numerical Validation and Comparison

  • FORM generally achieves competitive approximation accuracy while requiring only a fraction of baseline solve time across the reported scenarios.The scenarios test extended time, unseen initial conditions, and different geometry; accuracies and solve times are averaged across them.Source: D. Numerical Validation and Comparison · p. 5
  • The evaluation uses Water, Sand, Jell-O, and Plasticine, comparing FORM with NCLaw and an oracle scheme across extended time, unseen initial conditions, and different geometry.One trajectory per material type is used for inference across all testing scenarios.Source: D. Numerical Validation and Comparison · p. 5
  • Pretrained function-encoder bases sacrifice negligible performance while retaining fast inference when only general material types are known.Source: D. Numerical Validation and Comparison · p. 5

IV. MATERIAL-CONDITIONED ROBOT MOTION OPTIMIZATION

The planner optimizes a low-dimensional set of robot-motion parameters using the identified material model. It evaluates candidate actions in simulation and executes the selected motion open loop without updating the model.

IV. MATERIAL-CONDITIONED ROBOT MOTION OPTIMIZATION

  • Candidate motions are optimized using the identified material parameters, with a low-dimensional action parameterization constrained to an admissible set.The parameters define robot motion and keep candidate evaluation efficient.Source: §IV · p. 5
  • For each candidate action, MPM predicts the material response from the initial state while holding the identified model fixed.Tool interactions are represented by meshes and corresponding boundary conditions.Source: §IV · p. 5
  • The cost J measures task error and constraint penalties, including surface distance in shaping and absolute volume error in pouring.G denotes the task goal.Source: §IV · p. 5
  • The search repeatedly simulates candidate actions, evaluates their costs, and returns the best motion evaluated when it stops or exhausts its budget.Source: §IV · p. 5
  • The selected motion is executed open loop; measurements collected during execution do not update the material model or replan the motion.Source: §IV · p. 5

V. RESULTS

The results section tests whether a material law identified from one probing interaction can guide planning and manipulation on simulation and a real robot. Correct identification is compared with an incorrect, swapped identification.

V. RESULTS

  • The experiments compare task execution using the correct material identification (matched ID) against an incorrect material identification (swapped ID).Source: §V · p. 5
  • The evaluation tests whether a material law identified from a single probing interaction can guide motion planning and manipulation involving deformable materials.Source: §V · p. 5
  • Tests are conducted in simulation and on a real Franka Panda robotic arm.Source: §V · p. 5

A. Elastic Material Manipulation

A bending probe identifies elastic properties for two materials, and the recovered models are used to plan rod insertion and elastic-club putting. Matched plans succeed in both tasks, while swapped plans fail.

A. Elastic Material Manipulation

  • A common bending probe supplies the material model used to plan both rod insertion and golf putting with an elastic club.The simulated tasks use homogeneous elastic materials A and B, with Young’s moduli of 80 and 240 kPa, respectively.Source: A. Elastic Material Manipulation · p. 5
  • Both matched rod-insertion plans insert without wall contact, with final-hold RMS target distances of 0.355 mm for A and 1.042 mm for B; both swapped plans collide and fail.The strip’s reconstructed motion and pusher force are used to estimate Young’s modulus; the resulting errors are 0.76% for A and 3.38% for B.Source: A. Elastic Material Manipulation · pp. 5–6
  • Both matched putting plans stop the ball inside the target, with center errors of 2.36 and 19.06 mm; swapped plans miss, with errors of 350.47 and 158.67 mm.The backswing is fixed while forward-stroke duration and aim angle are optimized.Source: A. Elastic Material Manipulation · p. 6

B. Elastoplastic Material Shaping

The shaping experiments identify elastoplastic models from a press and use them to plan pinching sequences for an X-shaped target. Simulation compares matched and swapped models, while hardware evaluates three physical materials by footprint IoU.

B. Elastoplastic Material Shaping

  • The task transforms a square block into a rounded X-shaped prism through alternating horizontal and vertical pinches, after identifying the material with a flat-probe compression.The study evaluates two simulated and three physical materials.Source: B. Elastoplastic Material Shaping · p. 6
  • The identified simulated parameters are (E, Y) = (80.795, 1.015) kPa for A and (81.396, 10.184) kPa for B, with all errors below 2%.A and B share E = 80 kPa and have yield thresholds Y = 1 and 10 kPa, respectively.Source: B. Elastoplastic Material Shaping · p. 6
  • Planning uses identified material models to optimize pinch sequences on fresh blocks; simulation uses six pinches, while hardware uses four.Source: B. Elastoplastic Material Shaping · p. 6
  • Matched shaping plans yield surface errors of 0.883 and 1.256 mm for A and B, versus 1.226 and 1.739 mm with swapped models.The comparison is shown at a common scale 1 s after finger withdrawal, against the target outline.Source: B. Elastoplastic Material Shaping · p. 7, Figure 4 · p. 7
  • Hardware footprint IoUs are 75.7% for Play-Doh, 72.4% for butter slime, and 77.8% for plasticine.Because internal particle tracking is unavailable, physical shapes are evaluated from surface scans using XY-footprint IoU against the target.Source: B. Elastoplastic Material Shaping · p. 7

C. Pouring a Target Volume

A single exploratory pour supplies the viscosity estimate and contact calibration used to plan glycerol transfers across six target volumes; the section reports a maximum mean-volume error of 3.8 mL and direct model reuse for planning.

C. Pouring a Target Volume

  • A single 60° exploratory pour yields an effective Newtonian viscosity of 3.44 Pa s and calibrates a wall-contact coefficient of 0.272.The final received volume calibrates contact while the estimated viscosity remains fixed.Source: C. Pouring a Target Volume · p. 7
  • The identified model selects source-cup final tilt angles for six target volumes from 60 to 160 mL, with viscosity and contact coefficients held fixed.Tilt duration uses a commanded angular speed of 10°/s; hold and return commands are each 2 s.Source: C. Pouring a Target Volume · p. 7
  • 3.8 mL is the largest absolute difference between mean received volume and target across six pouring targets.The figure compares frozen MPM predictions with glycerol hardware means and sample standard deviations over five trials per target.Source: C. Pouring a Target Volume · p. 7, Figure 6 · p. 8

VI. CONCLUSION

  • FORM identifies material properties from observed motion and contact loads without repeated simulation or gradient-based optimization, then reuses the model for prediction and planning under new actions and geometries.Identification and forward MPM use the same discretization.Source: §VI · p. 7
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