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DiSECt: A Differentiable Simulation Engine for Autonomous Robotic Cutting

Eric Heiden, Miles Macklin, Yashraj Narang, Dieter Fox, Animesh Garg, Fabio Ramos

arXiv:2105.12244v1cs.RO

TL;DR

Robotic cutting simulators are useful for control and data generation, but cutting combines complex physical phenomena and accurate simulation can require costly computation. DiSECt uses differentiable FEM with continuous contact and spring-based damage models; it reproduces commercial-solver and real-world data, generalizes across settings, and supports force-reducing motion optimization.

  • Problem

    Cutting soft materials combines contact, friction, deformation, damage, and fracture, while accurate simulation methods can require costly remeshing or millions of particle interactions.

    Source: §I · p. 1

  • Method

    DiSECt combines a mesh-based FEM model with continuous knife contact and spring-based damage that progressively weakens to produce cracks.

    Source: §I · p. 1, §VI · p. 10

  • Results

    The calibrated simulator reproduces commercial-simulator data in a fraction of the time, closely matches real-world cutting data, generalizes across velocities and objects, and reduces mean knife force by 15% relative to a vertical cut.

    Source: §VI · p. 10

  • Takeaways & Limitations

    The simulator supports parameter calibration and constrained optimization of knife motions, including pressing-and-slicing behavior that reduces mean force relative to a vertical cut.

    Source: §I · p. 2, §VI · p. 10

Abstract

from arXiv · show

Robotic cutting of soft materials is critical for applications such as food processing, household automation, and surgical manipulation. As in other areas of robotics, simulators can facilitate controller verification, policy learning, and dataset generation. Moreover, differentiable simulators can enable gradient-based optimization, which is invaluable for calibrating simulation parameters and optimizing controllers. In this work, we present DiSECt: the first differentiable simulator for cutting soft materials. The simulator augments the finite element method (FEM) with a continuous contact model based on signed distance fields (SDF), as well as a continuous damage model that inserts springs on opposite sides of the cutting plane and allows them to weaken until zero stiffness, enabling crack formation. Through various experiments, we evaluate the performance of the simulator. We first show that the simulator can be calibrated to match resultant forces and deformation fields from a state-of-the-art commercial solver and real-world cutting datasets, with generality across cutting velocities and object instances. We then show that Bayesian inference can be performed efficiently by leveraging the differentiability of the simulator, estimating posteriors over hundreds of parameters in a fraction of the time of derivative-free methods. Finally, we illustrate that control parameters in the simulation can be optimized to minimize cutting forces via lateral slicing motions. We publish videos and additional results on our project website at https://diff-cutting-sim.github.io.

I. INTRODUCTION

Robotic cutting simulators can support controller verification, policy learning, and dataset generation, but accurate cutting simulation is computationally demanding. DiSECt combines mesh-based mechanics with continuous contact and damage models so simulation parameters and cutting motions can be optimized using gradients.

I. INTRODUCTION

  • Cutting simulators can help verify controllers, train policies, and generate datasets, while avoiding costly or time-consuming real-world trials.The motivation highlights safety-critical settings such as robotic surgery, where cutting is destructive and irreversible.Source: §I · p. 1

A. Modeling and Simulation of Cutting

  • Cutting simulation spans mesh-based FEM, particle-based methods, and hybrids, while accurate approaches can require costly remeshing or millions of particle interactions.Classical FEM handles crack propagation through mesh adaptation; virtual-node methods instead augment intersected elements, and DiSECt uses this augmentation once to avoid discontinuous remeshing and compute gradients.Source: §I · p. 1, A. Modeling and Simulation of Cutting · p. 2

I. INTRODUCTION

  • DiSECt is presented as the first differentiable simulator for cutting soft materials, with continuous knife contact and spring-based damage that weakens until cracks form.The object uses a mesh representation, with virtual nodes inserted along a predefined cutting plane during preprocessing.Source: §I · pp. 1–2

B. Differentiable Simulation

C. Parameter Inference for Simulators

The paper motivates parameter inference as a way to fit simulator parameters to physical observations, including uncertainty estimates. DiSECt combines tetrahedral FEM with one-time mesh preprocessing and springs that weaken under knife contact to model damage continuously.

C. Parameter Inference for Simulators

  • Parameter inference can produce point estimates or distributions over simulator parameters, and posterior estimates can guide domain randomization and policy learning.Gradient-free or finite-difference optimization has often been used when analytical gradients are unavailable or costly.Source: C. Parameter Inference for Simulators · p. 3

III. DISECT: DIFFERENTIABLE SIMULATOR FOR CUTTING

  • DiSECt is designed for physical plausibility, efficiently obtainable gradients, and enough degrees of freedom to identify localized material differences.The mesh-based model uses tetrahedral FEM and a Neo-Hookean constitutive model for biological tissue and large deformations.Source: §III · p. 3, A. Continuum Mechanics · p. 3

A. Continuum Mechanics

  • The continuum model derives elastic forces from a Neo-Hookean strain-energy density and includes strain-rate dissipation to model internal damping.The material properties include Young’s modulus, Poisson’s ratio, and density; forces are integrated using a semi-implicit Euler scheme.Source: A. Continuum Mechanics · p. 3

B. Mesh Pre-Processing

  • Before simulation, intersected tetrahedra are duplicated and virtual nodes inserted at cut-edge intersections; springs connect node pairs across the cutting surface.Knife contact forces progressively weaken spring stiffness to model damage continuously; the current approach assumes the entire cutting surface is known beforehand, and the practicality of interleaving augmentation for interactive inference remains unvalidated.Source: B. Mesh Pre-Processing · pp. 3–4, Figure 4 · p. 4

C. Contact Dynamics

DiSECt models knife contact with a signed distance field and continuous friction, while contact-driven weakening of cutting springs represents damage and crack formation. The same penalty-based contact model also handles contact with the ground.

C. Contact Dynamics

  • Knife contact uses an SDF to find the closest point on a mesh edge, then computes penetration depth, contact normal, and a squared-penetration normal force; relative velocity supplies friction.The closest-point search runs 20 Frank-Wolfe iterations over the edge's barycentric coordinate.Source: C. Contact Dynamics · p. 4
  • Ground contact uses a penalty model between mesh vertices and a half-space, while vertices touching the ground at least 1 cm from the cutting plane are fixed.The boundary condition is intended to prevent the object from sliding off the table during cutting.Source: C. Contact Dynamics · p. 4

D. Damage Mechanics

  • As the knife applies force, contacted cutting springs weaken linearly according to the force and γ, approximating damage as a reduction in material stiffness.The springs can weaken to zero stiffness, allowing a crack to form.Source: D. Damage Mechanics · p. 4

IV. SIMULATION PARAMETER INFERENCE

DiSECt supports shared or per-spring parameter inference, using differentiable simulation gradients for point estimation and posterior sampling. SGLD adds noise to gradient-based updates to approximate posteriors, while BayesSim provides a derivative-free baseline.

IV. SIMULATION PARAMETER INFERENCE

  • Per-spring parameterization requires tuning hundreds of variables, whereas shared parameterization infers only one scalar per parameter type.The two parameterizations provide low- and high-dimensional calibration settings.Source: §IV · p. 5
  • BayesSim estimates parameters without gradients by learning a conditional density over simulation parameters given trajectories or their summary statistics.The paper uses BayesSim as a likelihood-free baseline.Source: §IV · p. 6

A. Gradient-Based Optimization

  • Adam uses gradients of the trajectory-matching loss to find a locally optimal point estimate, scaling parameter gradients by their running averages and variances.The loss compares real and simulated trajectories.Source: A. Gradient-Based Optimization · p. 6

B. Stochastic Gradient Langevin Dynamics

  • SGLD combines parameter gradients with Gaussian noise and a preconditioner to sample an approximate posterior after burn-in.Its preconditioner approximates the posterior Fisher information matrix and is updated sequentially using the energy gradient.Source: B. Stochastic Gradient Langevin Dynamics · p. 6

C. Likelihood-free Inference via BayesSim

BayesSim estimates simulator parameters without gradients by learning a conditional density from simulated trajectories. In a synthetic two-parameter test, gradient-based SGLD produced a sharper posterior around the ground truth than BayesSim or HMC.

C. Likelihood-free Inference via BayesSim

  • BayesSim estimates parameters for a derivative-free simulator by learning a conditional density from parameter-conditioned trajectories or trajectory summaries.The learned conditional density is represented as a Gaussian mixture model.Source: C. Likelihood-free Inference via… · p. 6

V. EXPERIMENTS

  • The synthetic-data experiment trained on 500 force trajectories while varying two parameters under the shared parameterization, using a low-dimensional setting to sample the uniform prior adequately.The estimated parameters were contact stiffness sdf_ke and cutting-spring stiffness cut_spring_ke.Source: A. Parameter Inference from Synthetic… · p. 7

A. Parameter Inference from Synthetic Data

  • SGLD yielded a significantly sharper posterior around the ground-truth parameters within 90 burn-in iterations, while HMC found a slightly wider posterior in approximately 50 iterations.BayesSim also captured a posterior around the ground-truth values.Source: A. Parameter Inference from Synthetic… · p. 7

B. Parameter Inference from High-fidelity Simulator

DiSECt’s parameters were calibrated against commercial-simulator and real-world cutting data, then tested on conditions beyond those used for calibration. Results show improved fitting with gradient-based inference and reveal that highly individualized parameters can overfit short training trajectories.

B. Parameter Inference from High-fidelity Simulator

  • Commercial-simulator trajectories took an average of 1,941 minutes to generate, while DiSECt simulated a 1 s trajectory in 30 s and computed its cost gradient in 90 s.The commercial simulations used four CPUs; DiSECt ran on an NVIDIA RTX 2080 GPU.Source: B. Parameter Inference from… · p. 7
  • 4.714 N average MAE for SGLD versus 26.860 N for BayesSim; individually optimizing 1,737 parameters further lowered average MAE to 3.075 N.SGLD used 300 trajectory simulations, compared with 2,500 trajectories for BayesSim.Source: B. Parameter Inference from… · p. 7
  • After 300 Adam iterations, nodal-position error fell from 1.554 mm to 1.289 mm, while knife-force MAE fell from 28.366 N to 0.549 N.The cost combined knife-force error with vertex-position error at 18 reference time steps.Source: B. Parameter Inference from… · pp. 7–8, Figure 8 · p. 7

C. Parameter Inference from Real World Measurements

1) Generalization to longer simulations:

  • For a 0.9 s test after training on 0.4 s, shared parameters achieved 4.802 N MAE versus 5.921 N for individually tuned parameters.During the shorter rollout, springs not yet reached by the knife had zero parameter gradients, whereas shared tuning updated all cutting springs.Source: 1) Generalization to longer simulations · p. 8

2) Generalization to different knife velocities:

The experiments test parameter transfer across knife velocities and object geometries, then optimize knife motion to balance force and speed. Individualized spring parameters often improve generalization, and constrained trajectory optimization produces a pressing-and-slicing motion with lower mean force than a vertical cut.

2) Generalization to different knife velocities:

  • Individual spring parameters achieved up to four-fold more accurate normalized MAE than shared parameters when testing velocities of 35, 45, 55, and 65 mms−1 after calibration at 50 mms−1.The comparison used knife-force profiles from the commercial simulator.Source: 2) Generalization to different knife… · p. 8

3) Generalization to different geometries:

  • Optimal transport transfers spring parameters between meshes using spatial correspondences, and individualized transfer significantly improved normalized MAE in most cases over averaging source parameters.The authors report that this transfer between topologically different meshes indicates parameters implicitly encode material properties that generalize across mesh topologies.Source: 3) Generalization to different… · p. 9, Table I · p. 9, Figure 12 · p. 10

E. Controlling Knife Velocity

  • Constrained trajectory optimization reduced mean knife force to 76.726 N from 89.698 N before optimization, close to the unconstrained result of 76.498 N.The constraint kept sideways motion within the 15 cm blade length; the optimization penalized mean force and inverse velocity.Source: E. Controlling Knife Velocity · pp. 9–10, Figure 13 · p. 10

VI. CONCLUSIONS

  • Across the control experiment, pressing-and-slicing behavior emerged and reduced mean knife force by 15% relative to a vertical cut.The conclusion attributes the result to sample-efficient constrained optimization on the differentiable simulator.Source: §VI · p. 10, E. Controlling Knife Velocity · p. 10

APPENDIX A ADDITIONAL ALGORITHMIC DETAILS

The appendix describes Adam’s parameter updates and compares loss functions for matching knife-force profiles. It reports that L1 loss converged relatively quickly and compared favorably with the alternatives tested.

A. Adam Optimizer

  • Adam updates parameters using a learning rate and bias-corrected first- and second-order decaying averages, with ε preventing numerical issues.The appendix also presents an SGLD algorithm using the Adam update rule.Source: A. Adam Optimizer · p. 14

B. Loss Functions

  • The Frank-Wolfe algorithm is presented for finding a barycentric coordinate on an edge with the lowest signed distance to the SDF.The appendix also includes algorithms for stochastic gradient descent with Adam and SGLD with an Adam update rule.Source: B. Loss Functions · p. 14
  • L1 loss compared favorably with other tested cost functions, converging relatively quickly to true parameters while showing bouncing near a local optimum.The authors use L1 loss in the likelihood term for probabilistic inference, corresponding to a Laplace likelihood distribution.Source: B. Loss Functions · p. 14

C. BayesSim Implementation

BayesSim learns a conditional density over simulation parameters from simulated knife-force trajectories and uses observed trajectories to infer a posterior. The appendix also formulates optimal transport for transferring cutting-spring parameters between meshes using vertex coordinates and weights.

C. BayesSim Implementation

  • BayesSim uses simulated samples to learn q(θ|φ), then computes a posterior over simulation parameters given an observed real trajectory.The parameter-inference problem may admit multiple solutions.Source: C. BayesSim Implementation · p. 14
  • BayesSim trains a 10-component mixture density network on 500 simulated knife-force trajectories, using 90-dimensional summaries downsampled from 90,000 time steps.Parameter values are projected to the unit interval because the MDN performed more accurately with homogeneous value ranges.Source: C. BayesSim Implementation · pp. 14–15

D. Optimal Transport of Cutting Spring Parameters

  • Optimal transport minimizes the cost of moving flow between weighted vertex sets, where the cost matrix uses Euclidean distances between vertices.The formulation assumes uniform weights for both vertex sets; the network simplex typically has O(n^3) complexity, with sparsity available to reduce cost.Source: D. Optimal Transport of Cutting Spring… · p. 15

APPENDIX B DETAILS OF EXPERIMENTAL SETUP

The appendix documents DiSECt’s parameterization and commercial-solver setup, then evaluates generalization across cutting velocities, rollout duration, and potato meshes.

A. Simulation Parameters

  • Simulation parameters can be shared as one scalar across cutting springs or individually tuned as a vector, with parameter limits enforced by sigmoid projection.Table A2 lists the model parameters, descriptions, and default values.Source: A. Simulation Parameters · p. 15, Table A2 · p. 16

B. Commercial Simulation Setup

  • Commercial-solver scenes combine rigid knives and tables with deformable apple, cucumber, or potato models and frictional contact.The objects use sphere, cylinder, or rectangular primitives with a 10 mm-thick cuttable slice; the slice is simulated with SPG and the remaining volume with FEM.Source: B. Commercial Simulation Setup · p. 16

A. Generalization Results

  • Apple trajectories calibrated on 0.4 s of reference data are evaluated over a 0.9 s rollout.Figure A4 contrasts individually optimized and shared parameters against the ground-truth trajectory.Source: A. Generalization Results · p. 16, Figure A4 · p. 17
  • Individual cutting-spring parameters outperform shared parameters across tested cucumber knife velocities, supporting better generalization to novel velocities.Parameters were calibrated at 50 mm/s and evaluated at other downward velocities; Figure A5 reports NMAE.Source: A. Generalization Results · pp. 16–17
  • Optimal-transport correspondences transfer cutting-spring parameters between topologically different potato meshes, producing a close fit to the ground-truth trajectory.The mapping uses Earth Mover’s Distance between cutting springs and weights source-to-target interface positions.Source: Figure A2 · p. 17

B. Posterior Over Simulation Parameters

The appendix visualizes posteriors over shared simulation parameters inferred from commercial-simulator knife-force profiles.

B. Posterior Over Simulation Parameters

  • Figure A6 and Figure A7 show posteriors from iterative BayesSim and SGLD, respectively, for shared cutting-spring simulation parameters inferred from knife-force profiles of an apple-material sphere mesh, using ground truth from a high-fidelity commercial simulator.Source: B. Posterior Over Simulation Parameters · p. 17

APPENDIX D KNIFE MOTION TRAJECTORY OPTIMIZATION

The appendix parameterizes knife motion with time-spaced keyframes and smooth RBF interpolation. It optimizes a force-and-motion objective subject to constraints on the trajectory.

APPENDIX D KNIFE MOTION TRAJECTORY OPTIMIZATION

  • Knife motion is represented by equidistant keyframes whose parameters specify lateral velocity amplitude and frequency and vertical velocity.Figure A8 illustrates five keypoints and their resulting continuous trajectory.Source: Appendix D · pp. 17–18, Figure A8 · p. 20
  • An RBF kernel weights keyframe parameters across the trajectory, keeping every keyframe’s contribution nonzero at all times to ease gradient-based optimization.The kernel width controls how smoothed the contributions become; the appendix uses σ = 0.03 for a 0.9 s trajectory with five keyframes.Source: Appendix D · p. 18
  • The objective minimizes mean knife force plus integrated vertical knife velocity, penalizing actuation effort while maintaining cutting progress.The force term returns the knife-force norm at each simulation step; the trajectory uses five keyframes over 0.9 s.Source: Appendix D · p. 19
  • A hard constraint limits knife travel along z to prevent trivially reducing force by moving beyond the blade, while MDMM supplies a penalty term for gradient-based optimization.The inequality constraint is converted to an equality constraint using a slack variable.Source: Appendix D · pp. 19–20

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