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DisMech: A Discrete Differential Geometry-based Physical Simulator for Soft Robots and Structures

Andrew Choi, Ran Jing, Andrew Sabelhaus, Mohammad Khalid Jawed

TL;DR

DisMech introduces a fully implicit discrete differential geometry-based simulator for soft rod-like robots and deformable structures, achieving order-of-magnitude speedups over prior methods while maintaining physical accuracy. Built on the Discrete Elastic Rods framework, it supports arbitrary rod connections, contact-rich 2D/3D environments, and actuation via natural curvatures, with a gradient-descent approach to map hardware trajectories to control inputs. The authors validate DisMech against theory and Elastica across dynamic cantilever, oscillating helix, and friction tests, and demonstrate practical demonstrations including a spider robot and a soft entanglement gripper, plus real2sim open-loop control using gradient-descent natural-curvature optimization. The work enables rapid design, prototyping, and sim2real planning for soft robotics and deformable-object manipulation, and opens pathways to shell integration, shearing modeling, and reinforcement-learning workflows for advanced control.

Abstract

Fast, accurate, and generalizable simulations are a key enabler of modern advances in robot design and control. However, existing simulation frameworks in robotics either model rigid environments and mechanisms only, or if they include flexible or soft structures, suffer significantly in one or more of these performance areas. To close this "sim2real" gap, we introduce DisMech, a simulation environment that models highly dynamic motions of rod-like soft continuum robots and structures, quickly and accurately, with arbitrary connections between them. Our methodology combines a fully implicit discrete differential geometry-based physics solver with fast and accurate contact handling, all in an intuitive software interface. Crucially, we propose a gradient descent approach to easily map the motions of hardware robot prototypes to control inputs in DisMech. We validate DisMech through several highly-nuanced soft robot simulations while demonstrating an order of magnitude speed increase over previous state of the art. Our real2sim validation shows high physical accuracy versus hardware, even with complicated soft actuation mechanisms such as shape memory alloy wires. With its low computational cost, physical accuracy, and ease of use, DisMech can accelerate translation of sim-based control for both soft robotics and deformable object manipulation.

DisMech: A Discrete Differential Geometry-based Physical Simulator for Soft Robots and Structures

TL;DR

DisMech introduces a fully implicit discrete differential geometry-based simulator for soft rod-like robots and deformable structures, achieving order-of-magnitude speedups over prior methods while maintaining physical accuracy. Built on the Discrete Elastic Rods framework, it supports arbitrary rod connections, contact-rich 2D/3D environments, and actuation via natural curvatures, with a gradient-descent approach to map hardware trajectories to control inputs. The authors validate DisMech against theory and Elastica across dynamic cantilever, oscillating helix, and friction tests, and demonstrate practical demonstrations including a spider robot and a soft entanglement gripper, plus real2sim open-loop control using gradient-descent natural-curvature optimization. The work enables rapid design, prototyping, and sim2real planning for soft robotics and deformable-object manipulation, and opens pathways to shell integration, shearing modeling, and reinforcement-learning workflows for advanced control.

Abstract

Fast, accurate, and generalizable simulations are a key enabler of modern advances in robot design and control. However, existing simulation frameworks in robotics either model rigid environments and mechanisms only, or if they include flexible or soft structures, suffer significantly in one or more of these performance areas. To close this "sim2real" gap, we introduce DisMech, a simulation environment that models highly dynamic motions of rod-like soft continuum robots and structures, quickly and accurately, with arbitrary connections between them. Our methodology combines a fully implicit discrete differential geometry-based physics solver with fast and accurate contact handling, all in an intuitive software interface. Crucially, we propose a gradient descent approach to easily map the motions of hardware robot prototypes to control inputs in DisMech. We validate DisMech through several highly-nuanced soft robot simulations while demonstrating an order of magnitude speed increase over previous state of the art. Our real2sim validation shows high physical accuracy versus hardware, even with complicated soft actuation mechanisms such as shape memory alloy wires. With its low computational cost, physical accuracy, and ease of use, DisMech can accelerate translation of sim-based control for both soft robotics and deformable object manipulation.
Paper Structure (23 sections, 20 equations, 6 figures, 2 tables, 1 algorithm)

This paper contains 23 sections, 20 equations, 6 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Elastic Energies
  5. Stretching Energy
  6. Bending Energy
  7. Twisting Energy
  8. Elastic Forces
  9. Contact and Friction
  10. Time Stepping and Numerical Integration Schemes
  11. Elastic Joints
  12. Actuation via Natural Curvatures
  13. Theoretical Validation
  14. Dynamic Cantilever Beam
  15. Oscillating Helix under Gravity
  16. ...and 8 more sections

Figures (6)

  • Figure 1: Discrete rod schematic with relevant notations describing the rod's discrete bending and twisting at node $\mathbf q_i$.
  • Figure 2: Rendering of a four-legged spider-like soft robot constructed using DisMech's API. Moving chronologically from left to right, the robot is dropped from a height where it then makes contact with an incline plane. After some initial sliding, the influence of sticking friction results in the robot's eventual equilibrium position in the rightmost column.
  • Figure 3: Simulation results for DisMech compared with Elastica and theory (when applicable). Each plot refers to a specific experiment shown in Table \ref{['tab:performance_comparison']}. Plots (a1) and (a2) showcase the deflection of the cantilever beam experiment for different material properties. Likewise, plots (b1) and (b2) showcase the tip position of the helical rod experiment for different material and geometric properties. As the helix experiment does not have an analytical solution to compare against, we show in plot (b3) that both DisMech and Elastica reach the same static equilibrium point when damping is introduced into the system as a sanity check. Finally, plot (c) showcases the kinetic energy of the rod as a function of an enacted external force for a friction coefficient of $\mu = 0.4$.
  • Figure 4: Renderings of an active entanglement gripper Becker2022active_entanglement. The top row showcases contact-only entanglement whereas the bottom row showcases entanglement with friction $\mu=0.5$. Note the influence of stiction causing more distorted helices in the latter example.
  • Figure 5: Snapshots showcasing real2sim realization of a SMA actuated dual soft limb manipulator Pacheco2023comparison. Using our gradient descent approach, we showcase excellent agreement between the real and simulated curvatures for a wide variety of geometric configurations.
  • ...and 1 more figures