Sim-to-Real of Soft Robots With Learned Residual Physics

Authors: Junpeng Gao, Mike Y. Michelis, Andrew Spielberg, Robert K. Katzschmann · IEEE Robotics and Automation Letters (RA-L) 2024

Licences

Open Access
Paper: CC BY 4.0

Everything below draws on the full paper under its CC BY 4.0 licence; its figure is credited to the authors.

TL;DR

Learns a residual body force on a differentiable FEM soft-robot simulation from sparse mocap markers; marker error falls 60.3% (beam) and 31.9% (pneumatic arm) below system identification.

Why it matters

Soft robots are hard to model, which limits model-based control and design work on them. The method keeps a coarse analytical simulator as the physical prior and learns only the error, needing only sparse motion-capture markers on the real robot instead of full-state sensing. It also let the authors keep suboptimal but non-stiff, faster-to-solve parameters while matching reality more closely than the slower simulation with system-identified parameters.

Problem

Soft-robot simulators expose only a few tunable parameters such as stiffness, density and Poisson's ratio, so system identification cannot fix errors caused by a wrong material model, coarse discretisation, fabrication defects, viscoelasticity or hysteresis. Earlier residual physics methods learned corrections only for low-dimensional state spaces, not for the roughly 10^3 degrees of freedom of a soft-body mesh, and real robots can only be observed through a few motion markers.

Proposed solution

The method runs the differentiable FEM simulator DiffPD and, for each recorded time step, uses gradient-based optimisation (L-BFGS-B) to find the external force on every mesh node that makes simulated marker positions match the measured ones. These optimised forces form an augmented dataset on which an MLP with skip connections is trained to predict the residual force from the current positions, velocities and actuation forces. At run time the network's force is added to each simulator step in an autoregressive rollout.

Key insights

A single residual body force applied over the whole mesh can absorb errors from a wrong material model and compressibility assumption that parameter tuning cannot reach.
Splitting the problem into per-step force optimisation through a differentiable simulator, then supervised learning on those forces, turns sparse marker data into dense training labels.
In simulation, about 4 markers were enough for a median full-state reconstruction error below 0.1 mm, though the spread stayed high until 10 markers.
System identification on the real beam converged to a Young's modulus of 810 kPa, far from the manufacturer value of 215 kPa, showing that the best-fit parameters were compensating for unmodelled effects.

Main results

Sim-to-sim beam: mean rollout error fell from 4.49 ± 1.47 mm to 0.08 ± 0.28 mm (oscillating) and from 4.36 ± 1.54 mm to 0.03 ± 0.07 mm (twisting).
Sim-to-real silicone beam: mean marker error 5.46 ± 1.78 mm (original), 1.32 ± 1.38 mm (system identification), 0.52 ± 0.48 mm (residual physics), a 60.3% reduction against system identification.
Sim-to-real SoPrA pneumatic arm: 7.77 ± 3.72 mm (original), 7.57 ± 3.59 mm (system identification), 5.15 ± 2.67 mm (residual physics), a 31.9% reduction.
Run time per beam trajectory: 0.711 s with the original parameters, 2.218 s with system-identified parameters (about 3.12× slower) and 1.393 s with residual physics (about 1.96×); network inference took 0.112 s.
Trained on the first 5 s of each arm trajectory and rolled out to 10 s, residual physics reached 6.10 ± 3.22 mm against 7.57 ± 3.59 mm for system identification.

Limitations

Building the training set requires a computationally expensive per-step optimisation in pre-processing.
Learned dynamics do not generalise to out-of-distribution data; generalisation suffered on the arm at 1.75× the training actuation pressure.
Errors accumulate in long autoregressive rollouts, and contact interactions are not handled.
Each network is trained for a single robot geometry; one network across soft-robot morphologies is left to future work.
Arm pressures were clipped to 20 kPa because the fibre reinforcements are not modelled in the simulator, and the injected forces add numerical stiffness that makes the hybrid simulation slower than the base simulation.

Field impact

The paper won the RA-L 2025 Best Paper Award and has 54 citations. The licensed copy gives no code, data or hardware release.

Abstract

Accurately modeling soft robots in simulation is computationally expensive and commonly falls short of representing the real world. This well-known discrepancy, known as the sim-to-real gap, can have several causes, such as coarsely approximated geometry and material models, manufacturing defects, viscoelasticity and plasticity, and hysteresis effects. Residual physics networks learn from real-world data to augment a discrepant model and bring it closer to reality. Here, we present a residual physics method for modeling soft robots with large degrees of freedom. We train neural networks to learn a residual term — the modeling error between simulated and physical systems. Concretely, the residual term is a force applied on the whole simulated mesh, while real position data is collected with only sparse motion markers. The physical prior of the analytical simulation provides a starting point for the residual network, and the combined model is more informed than if physics were learned tabula rasa. We demonstrate our method on 1) a silicone elastomeric beam and 2) a soft pneumatic arm with hard-to-model, anisotropic fiber reinforcements. Our method outperforms traditional system identification up to 60%. We show that residual physics need not be limited to low degrees of freedom but can effectively bridge the sim-to-real gap for high dimensional systems.

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