RAFL: Generalizable Sim-to-Real of Soft Robots with Residual Acceleration Field Learning
Soft robot simulators suffer from a sim-to-real gap that widens when optimizing morphology, because calibration parameters identified on one geometry often fail to transfer to unseen shapes. This paper proposes Residual Acceleration Field Learning (RAFL), which learns local corrective accelerations defined on quadrature elements rather than global nodal forces. By operating on deformation and velocity gradients in material space, the model becomes independent of mesh topology and discretization, enabling zero-shot generalization across geometries.
The paper presents a well-motivated and empirically validated approach to generalizable sim-to-real transfer. The core insight—that geometry-agnostic residual fields should be defined locally in material space rather than globally on nodes—is sound and effectively implemented. The experiments convincingly demonstrate that system identification suffers from negative transfer across morphologies, while RAFL provides consistent zero-shot improvements. However, the evaluation is limited to passive dynamics without actuation or contact, and the generalization to fundamentally different shapes (fish-tails) shows higher absolute errors than beam-to-beam transfer.
The local feature design is physically principled and the gains are real. The authors define residual accelerations on Gaussian quadrature samples using deformation gradients, strain rates, and spin tensors co-rotated into the rest frame. This produces a 34-dimensional feature vector (Table I) fed to a small MLP that enforces rotational equivariance and zero residual at rest. The resulting model contains roughly 0.02% of the parameters of the supervised residual baseline yet transfers across discretizations where the baseline is architecturally inapplicable.
The scope is narrow: experiments consider only passive cantilever beams and fish-tails under gravity, with no actuation, contact, or collision. While RAFL generalizes better than baselines, the fish-tail results (Table IV) show errors of 3-8 mm even after correction, roughly an order of magnitude higher than the canonical beam. This suggests the local feature set may not capture all relevant physics for complex geometries. Additionally, the paper does not quantify how the learned residuals affect convergence of morphology optimization loops—a claimed motivating application.
The comparison to system identification (SysID) and supervised residual learning (SRL) is fair and thorough. SysID jointly optimizes Young's modulus $E$ and Poisson's ratio $\nu$ but exhibits negative transfer when applied to new geometries (Fig. 5), confirming that fitted parameters absorb geometry-dependent effects. SRL pre-computes residual targets via per-step optimization then regresses nodal forces, which cannot generalize to different mesh topologies. In contrast, RAFL trains end-to-end through the differentiable simulator (Eq. 7) and achieves zero-shot transfer to both scaled and non-scaled geometries.
The authors provide code and specify hyperparameters. The repository is listed as github.com/generalroboticslab/RAFL.git, built on the DiffPD simulator. Material properties (Smooth-On Dragon Skin 10, $\rho=1070$ kg/m$^3$, $E=215$ kPa, $\nu=0.45$) and network architecture (4-layer MLP, 64 hidden units, Adam for 100 epochs) are documented. However, the paper omits training wall-clock times, details of the initial state estimation procedure (described as "optimizing a sequence of virtual forces"), and does not release the processed marker trajectory datasets—only the code.
Differentiable simulators enable gradient-based optimization of soft robots over material parameters, control, and morphology, but accurately modeling real systems remains challenging due to the sim-to-real gap. This issue becomes more pronounced when geometry is itself a design variable. System identification reduces discrepancies by fitting global material parameters to data; however, when constitutive models are misspecified or observations are sparse, identified parameters often absorb geometry-dependent effects rather than reflect intrinsic material behavior. More expressive constitutive models can improve accuracy but substantially increase computational cost, limiting practicality. We propose a residual acceleration field learning (RAFL) framework that augments a base simulator with a transferable, element-level corrective dynamics field. Operating on shared local features, the model is agnostic to global mesh topology and discretization. Trained end-to-end through a differentiable simulator using sparse marker observations, the learned residual generalizes across shapes. In both sim-to-sim and sim-to-real experiments, our method achieves consistent zero-shot improvements on unseen morphologies, while system identification frequently exhibits negative transfer. The framework also supports continual refinement, enabling simulation accuracy to accumulate during morphology optimization.
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