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Data-driven Model Reduction for Soft Robots via Lagrangian Operator Inference

Harsh Sharma, Iman Adibnazari, Jacobo Cervera-Torralba, Michael T. Tolley, Boris Kramer

TL;DR

The paper addresses data-driven, nonintrusive surrogate construction for high-dimensional soft robots by exploiting Lagrangian structure to learn linear reduced-order models via Lagrangian Operator Inference. It compares LOpInf against DMDc and ERA/OKID on an anguilliform swimming soft robot with $231{,}336$ DOF, showing that structure-preserving ROMs achieve higher predictive accuracy and robustness to unseen inputs, especially outside the training data. The results indicate that LOpInf often outperforms competing methods in time extrapolation and generalization, highlighting the value of preserving physical structure in data-driven reductions for real-time control of soft robots. The work suggests future directions toward nonlinear reductions based on Koopman operator theory, spectral submanifold reduction, and structure-preserving machine learning.

Abstract

Data-driven model reduction methods provide a nonintrusive way of constructing computationally efficient surrogates of high-fidelity models for real-time control of soft robots. This work leverages the Lagrangian nature of the model equations to derive structure-preserving linear reduced-order models via Lagrangian Operator Inference and compares their performance with prominent linear model reduction techniques through an anguilliform swimming soft robot model example with 231,336 degrees of freedom. The case studies demonstrate that preserving the underlying Lagrangian structure leads to learned models with higher predictive accuracy and robustness to unseen inputs.

Data-driven Model Reduction for Soft Robots via Lagrangian Operator Inference

TL;DR

The paper addresses data-driven, nonintrusive surrogate construction for high-dimensional soft robots by exploiting Lagrangian structure to learn linear reduced-order models via Lagrangian Operator Inference. It compares LOpInf against DMDc and ERA/OKID on an anguilliform swimming soft robot with DOF, showing that structure-preserving ROMs achieve higher predictive accuracy and robustness to unseen inputs, especially outside the training data. The results indicate that LOpInf often outperforms competing methods in time extrapolation and generalization, highlighting the value of preserving physical structure in data-driven reductions for real-time control of soft robots. The work suggests future directions toward nonlinear reductions based on Koopman operator theory, spectral submanifold reduction, and structure-preserving machine learning.

Abstract

Data-driven model reduction methods provide a nonintrusive way of constructing computationally efficient surrogates of high-fidelity models for real-time control of soft robots. This work leverages the Lagrangian nature of the model equations to derive structure-preserving linear reduced-order models via Lagrangian Operator Inference and compares their performance with prominent linear model reduction techniques through an anguilliform swimming soft robot model example with 231,336 degrees of freedom. The case studies demonstrate that preserving the underlying Lagrangian structure leads to learned models with higher predictive accuracy and robustness to unseen inputs.
Paper Structure (3 sections, 1 equation, 4 figures)

This paper contains 3 sections, 1 equation, 4 figures.

Table of Contents

  1. Time extrapolation when trained on a single episode
  2. Robustness to unseen control inputs
  3. Conclusions

Figures (4)

  • Figure 2: Time extrapolation study (training with data from Ep 1). LOpInf ROMs and ERA/OKID ROMs generally achieve lower output error than the DMDc ROMs for both training and testing regimes.
  • Figure 3: Time extrapolation study (training with data from Ep 1). All the ROMs capture both $y_{10}(t)$ and $y_{20}(t)$ accurately in the training data regime. In the test data regime, both the LOpInf ROM and the ERA/OKID ROM provide accurate predictions whereas the DMDc ROM fails to generalize outside the training regime. The solid magenta line indicates the end of the training time interval.
  • Figure 4: Robustness to unseen inputs (relative output error comparison). The LOpInf ROM achieves lower output error than both the DMDc ROM and the ERA/OKID ROM for all test episodes.
  • Figure 5: Robustness to unseen inputs (centerline prediction for Ep 3). The LOpInf ROM and the DMDc ROM provide reasonable predictions up to $t=1$ s whereas the ERA/OKID ROM yields inaccurate solutions from the start. At $t=2$ s, all three data-driven linear ROMs fail to capture the twist in the centerline shape.