# Direct and inverse modeling of soft robots by learning a condensed FEM model

arXiv: https://arxiv.org/abs/2307.11408 · HTML: https://mlsanity.com/paper/2307.11408/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 21 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [State Representation Learning for Control: An Overview](https://mlsanity.com/paper/1802.04181/) (2018)
- [Discrete Cosserat Approach for Multi-Section Soft Robots Dynamics](https://mlsanity.com/paper/1702.03660/) (2017)
- [Unsupervised state representation learning with robotic priors: a robustness benchmark](https://mlsanity.com/paper/1709.05185/) (2017)
- [SENSORIMOTOR GRAPH: Action-Conditioned Graph Neural Network for Learning Robotic Soft Hand Dynamics](https://mlsanity.com/paper/2107.08492/) (2021)
- [Learning Robot Structure and Motion Embeddings using Graph Neural Networks](https://mlsanity.com/paper/2109.07543/) (2021)

## Built on by (most cited first, 1 of 1)

- [Development of a PPO-Reinforcement Learned Walking Tripedal Soft-Legged Robot using SOFA](https://mlsanity.com/paper/2504.09242/) (2025)

## Abstract (arXiv)

The Finite Element Method (FEM) is a powerful modeling tool for predicting the behavior of soft robots. However, its use for control can be difficult for non-specialists of numerical computation: it requires an optimization of the computation to make it real-time. In this paper, we propose a learning-based approach to obtain a compact but sufficiently rich mechanical representation. Our choice is based on nonlinear compliance data in the actuator/effector space provided by a condensation of the FEM model. We demonstrate that this compact model can be learned with a reasonable amount of data and, at the same time, be very efficient in terms of modeling, since we can deduce the direct and inverse kinematics of the robot. We also show how to couple some models learned individually in particular on an example of a gripper composed of two soft fingers. Other results are shown by comparing the inverse model derived from the full FEM model and the one from the compact learned version. This work opens new perspectives, namely for the embedded control of soft robots, but also for their design. These perspectives are also discussed in the paper.