# Pseudo-rigid body networks: learning interpretable deformable object dynamics from partial observations

arXiv: https://arxiv.org/abs/2307.07975 · HTML: https://mlsanity.com/paper/2307.07975/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 16 Jul 2023.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Position Information in Transformers: An Overview](https://mlsanity.com/paper/2102.11090/) (2021)
- [Deep Regression on Manifolds: A 3D Rotation Case Study](https://mlsanity.com/paper/2103.16317/) (2021)
- [Self-Supervised Learning of State Estimation for Manipulating Deformable Linear Objects](https://mlsanity.com/paper/1911.06283/) (2019)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Piecewise Affine Curvature model: a reduced-order model for soft robot-environment interaction beyond PCC](https://mlsanity.com/paper/2211.10188/) (2022)

## Abstract (arXiv)

Accurately predicting deformable linear object (DLO) dynamics is challenging, especially when the task requires a model that is both human-interpretable and computationally efficient. In this work, we draw inspiration from the pseudo-rigid body method (PRB) and model a DLO as a serial chain of rigid bodies whose internal state is unrolled through time by a dynamics network. This dynamics network is trained jointly with a physics-informed encoder that maps observed motion variables to the DLO's hidden state. To encourage the state to acquire a physically meaningful representation, we leverage the forward kinematics of the PRB model as a decoder. We demonstrate in robot experiments that the proposed DLO dynamics model provides physically interpretable predictions from partial observations while being on par with black-box models regarding prediction accuracy. The project code is available at: http://tinyurl.com/prb-networks