# Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2502.01916 · HTML: https://mlsanity.com/paper/2502.01916/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 77 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 26 of 26)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [A Critical Review of Recurrent Neural Networks for Sequence Learning](https://mlsanity.com/paper/1506.00019/) (2015)
- [A System for Massively Parallel Hyperparameter Tuning](https://mlsanity.com/paper/1810.05934/) (2018)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems](https://mlsanity.com/paper/1907.04489/) (2019)
- [Physics-Informed Neural Nets for Control of Dynamical Systems](https://mlsanity.com/paper/2104.02556/) (2021)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators](https://mlsanity.com/paper/2109.10793/) (2021)
- [Model Based Control of Soft Robots: A Survey of the State of the Art and Open Challenges](https://mlsanity.com/paper/2110.01358/) (2021)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Soft Robots Modeling: a Structured Overview](https://mlsanity.com/paper/2112.03645/) (2021)
- [Physics-informed Neural Networks to Model and Control Robots: a Theoretical and Experimental Investigation](https://mlsanity.com/paper/2305.05375/) (2023)
- [Sim-to-Real of Soft Robots with Learned Residual Physics](https://mlsanity.com/paper/2402.01086/) (2024)
- [CusADi: A GPU Parallelization Framework for Symbolic Expressions and Optimal Control](https://mlsanity.com/paper/2408.09662/) (2024)
- [Rod models in continuum and soft robot control: a review](https://mlsanity.com/paper/2407.05886/) (2024)
- [Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systems](https://mlsanity.com/paper/2408.14951/) (2024)
- [PINN-Ray: A Physics-Informed Neural Network to Model Soft Robotic Fin Ray Fingers](https://mlsanity.com/paper/2407.08222/) (2024)
- [Learning-based Nonlinear Model Predictive Control of Articulated Soft Robots using Recurrent Neural Networks](https://mlsanity.com/paper/2411.05616/) (2024)
- [Learning physics-informed simulation models for soft robotic manipulation: A case study with dielectric elastomer actuators](https://mlsanity.com/paper/2202.12977/) (2022)
- [Learning-based Position and Stiffness Feedforward Control of Antagonistic Soft Pneumatic Actuators using Gaussian Processes](https://mlsanity.com/paper/2303.01840/) (2023)
- [Optimal Control for Articulated Soft Robots](https://mlsanity.com/paper/2306.01934/) (2023)
- [SPONGE: Open-Source Designs of Modular Articulated Soft Robots](https://mlsanity.com/paper/2404.10734/) (2024)
- [Knowledge-based Neural Ordinary Differential Equations for Cosserat Rod-based Soft Robots](https://mlsanity.com/paper/2408.07776/) (2024)

## Built on by (most cited first, 3 of 3)

- [Adaptive Model-Predictive Control of a Soft Continuum Robot Using a Physics-Informed Neural Network Based on Cosserat Rod Theory](https://mlsanity.com/paper/2508.12681/) (2025)
- [Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equations](https://mlsanity.com/paper/2605.06246/) (2026)
- [Constraint-Aware Physics-Informed Neural Networks for Static Shape Estimation of Co-Manipulative Continuum Robots](https://mlsanity.com/paper/2608.26273/) (2026)

## Abstract (arXiv)

Soft robots can revolutionize several applications with high demands on dexterity and safety. When operating these systems, real-time estimation and control require fast and accurate models. However, prediction with first-principles (FP) models is slow, and learned black-box models have poor generalizability. Physics-informed machine learning offers excellent advantages here, but it is currently limited to simple, often simulated systems without considering changes after training. We propose physics-informed neural networks (PINNs) for articulated soft robots (ASRs) with a focus on data efficiency. The amount of expensive real-world training data is reduced to a minimum -- one dataset in one system domain. Two hours of data in different domains are used for a comparison against two gold-standard approaches: In contrast to a recurrent neural network, the PINN provides a high generalizability. The prediction speed of an accurate FP model is exceeded with the PINN by up to a factor of 467 at slightly reduced accuracy. This enables nonlinear model predictive control (MPC) of a pneumatic ASR. Accurate position tracking with the MPC running at 47 Hz is achieved in six dynamic experiments.