# Adaptive Model-Predictive Control of a Soft Continuum Robot Using a Physics-Informed Neural Network Based on Cosserat Rod Theory

arXiv: https://arxiv.org/abs/2508.12681 · HTML: https://mlsanity.com/paper/2508.12681/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 95 references that are in the map.
- First posted on arXiv 18 Aug 2025.

## Builds on (most cited first, 24 of 24)

- [A System for Massively Parallel Hyperparameter Tuning](https://mlsanity.com/paper/1810.05934/) (2018)
- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Physics-Informed Neural Nets for Control of Dynamical Systems](https://mlsanity.com/paper/2104.02556/) (2021)
- [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)
- [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)
- [Input-to-State Stable Coupled Oscillator Networks for Closed-form Model-based Control in Latent Space](https://mlsanity.com/paper/2409.08439/) (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)
- [PDE-based Dynamic Control and Estimation of Soft Robotic Arms](https://mlsanity.com/paper/2203.13724/) (2022)
- [A Unified and Modular Model Predictive Control Framework for Soft Continuum Manipulators under Internal and External Constraints](https://mlsanity.com/paper/2204.13710/) (2022)
- [Learning Low-Dimensional Strain Models of Soft Robots by Looking at the Evolution of Their Shape with Application to Model-Based Control](https://mlsanity.com/paper/2411.00138/) (2024)
- [Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.01916/) (2025)
- [Continuum Robot State Estimation Using Gaussian Process Regression on SE(3)](https://mlsanity.com/paper/2210.14842/) (2022)
- [Learning Soft Robot Dynamics using Differentiable Kalman Filters and Spatio-Temporal Embeddings](https://mlsanity.com/paper/2308.09868/) (2023)
- [Estimating Infinite-Dimensional Continuum Robot States From the Tip](https://mlsanity.com/paper/2311.01517/) (2023)
- [Backstepping Control of Tendon-Driven Continuum Robots in Large Deflections Using the Cosserat Rod Model](https://mlsanity.com/paper/2412.12035/) (2024)
- [Physics-informed Split Koopman Operators for Data-efficient Soft Robotic Simulation](https://mlsanity.com/paper/2502.00162/) (2025)
- [FBG-Based Position Estimation of Highly Deformable Continuum Manipulators: Model-Dependent vs. Data-Driven Approaches](https://mlsanity.com/paper/1812.08629/) (2018)
- [Piecewise Linear Strain Cosserat Model for Soft Slender Manipulator](https://mlsanity.com/paper/2206.03546/) (2022)
- [Intuitive Telemanipulation of Hyper-Redundant Snake Robots within Locomotion and Reorientation using Task-Priority Inverse Kinematics](https://mlsanity.com/paper/2303.00065/) (2023)
- [Real-time Dynamics of Soft Manipulators with Cross-section Inflation: Application to the Octopus Muscular Hydrostat](https://mlsanity.com/paper/2412.03046/) (2024)

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

- [Learning Visually Interpretable Oscillator Networks for Soft Continuum Robots from Video](https://mlsanity.com/paper/2511.18322/) (2025)
- [A Flow Matching Framework for Soft-Robot Inverse Dynamics](https://mlsanity.com/paper/2604.03006/) (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)

Dynamic control of soft continuum robots (SCRs) holds great potential for expanding their applications, but remains a challenging problem due to the high computational demands of accurate dynamic models. While data-driven approaches like Koopman-operator-based methods have been proposed, they typically lack adaptability and cannot reconstruct the full robot shape, limiting their applicability. This work introduces a real-time-capable nonlinear model-predictive control (MPC) framework for SCRs based on a domain-decoupled physics-informed neural network (DD-PINN) with adaptable bending stiffness. The DD-PINN serves as a surrogate for the dynamic Cosserat rod model with a speed-up factor of up to 44,000. It is also used within an unscented Kalman filter for estimating the model states and bending compliance from end-effector position measurements. We implement a nonlinear evolutionary MPC running at 70 Hz on the GPU. In simulation, it demonstrates accurate tracking of dynamic trajectories and setpoint control with end-effector position errors below 3 mm (2.3% of the actuator's length). In real-world experiments, the controller achieves similar accuracy and accelerations up to 3.55 m/s2.