# Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Control

arXiv: https://arxiv.org/abs/1902.02827 · HTML: https://mlsanity.com/paper/1902.02827/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2019.

## Built on by (most cited first, 23 of 23)

- [Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems](https://mlsanity.com/paper/2111.14889/) (2021)
- [Residual Dynamic Mode Decomposition: Robust and verified Koopmanism](https://mlsanity.com/paper/2205.09779/) (2022)
- [The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems](https://mlsanity.com/paper/2209.02244/) (2022)
- [Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems](https://mlsanity.com/paper/2308.10697/) (2023)
- [Efficient Dynamics Modeling in Interactive Environments with Koopman Theory](https://mlsanity.com/paper/2306.11941/) (2023)
- [Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2403.02524/) (2024)
- [Online Estimation of the Koopman Operator Using Fourier Features](https://mlsanity.com/paper/2212.01503/) (2022)
- [Data-driven End-to-end Learning of Pole Placement Control for Nonlinear Dynamics via Koopman Invariant Subspaces](https://mlsanity.com/paper/2208.08883/) (2022)
- [Online Real-time Learning of Dynamical Systems from Noisy Streaming Data: A Koopman Operator Approach](https://mlsanity.com/paper/2212.05259/) (2022)
- [Linear Matrix Inequality Approaches to Koopman Operator Approximation](https://mlsanity.com/paper/2102.03613/) (2021)
- [System Norm Regularization Methods for Koopman Operator Approximation](https://mlsanity.com/paper/2110.09658/) (2021)
- [Imitation Learning with Limited Actions via Diffusion Planners and Deep Koopman Controllers](https://mlsanity.com/paper/2410.07584/) (2024)
- [High-bandwidth nonlinear control for soft actuators with recursive network models](https://mlsanity.com/paper/2101.01139/) (2021)
- [Toward smart composites: small-scale, untethered prediction and control for soft sensor/actuator systems](https://mlsanity.com/paper/2205.10940/) (2022)
- [Closed-Loop Koopman Operator Approximation](https://mlsanity.com/paper/2303.15318/) (2023)
- [Latent Linear Quadratic Regulator for Robotic Control Tasks](https://mlsanity.com/paper/2407.11107/) (2024)
- [KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planning](https://mlsanity.com/paper/2509.09074/) (2025)
- [Real-Time Reinforcement Learning for Dynamic Tasks with a Parallel Soft Robot](https://mlsanity.com/paper/2509.19525/) (2025)
- [Koopman Learning with Episodic Memory](https://mlsanity.com/paper/2311.12615/) (2023)
- [KEEC: Koopman Embedded Equivariant Control](https://mlsanity.com/paper/2312.01544/) (2023)
- [Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures](https://mlsanity.com/paper/2507.19787/) (2025)
- [Bayesian Transfer Operators in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2509.22482/) (2025)
- [An Interpretable Data-Driven Model of the Flight Dynamics of Hawks](https://mlsanity.com/paper/2602.19196/) (2026)

## Abstract (arXiv)

Controlling soft robots with precision is a challenge due in large part to the difficulty of constructing models that are amenable to model-based control design techniques. Koopman Operator Theory offers a way to construct explicit linear dynamical models of soft robots and to control them using established model-based linear control methods. This method is data-driven, yet unlike other data-driven models such as neural networks, it yields an explicit control-oriented linear model rather than just a "black-box" input-output mapping. This work describes this Koopman-based system identification method and its application to model predictive controller design. A model and MPC controller of a pneumatic soft robot arm was constructed via the method, and its performance was evaluated over several trajectory following tasks in the real-world. On all of the tasks, the Koopman-based MPC controller outperformed a benchmark MPC controller based on a linear state-space model of the same system.