# Data-Driven Predictive Control of Nonholonomic Robots Based on a Bilinear Koopman Realization: Data Does Not Replace Geometry

arXiv: https://arxiv.org/abs/2411.07192 · HTML: https://mlsanity.com/paper/2411.07192/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 11 Nov 2024.

## Builds on (most cited first, 17 of 17)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [Optimal construction of Koopman eigenfunctions for prediction and control](https://mlsanity.com/paper/1810.08733/) (2018)
- [Finite-data error bounds for Koopman-based prediction and control](https://mlsanity.com/paper/2108.07102/) (2021)
- [Advantages of Bilinear Koopman Realizations for the Modeling and Control of Systems with Unknown Dynamics](https://mlsanity.com/paper/2010.09961/) (2020)
- [Data-Driven Model Predictive Control using Interpolated Koopman Generators](https://mlsanity.com/paper/2003.07094/) (2020)
- [Koopman Form of Nonlinear Systems with Inputs](https://mlsanity.com/paper/2207.12132/) (2022)
- [Data-driven MPC with stability guarantees using extended dynamic mode decomposition](https://mlsanity.com/paper/2308.00296/) (2023)
- [Equivariance and partial observations in Koopman operator theory for partial differential equations](https://mlsanity.com/paper/2307.15325/) (2023)
- [Reprojection methods for Koopman-based modelling and prediction](https://mlsanity.com/paper/2307.16188/) (2023)
- [Koopman-based feedback design with stability guarantees](https://mlsanity.com/paper/2312.01441/) (2023)
- [Towards reliable data-based optimal and predictive control using extended DMD](https://mlsanity.com/paper/2202.09084/) (2022)
- [Model Predictive Control, Cost Controllability, and Homogeneity *](https://mlsanity.com/paper/1906.05112/) (2019)
- [Model Predictive Control of Non-Holonomic Vehicles: Beyond Differential-Drive](https://mlsanity.com/paper/2205.11400/) (2022)
- [On Koopman-based surrogate models for non-holonomic robots](https://mlsanity.com/paper/2303.09144/) (2023)
- [Koopman-driven grip force prediction through EMG sensing](https://mlsanity.com/paper/2409.17340/) (2024)

## Abstract (arXiv)

Advances in machine learning and the growing trend towards effortless data generation in real-world systems has led to an increasing interest for data-inferred models and data-based control in robotics. It seems appealing to govern robots solely based on data, bypassing the traditional, more elaborate pipeline of system modeling through first-principles and subsequent controller design. One promising data-driven approach is the Extended Dynamic Mode Decomposition (EDMD) for control-affine systems, a system class which contains many vehicles and machines of immense practical importance including, e.g., typical wheeled mobile robots. EDMD can be highly data-efficient, computationally inexpensive, can deal with nonlinear dynamics as prevalent in robotics and mechanics, and has a sound theoretical foundation rooted in Koopman theory. On this background, this present paper examines how EDMD models can be integrated into predictive controllers for nonholonomic mobile robots. In addition to the conventional kinematic mobile robot, we also cover the complete data-driven control pipeline - from data acquisition to control design - when the robot is not treated in terms of first-order kinematics but in a second-order manner, allowing to account for actuator dynamics. Using only real-world measurement data, it is shown in both simulations and hardware experiments that the surrogate models enable high-precision predictive controllers in the studied cases. However, the findings raise significant concerns about purely data-centric approaches that overlook the underlying geometry of nonholonomic systems, showing that, for nonholonomic systems, some geometric insight seems necessary and cannot be easily compensated for with large amounts of data.