Deep Bilinear Koopman Model for Real-Time Vehicle Control in Frenet Frame
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915395082911744 |
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| author | Abtahi, Mohammad Araghi, Farhang Motallebi Mojahed, Navid Nazari, Shima |
| author_facet | Abtahi, Mohammad Araghi, Farhang Motallebi Mojahed, Navid Nazari, Shima |
| contents | Accurate modeling and control of autonomous vehicles remain a fundamental challenge due to the nonlinear and coupled nature of vehicle dynamics. While Koopman operator theory offers a framework for deploying powerful linear control techniques, learning a finite-dimensional invariant subspace for high-fidelity modeling continues to be an open problem. This paper presents a deep Koopman approach for modeling and control of vehicle dynamics within the curvilinear Frenet frame. The proposed framework uses a deep neural network architecture to simultaneously learn the Koopman operator and its associated invariant subspace from the data. Input-state bilinear interactions are captured by the algorithm while preserving convexity, which makes it suitable for real-time model predictive control (MPC) application. A multi-step prediction loss is utilized during training to ensure long-horizon prediction capability. To further enhance real-time trajectory tracking performance, the model is integrated with a cumulative error regulator (CER) module, which compensates for model mismatch by mitigating accumulated prediction errors. Closed-loop performance is evaluated through hardware-in-the-loop (HIL) experiments using a CarSim RT model as the target plant, with real-time validation conducted on a dSPACE SCALEXIO system. The proposed controller achieved significant reductions in tracking error relative to baseline controllers, confirming its suitability for real-time implementation in embedded autonomous vehicle systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_12578 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deep Bilinear Koopman Model for Real-Time Vehicle Control in Frenet Frame Abtahi, Mohammad Araghi, Farhang Motallebi Mojahed, Navid Nazari, Shima Systems and Control Machine Learning Robotics 93C10 (Primary), 93B40, 93C41, 68T07, 93B45 (Secondary) I.2.8; I.2.6; G.1.6; J.7 Accurate modeling and control of autonomous vehicles remain a fundamental challenge due to the nonlinear and coupled nature of vehicle dynamics. While Koopman operator theory offers a framework for deploying powerful linear control techniques, learning a finite-dimensional invariant subspace for high-fidelity modeling continues to be an open problem. This paper presents a deep Koopman approach for modeling and control of vehicle dynamics within the curvilinear Frenet frame. The proposed framework uses a deep neural network architecture to simultaneously learn the Koopman operator and its associated invariant subspace from the data. Input-state bilinear interactions are captured by the algorithm while preserving convexity, which makes it suitable for real-time model predictive control (MPC) application. A multi-step prediction loss is utilized during training to ensure long-horizon prediction capability. To further enhance real-time trajectory tracking performance, the model is integrated with a cumulative error regulator (CER) module, which compensates for model mismatch by mitigating accumulated prediction errors. Closed-loop performance is evaluated through hardware-in-the-loop (HIL) experiments using a CarSim RT model as the target plant, with real-time validation conducted on a dSPACE SCALEXIO system. The proposed controller achieved significant reductions in tracking error relative to baseline controllers, confirming its suitability for real-time implementation in embedded autonomous vehicle systems. |
| title | Deep Bilinear Koopman Model for Real-Time Vehicle Control in Frenet Frame |
| topic | Systems and Control Machine Learning Robotics 93C10 (Primary), 93B40, 93C41, 68T07, 93B45 (Secondary) I.2.8; I.2.6; G.1.6; J.7 |
| url | https://arxiv.org/abs/2507.12578 |