# Learning Predictive Control with Deep Koopman Operators for Autonomous Vehicle Motion Planning

arXiv: https://arxiv.org/abs/2606.08136 · HTML: https://mlsanity.com/paper/2606.08136/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for driving, one of 9 directions in End-to-end autonomous driving.
- Builds on 20 of its 49 references that are in the map.
- First posted on arXiv 6 Jun 2026.

## Placed in

- End-to-end autonomous driving / [Reinforcement learning for driving](https://mlsanity.com/driving/reinforcement-learning-for-driving/)
- Deep reinforcement learning methods / [RL for autonomous driving and traffic](https://mlsanity.com/deeprl/rl-for-autonomous-driving-and-traffic/)

## Builds on (most cited first, 20 of 20)

- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [Drive Like a Human: Rethinking Autonomous Driving with Large Language Models](https://mlsanity.com/paper/2307.07162/) (2023)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [Interpretable End-to-end Urban Autonomous Driving with Latent Deep Reinforcement Learning](https://mlsanity.com/paper/2001.08726/) (2020)
- [Drive as You Speak: Enabling Human-Like Interaction with Large Language Models in Autonomous Vehicles](https://mlsanity.com/paper/2309.10228/) (2023)
- [Model-free Deep Reinforcement Learning for Urban Autonomous Driving](https://mlsanity.com/paper/1904.09503/) (2019)
- [Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function](https://mlsanity.com/paper/2007.11718/) (2020)
- [Model Predictive Contouring Control for Collision Avoidance in Unstructured Dynamic Environments](https://mlsanity.com/paper/2010.10190/) (2020)
- [Deep Variational Koopman Models: Inferring Koopman Observations for Uncertainty-Aware Dynamics Modeling and Control](https://mlsanity.com/paper/1902.09742/) (2019)
- [Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control](https://mlsanity.com/paper/1912.10360/) (2019)
- [Near-Optimal Rapid MPC using Neural Networks: A Primal-Dual Policy Learning Framework](https://mlsanity.com/paper/1912.04744/) (2019)
- [Deep Neural Networks with Koopman Operators for Modeling and Control of Autonomous Vehicles](https://mlsanity.com/paper/2007.02219/) (2020)
- [The Convex Feasible Set Algorithm for Real Time Optimization in Motion Planning](https://mlsanity.com/paper/1709.00627/) (2017)
- [Physically Analyzable AI-Based Nonlinear Platoon Dynamics Modeling During Traffic Oscillation: A Koopman Approach](https://mlsanity.com/paper/2406.14696/) (2024)
- [DeepKoCo: Efficient latent planning with a task-relevant Koopman representation](https://mlsanity.com/paper/2011.12690/) (2020)
- [Model-Based Safe Reinforcement Learning with Time-Varying State and Control Constraints: An Application to Intelligent Vehicles](https://mlsanity.com/paper/2112.11217/) (2021)
- [Robust Learning-based Predictive Control for Discrete-time Nonlinear Systems with Unknown Dynamics and State Constraints](https://mlsanity.com/paper/1911.09827/) (2019)
- [Accept Synthetic Objects as Real: End-to-End Training of Attentive Deep Visuomotor Policies for Manipulation in Clutter](https://mlsanity.com/paper/1909.11128/) (2019)
- [Safety-critical Control with Control Barrier Functions: A Hierarchical Optimization Framework](https://mlsanity.com/paper/2410.15877/) (2024)

## Built on by (most cited first, 1 of 1)

- [Koopman Dreamer: Spectrally Constrained Latent Dynamics for Stable World-Model Imagination](https://mlsanity.com/paper/2607.19719/) (2026)

## Abstract (arXiv)

Model Predictive Control (MPC) is widely used for autonomous-vehicle (AV) motion planning, but its real-time applicability is often limited by the need for accurate models and online solution of nonlinear, nonconvex optimization problems in dynamic road environments. Actor-critic reinforcement learning offers a promising alternative for online policy generation, yet its policy-learning process often lacks explicit control-theoretic structure. This article proposes a learning predictive control (LPC) framework with deep Koopman operators for efficient real-time motion planning under nonconvex constraints. To address nonlinear and uncertain vehicle dynamics, a deep-Koopman-based predictor is used to lift the system into an interpretable linear observable space in a data-driven manner. Unlike traditional MPC, which computes open-loop control sequences, the proposed LPC framework yields a closed-loop state-feedback policy within each prediction interval through receding-horizon actor-critic learning. To ensure safety under nonconvex environmental constraints, LPC constructs convex local surrogate representations of obstacles and defines corresponding potential-field functions. These functions and their gradients are directly embedded into the actor-critic structure, enabling efficient, safety-aware policy learning. Extensive simulations and real-world experiments on the HongQi-EHS3 platform demonstrate favorable performance in diverse obstacle-avoidance scenarios in terms of safety, computational efficiency, and driving comfort, compared with benchmark methods such as CBF-MPC and LMPCC.