Deep Koopman model stabilizes vehicle dynamics in 0.421 ms for autonomous driving

Accurate modeling of vehicle dynamics is critical for autonomous driving safety, especially during extreme maneuvers. Deep Koopman operator theory offers a global linearization framework, but its online application suffers from a rank-deficient problem in the high-dimensional lifted state space, breaking traditional recursive least squares updates. To solve this, researchers propose a novel tire-force-driven modeling framework that embeds 7DOF dynamic equilibrium constraints into the offline Deep Koopman learning objective, ensuring structural fidelity and physical interpretability.

For online updates, the team reformulated the operator update as a minimum-norm solution and developed the Physics-Informed Variable Step-Size Normalized Least Mean Squares (PI-VSS-NLMS) algorithm. This uses NLMS’s projection property as a stable pseudo-inverse solver, with an anchoring mechanism to suppress parameter drift. Extensive simulations in CarSim and Hardware-in-the-Loop tests on dSPACE MicroAutobox III confirm robust prediction accuracy under unseen excitations, with an average execution time of just 0.421 ms—proving real-time feasibility and bridging the gap between theoretical models and safe autonomous driving deployment.