Koopman Operator-Based Optimal Control for High-Speed Autonomous Vehicle Path Tracking: An Experimental Study

Abstract

This paper presents a Koopman-operator-based optimal control framework for high-speed lateral path tracking and validates it through closed-loop experiments on a full-size autonomous electric vehicle. The path-tracking error dynamics are identified from real driving data using extended dynamic mode decomposition with control. The lifting dictionary combines the measured physical states with thin-plate-spline radial basis functions, while maximum-absolute scaling is used to improve numerical conditioning. Road curvature and longitudinal velocity are included as measurable exogenous inputs. Because steady-state autonomous highway driving provides limited dynamic excitation, and because artificial steering excitation is unsafe in public traffic, the identification dataset combines autonomous lane-centering recordings with open-loop excitation maneuvers performed by a human driver. Two optimal controllers are evaluated: an infinite-horizon linear quadratic regulator and an input-constrained model predictive controller with curvature-and-velocity feedforward. Both Koopman-based controllers are compared with analytical single-track-model baselines using a common weight-mapping scheme. In highway tests at 80 km/h, the Koopman-based model predictive controller reduces the lateral-position root-mean-square error by up to 43.7% relative to the analytical model predictive controller, while the Koopman-based linear quadratic regulator reduces it by up to 19.2% relative to its analytical counterpart. Most of the improvement is obtained with 20 radial basis functions, after which the tracking performance saturates. The largest tested Koopman configuration runs in under $20~\mu $ s on an automotive-grade embedded target, demonstrating improved tracking accuracy without sacrificing real-time feasibility.