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

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~μ s on an automotive-grade embedded target, demonstrating improved tracking accuracy without sacrificing real-time feasibility.