  This paper proposes Koopman operator-based Stochastic Model Predictive
Control (K-SMPC) for enhanced lateral control of autonomous vehicles. The
Koopman operator is a linear map representing the nonlinear dynamics in an
infinite-dimensional space. Thus, we use the Koopman operator to represent the
nonlinear dynamics of a vehicle in dynamic lane-keeping situations. The
Extended Dynamic Mode Decomposition (EDMD) method is adopted to approximate the
Koopman operator in a finite-dimensional space for practical implementation. We
consider the modeling error of the approximated Koopman operator in the EDMD
method. Then, we design K-SMPC to tackle the Koopman modeling error, where the
error is handled as a probabilistic signal. The recursive feasibility of the
proposed method is investigated with an explicit first-step state constraint by
computing the robust control invariant set. A high-fidelity vehicle simulator,
i.e., CarSim, is used to validate the proposed method with a comparative study.
From the results, it is confirmed that the proposed method outperforms other
methods in tracking performance. Furthermore, it is observed that the proposed
method satisfies the given constraints and is recursively feasible.
