K-SMPC: Koopman Operator-Based Stochastic Model Predictive Control for Enhanced Lateral Control of Autonomous Vehicles

Abstract

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.