Autonomous Driving using Linear Model Predictive Control with a Koopman Operator based Bilinear Vehicle Model

Abstract

This paper presents a real-time Model Predictive Control (MPC) formulation for autonomous driving based on a lifted bilinear vehicle model developed using the Koopman operator. Koopman operator based models can closely mimic the original nonlinear behaviors with a higher dimensional linear structure, which is attractive for computationally efficient linear MPC formulations for controlling nonlinear systems. However, current linear models based on linear Koopman realizations cannot capture the control-affine dynamics in nonlinear systems. This may result in large discrepancies between the original nonlinear system and the data-driven linear model, hindering its use in MPC. To address this gap, first, a novel Koopman bilinear vehicle model that takes control-affine dynamics into consideration is constructed and tested in open-loop simulations. This bilinear Koopman model is then linearized to serve as a prediction model in MPC, and is shown to have higher accuracy compared to the state-of-the-art linear models. The model is then used to develop a linear MPC formulation for simultaneous planning and control of an autonomous vehicle. The formulation is tested on lane change scenarios with obstacles against the nonlinear MPC and standard linear MPC benchmarks. The results show that the new formulation can achieve a lane change performance closer to the nonlinear MPC with a computational performance similar to the standard linear MPC. The new formulation is observed to be successful in handling high speeds where the standard linear MPC fails.