Closed-Loop Modeling of a Quintic Trajectory Planning and PID Motion Control System

Autonomous and assisted driving features such as lane centering, lane change, and evasive maneuver assistance rely on two interconnected modules, trajectory planning and motion control. To optimize performance by tuning parameters and to understand system characteristics, a closed-loop model that encompasses both trajectory planning and motion control, as well as the vehicle's lateral dynamics, is necessary. Although several studies have focused on developing closed-loop models that involve the motion control module, relatively little research has been conducted on developing combined representative models that integrate trajectory planning and motion control with vehicle lateral dynamics. This study aims to derive a closed-loop transfer function that includes a quintic trajectory planning module in the Frenet coordinate and a PID motion controller, with the objective of improving the lane centering feature performance in a real vehicle.