This paper introduces an accurate nonlinear model predictive control-based algorithm for trajectory following. For accuracy, the algorithm incorporates both the planned state and control trajectories into its cost functional. Current following algorithms do not incorporate control trajectories into their cost functionals. Comparisons are made against two trajectory following algorithms, where the trajectory planning problem is to safely follow a person using an automated ATV with control delays in a dynamic environment while simultaneously optimizing speed and steering, minimizing control effort, and minimizing the time-to-goal. Results indicate that the proposed algorithm reduces collisions, tracking error, orientation error, and time-to-goal. Therefore, tracking the control trajectories with the trajectory following algorithm helps the vehicle follow the planned state trajectories more accurately, which ultimately improves safety, especially in dynamic environments