Constrained optimization control techniques with preview are designed in this paper to derive optimal velocity trajectories in longitudinal vehicle following mode, while ensuring that the gap from the lead vehicle is both safe and short enough to prevent cut-ins from other lanes. The lead vehicle associated with the Federal Test Procedures (FTP)  is used as an example of the achieved benefits with such controlled velocity trajectories of the following vehicle. Fuel Consumption (FC) is indirectly minimized by minimizing the accelerations and decelerations as the autonomous vehicle follows the hypothetical lead. Implementing the cost function in offline Dynamic Programming (DP) with full drive cycle preview showed up to a 17% increase in Fuel Economy (FE). Real time implementation with Model Predictive Control (MPC) showed improvements in FE, proportional to the prediction horizon. Specifically, 20s preview MPC was able to match the DP results. A minimum of 1.5s preview of the lead vehicle velocity with velocity tracking of the lead was required to obtain an increase in FE.
The optimal velocity trajectory found from these algorithms exceeded the presently allowable error from standard drive cycles for FC testing. However, the trajectory was still safe and acceptable from the perspective of traffic flow. Based on our results, regulators need to consider relaxing the constant velocity error margins around the standard velocity trajectories dictated by the FTP to encourage FE increase in autonomous driving.