Optimal vehicle trajectory planning in the context of cooperative merging on highways

One of the main triggers of traffic congestion on highways is vehicle merging at on-ramps. The development of automated procedures for cooperative vehicle merging is aimed to ensure safety and alleviate congestion problems. In this work, a longitudinal trajectory planning methodology is presented, developed to assist the merging of vehicles on highways; it achieves safe and traffic-efficient merging, while minimizing the engine effort and passenger discomfort through the minimization of acceleration and its first and second derivatives during the merging maneuver. The problem is formulated as a finite-horizon optimal control problem and is solved analytically. This enables the solution to be stored on-board, saving computational time and rendering the methodology suitable for practical applications. The tunable weights, used for taking into account the different optimization criteria, may serve as parameters to match the individual driver's preferences. The proposed methodology is first developed for a pair of cooperating vehicles, a merging one and its putative leader. Moreover, an alternative solution procedure via a time-variant Linear-Quadratic Regulator approach is also presented. A Model Predictive Control (MPC) scheme is utilized to compensate possible disturbances in the trajectories of the cooperating vehicles, whereby the analytical optimal solution is applied repeatedly in real time, using updated measurements, until the merging procedure is actually finalized. Subsequently, the methodology is generalized for a set of vehicles inside the merging area. Various numerical simulations illustrate the validity and applicability of the method.