Optimal control problems for safe and efficient lane changes of self-driving vehicles

Intelligent Transportation Systems (ITS) aim at increasing the traffic throughput and safety, reducing the total travel time and traffic congestion using novel achievements of communication and control technologies. In particular, the development of self-driving vehicles is an important application of ITS that is expected to show a considerable impact in the near future. When implementing self-driving vehicles, the realization of lane changes is a necessary task. Accordingly, this thesis focuses on the computation of longitudinal and lateral maneuvers during lane changes. The thesis first determines several models for the longitudinal and lateral vehicle dynamics that are deemed suitable for representing normal driving situations. In addition, a novel method for decoupling the longitudinal and lateral motion is proposed. Based on the vehicle models, an optimal control problem for lane change maneuvers is formulated and two methods for the solution of this optimal control problems are developed. The first method is a direct collocation method. Using a given number of collocation points, the optimal control problem is converted to a nonlinear programming problem that can be solved by standard nonlinear programming solvers. The second method is gradient-based. Using a first-order approximation of the system model, a gradient-based search achieves an approximation of the optimal control solution. It is observed during the thesis study that the optimal control solutions cannot be determined in real-time. In order to address this problem, the thesis further studies the approximation of the optimal control trajectories by curves that can be parametrized analytically and that can be computed in real-time. To this end, bi-elementary paths that are based on clothoid curves and their analytical approximation by bi-elementary arc-splines are found suitable. The thesis proposed computational methods for the fast computation of lane change trajectories using these curves. As an application of the developed results, the thesis considers the recent technology of cooperative adaptive cruise control (CACC) for tight vehicle following. Existing CACC designs assume straight roads and hence only consider the longitudinal vehicle dynamics. The thesis extends the existing results to the case of CACC on curved roads.