Coordination and control of autonomous vehicles at urban intersections

This thesis is devoted to the investigation of multi-agent systems theory within the context of autonomous intersection management. It is divided into two main parts: the first and main part addresses the problem of autonomous vehicles crossing an intersection; the second part focuses on the control of multi-agent systems in the scenario of a group of autonomous agents pursuing the objective of forming a uniformly spaced string. In the section regarding autonomous intersection management, a geometric approach is employed to establish the foundations of a framework for modeling autonomous intersections. After defining the geometry of the trajectories that vehicles follow, the collision conditions are rigorously modeled to enable the definition of a general optimization problem for describing the intersection scenario: the Intersection Crossing Problem (ICP). The ICP is a functional optimization problem and its solution gives the trajectories vehicles must follow in order to cross the intersection without crashing, while optimizing some predefined quantity of interest. Convex analysis and optimization theory are used to derive results stemming from the proposed theory, which are then used to develop an algorithm that is proven to solve a specialization of the ICP in a finite number of iterations. Practical considerations about the computation time are given to derive some approximation methods that are used to speed up the collision avoidance phase of the algorithm while ensuring safety. The other section deals with the consensus problem in a leaderless network of agents that have to reach a common velocity while forming a uniformly spaced string. Moreover, the final common velocity (reference velocity) is determined by the agents in a distributed and leaderless way. Then, the consensus protocol parameters are optimized for networks characterized by a communication topology described by a class of directed graphs having a directed spanning tree, in order to maximize the convergence rate and avoid oscillations. Finally, necessary and sufficient conditions are derived to guarantee consensus in the presence of a constant delay. The advantages of the optimized consensus protocol are enlightened by some simulation results and comparisons with a protocol proposed in the related literature. This thesis is organized into six chapters. Chapter 1 introduces the work and outlines its main contributions. Chapter 2 is the review of the available literature on the topic of autonomous intersection management and multi-agent systems. Chapter 3 covers the mathematical tools used to develop the proposed results. Chapter 4 presents the ICP and the proposed distributed algorithm for its solution. Chapter 5 exposes the contributions in the field of leaderless multi-agent systems. Chapter 6 contains remarks and considerations for future work.