Optimal Control of Automated Vehicles for Autonomous Intersection Management With Design Specifications

In this article, we study optimal control of automated vehicles (AVs) at an autonomous intersection with design specifications, where the intersection manager (computer) controls the acceleration/deceleration of AVs within a control region to determine their conflict-free trajectories. We develop a mathematical model to describe the cooperative dynamics of vehicles within the control zone of a signal-free intersection. Further, we formulate an optimization problem with the objective of maximizing traffic throughput while minimizing passenger discomfort. We then address the problem using mathematical programming to yield the optimal control input for each vehicle inside the control zone. We apply the proposed control mechanism for optimally coordinating the movement of AVs at an autonomous intersection subject to physical and safety constraints. In other words, the solution, if implemented, would allow vehicles to pass the intersection with safety guarantees (avoiding collisions), high-level efficiency (maximizing throughput), and good comfort (minimizing discomfort) without deploying traffic lights. In addition, we derive analytical specifications for the design and deployment of autonomous intersections, which appears to have been largely ignored in prior studies. Finally, we conduct a series of numerical experiments to show the effectiveness of the methodology proposed in this article. As the framework developed here is fairly general and can be extended to cover many complex traffic scenarios, we believe that the procedure presented in this article will be useful with the advent of AVs in the near future.