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This paper presents the design of a supervisory algorithm that monitors safety at road intersections and overrides drivers with a safe input when necessary. The design of the supervisor consists of two parts: safety verification and control design. Safety verification is the problem to determine if vehicles will be able to cross the intersection without colliding with current drivers' inputs. We translate this safety verification problem into a jobshop scheduling problem, which minimizes the maximum lateness and evaluates if the optimal cost is zero. The zero optimal cost corresponds to the case in which all vehicles can cross each conflict area without collisions. Computing the optimal cost requires solving a Mixed Integer Nonlinear Programming (MINLP) problem due to the nonlinear second-order dynamics of the vehicles. We therefore estimate this optimal cost by formulating two related Mixed Integer Linear Programming (MILP) problems that assume simpler vehicle dynamics. We prove that these two MILP problems yield lower and upper bounds of the optimal cost. We also quantify the worst case approximation errors of these MILP problems. We design the supervisor to override the vehicles with a safe control input if the MILP problem that computes the upper bound yields a positive optimal cost. We theoretically demonstrate that the supervisor keeps the intersection safe and is non-blocking. Computer simulations further validate that the algorithms can run in real time for problems of realistic size.

Abstract-This paper describes the design of a supervisory controller (supervisor) that manages controlled vehicles to avoid intersection collisions in the presence of uncontrolled vehicles. Two main problems are addressed: verification of the safety of all vehicles at intersections, and management of the inputs of controlled vehicles. As for the verification, we apply an inserted idle-time scheduling approach [1] where the term "inserted idle-time" represents the time interval when an intersection is deliberately held idle for uncontrolled vehicles to safely cross the intersection. As for the management, the supervisor is least restrictive in the sense that it overrides all controlled vehicles when an safety violation becomes imminent. In a centralized control system, a computational complexity issue arises. We address this with an efficient version of scheduling using an inflated intersection. The solutions assure the safety of uncontrolled as well as controlled vehicles. It also offers the advantages of increasing traffic flow and energy efficiency.

In this paper, we design a supervisor to prevent vehicle collisions at intersections. An intersection is modeled as an area containing multiple conflict points where vehicle paths cross in the future. At every time step, the supervisor determines whether there will be more than one vehicle in the vicinity of a conflict point at the same time. If there is, then an impending collision is detected, and the supervisor overrides the drivers to avoid collision. A major challenge in the design of a supervisor as opposed to an autonomous vehicle controller is to verify whether future collisions will occur based on the current drivers choices. This verification problem is particularly hard due to the large number of vehicles often involved in intersection collision, to the multitude of conflict points, and to the vehicles dynamics. In order to solve the verification problem, we translate the problem to a job-shop scheduling problem that yields equivalent answers. The job-shop scheduling problem can, in turn, be transformed into a mixed-integer linear program when the vehicle dynamics are first-order dynamics, and can thus be solved by using a commercial solver.

Abstract-This paper describes the implementation of a multi-vehicle supervisor to prevent collisions at intersections. The experiments are performed on an intersection testbed consisting of three RC cars. Here, we account for uncertainty in car dynamics and state measurement, and the presence of an uncontrolled car, which is human-driven. The supervisor overrides the controlled cars only when necessary to avoid a possible future collision. From the experiments, we demonstrate that intersection collisions are averted, that is, the cars continuously and safely run on the paths without stopping 92.8% of times.