Optimal and least restrictive supervisory control: Safety verification methods for human-driven vehicles at traffic intersections

Abstract

We consider a cooperative conflict resolution problem at traffic intersections. Our goal is to design a least restrictive supervisor able to identify the optimal corrections to a human-decided input with respect to a given performance index, while keeping the system safe. Here, safety is formulated in terms of a maximal safe controlled invariant set. Leveraging results from scheduling theory, we characterize the preorder of the optimal solution set and propose an efficient optimization algorithm providing Pareto optimal solutions. We illustrate the application of the proposed algorithm through simulations in which vehicles crossing an intersection are optimally overridden by the supervisor only when necessary to maintain safety.

Optimal Path Planning for Connected and Automated Vehicles at Urban Intersections

“…Miculescu and Karaman [17] used queueing theory and modeled the problem as a polling system with two queues and one server that determines the sequence of times assigned to the vehicles on each road. Other research efforts have employed scheduling theory based on which the vehicles can make a decision about the appropriate schedule of crossing an intersection [18], [19]. Colombo and Del Vecchio [20] constructed the invariant set for the control inputs that ensure lateral collision avoidance.…”

“…Moreover, we augment the double integrator model representing a CAV with an additional state corresponding to the distance from its preceding CAV, thus we are able to address the lateral colision constraint in the low-level optimization. Second, in several efforts reported in the literature to date, the upper-level optimization either (a) was implemented with centralized approaches [14], [15], [17]- [19]; or (b) was considered given [35], [38]; or (c) was implemented using a strict first-in-first-out queueing structure [27], [29], [32], [36]. In our proposed framework, the upper-level optimization yields, in a decentralized fashion, the optimal time for each CAV to pass a given traffic scenario along with the appropriate lane that needs to occupy.…”

An Algorithm for Supervised Driving of Cooperative Semi-Autonomous Vehicles

“…However, this scheme is rather intrusive as drivers completely relinquish control for a time, and handing back controls to a potentially distracted driver poses problems by itself. Colombo et al [7], [8] introduced the idea of a supervisory instance (called supervisor) tasked with preventing the system of vehicles from entering undesirable states by overriding the controls of one or several vehicles. In this more human-friendly approach, overriding only occurs when necessary, i.e.…”

“…Reference [25] leverages job-shop scheduling to develop a supervisor that considers several possible conflict points inside the intersection; however, vehicle dynamics are only modeled as first-order integrators, which is not realistic in a real-world setting. Campos et al [8] proposed a Pareto-optimal supervisor leading to a minimally deviating formulation by recursively finding the most constrained vehicle, reserving its optimal crossing time, and scheduling the crossing of the remaining vehicles using the previous schedule as constraints. This method allows to minimize the deviation between the overridden and desired controls, but may be computationally intensive.…”

“…In this article, we consider a method to ensure the safety of multiple semi-autonomous vehicles on conflicting paths, for instance crossing an intersection or entering a highway, while remaining compatible with the presence of human drivers. To this end, and inspired by earlier work in [7], [8], we propose a so-called Supervisor which monitors control inputs from each vehicle's driver, and is able to override these controls when they would result in an unsafe situation. More specifically, the role of the supervisor is twofold: first, knowing the current states of the vehicles, the supervisor should determine if the controls requested by the drivers would lead the vehicles into unsafe inevitable collision states [9].…”