Game-Theoretic Modeling of Multi-Vehicle Interactions at Uncontrolled Intersections

Game-Theoretic Modeling of Traffic in Unsignalized Intersection Network for Autonomous Vehicle Control Verification and Validation

“…where (x i , y i ), v i , and θ i represent, respectively, the vehicle's position in the ground-fixed frame, its speed, and its heading angle, the inputs a i and ω i represent, respectively, the vehicle's acceleration and heading angle rate, while t is the sampling period for decision-making. The second part s i,2 = (r i , ξ i ) contains additional information related to the vehicle's decision-making objective, including r i = (r i x , r i y ), representing a target/reference position to go, and ξ i , a feature vector containing key information about the road layout and geometry such as the road width, the angle of intersection, and etc [35]. When vehicle i is driving toward, in the middle of, or exiting a specific intersection, s i,2 stays constant with r i being a point located in the center of the vehicle's target lane; s i,2 gets updated after the vehicle has returned to straight road and is driving toward the next intersection.…”

“…In [35], we modeled the interactions among vehicles at unsignalized intersections, but using a different game-theoretic approach from the one used in this paper. Specifically, in [35], we modeled vehicle interactions based on a formulation of a leader-follower game; while in this paper, we consider the application of level-k game theory [36], [37].…”

“…In [35], we modeled the interactions among vehicles at unsignalized intersections, but using a different game-theoretic approach from the one used in this paper. Specifically, in [35], we modeled vehicle interactions based on a formulation of a leader-follower game; while in this paper, we consider the application of level-k game theory [36], [37]. The control strategies of all interacting vehicles modeled using the framework of [35] are homogeneous; while the control strategies of different vehicles modeled using the scheme of this paper are heterogeneous, differentiated by their level-k control policies with different k = 0, 1, 2, .…”

“…This heterogeneity can be used to represent the different driving styles among different drivers, e.g., aggressive driving versus cautious/conservative driving. In addition, [35] models a single intersection with up to 10 interacting vehicles; while in this paper, thanks to the effective application of the aforementioned solution approach integrating game theory, receding-horizon optimization, and imitation learning to obtain control policies, the scheme of this paper can be used to model much larger road systems involving many intersections and many vehicles with manageable online computational effort. This enables the investigation into driving characteristics that are exhibited when a vehicle drives through multiple road segments, such as overall travel time, fuel consumption, etc.…”

“…A road system with 15 intersections and 30 vehicles is illustrated as an example in Section IV. Furthermore, application of the developed traffic models to verification and validation of AV control systems is comprehensively discussed in this paper, but not in [35].…”