A decomposition algorithm for Nash equilibria in intersection management

Britzelmeier, Andreas; Dreves, Axel

doi:10.1080/02331934.2020.1786088

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…These conditions have been partially exploited, in combination with additional assumptions on the dynamics and the payoffs, to obtain scenarios in which it is easier to prove existence of NE and to find them. For example [20] makes convexity assumptions about the bestresponse sets and how the control signal parametrizes the dynamics, while [21] obtains similar results when paths are fixed and the vehicles control only the acceleration.…”

Section: Introductionmentioning

confidence: 92%

Urban Driving Games With Lexicographic Preferences and Socially Efficient Nash Equilibria

Zanardi

Mion

Bruschetta

et al. 2021

IEEE Robot. Autom. Lett.

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We describe Urban Driving Games (UDGs) as a particular class of differential games that model the interactions and incentives of the urban driving task. The drivers possess a "communal" interest, such as not colliding with each other, but are also self-interested in fulfilling traffic rules and personal objectives. Subject to their physical dynamics, the preference of the agents is expressed via a lexicographic relation that puts as first priority the shared objective of not colliding. Under mild assumptions, we show that communal UDGs have the structure of a lexicographic ordinal potential game which allows us to prove several interesting properties. Namely, socially efficient equilibria can be found by solving a single (lexicographic) optimal control problem and iterated best response schemes have desirable convergence guarantees.

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Section: Introductionmentioning

confidence: 92%

Urban Driving Games With Lexicographic Preferences and Socially Efficient Nash Equilibria

Zanardi

Mion

Bruschetta

et al. 2021

IEEE Robot. Autom. Lett.

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“…This kind of Nash equilibrium is particularly suited for socially aware motion planning as for such an equilibrium the Lagrange multipliers associated with the shared constraints are equal among all players, which introduces some notion of fairness among the players. This idea has been used in various recent papers on traffic control, i.e., without human drivers, such as [12], [13], where ellipsoidal constraints are used to enforce safety. As ellipsoidal overapproximations seem less suitable to model human behavior and may furthermore be conservative in small distances (where interaction is more pronounced), we instead extend the collision avoidance formulation of [14], which involves no approximation of rectangular obstacles.…”

Section: A Background and Motivationmentioning

confidence: 99%

“…(13d) The main idea behind the parameter estimation procedure is to select parameter values θ := (θ i ) i∈H , such that the observed behavior approximately matches the optimality conditions (13). This naturally leads to the following parameter estimation procedure: Given the current estimate θt for the parameters, set the updated parameters θt+1 as the solution of minimize θ, u, y ∇ u L Σ (u, y; θ)…”

Section: Online Learning Of Parametersmentioning

confidence: 99%

Learning MPC for Interaction-Aware Autonomous Driving: A Game-Theoretic Approach

Evens

Schuurmans

Patrinos

2022

2022 European Control Conference (ECC)

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We consider the problem of interaction-aware motion planning for automated vehicles in general traffic situations. We model the interaction between the controlled vehicle and surrounding road users using a generalized potential game, in which each road user is assumed to minimize a common cost function subject to shared (collision avoidance) constraints. We propose a quadratic penalty method to deal with the shared constraints and solve the resulting optimal control problem online using an Augmented Lagrangian method based on PANOC. Secondly, we present a simple methodology for learning preferences and constraints of other road users online, based on observed behavior. Through extensive simulations in a highway merging scenario, we demonstrate the practical efficacy of the overall approach as well as the benefits of the proposed online learning scheme.

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“…In contrast, in an emergency such as after a collision, interacting vehicles have to be explicitly cooperative to stabilise themselves on the road and protect their safety as well as others [21]. Platooning under Nash optimality [22], intersection management with generalised Nash equilibrium [23], and lane‐change via non‐cooperative game theory [24] are some of the CAVs problems solved by applying non‐cooperative games. In this paper, we propose a differential game‐based platoon control scheme under the framework of non‐cooperative differential games.…”

Section: Introductionmentioning

confidence: 99%

Connected and automated vehicle platoon formation control via differential games

Jond

Yildiz

2022

IET Intelligent Trans Sys

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In this study, the connected and automated vehicles platooning problem is resolved under a differential game framework. Three information topologies are considered here. Firstly, the Predecessor-following topology is utilised where the vehicles control the distance with respect to the merely nearest predecessor via a sensor link-based information flow. Secondly, the Two-predecessor-following topology is exploited where each vehicle controls the distance with respect to the two nearest predecessors. In this topology, the second predecessor is communicated via a Vehicle-to-vehicle link. The individual trajectories of connected and automated vehicles under the Nash equilibrium are derived in closed-form for these two information topologies. Finally, general information topology is examined and the differential game is formulated in this context. In all these options, Pontryagin's principle is employed to investigate the existence and uniqueness of the Nash equilibrium and obtain its corresponding trajectories. In the general topology, we suppose numerical computation of eigenvalues and eigenvectors. Finally, the stability behaviour of the platoon for the Predecessor-following, Two-predecessor-following and general topologies are investigated. All these approaches represent promising and powerful analytical representations of the connected and automated vehicle platoons under the differential games. Simulation experiments have verified the efficiency of the proposed models and their solutions as well as their better results in comparison with the Model Predictive Control.

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A decomposition algorithm for Nash equilibria in intersection management

Cited by 7 publications

References 18 publications

Urban Driving Games With Lexicographic Preferences and Socially Efficient Nash Equilibria

Urban Driving Games With Lexicographic Preferences and Socially Efficient Nash Equilibria

Learning MPC for Interaction-Aware Autonomous Driving: A Game-Theoretic Approach

Connected and automated vehicle platoon formation control via differential games

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