Multi-Hypothesis Interactions in Game-Theoretic Motion Planning

Laine, Forrest; Fridovich-Keil, David; Chiu, Chih-Yuan; Tomlin, Claire J.

doi:10.1109/icra48506.2021.9561695

Cited by 13 publications

(11 citation statements)

References 19 publications

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“…We consider two variants, with σ polite = 0 and σ polite = 5. This example is similar to games explored in [12]. Visualizations of the GFQNE solutions for the two variants are given in Figure 1, and computation details for the σ polite = 5 case are given in Table 1 (details for the case σ polite = 0 are omitted for brevity).…”

Section: Examplementioning

confidence: 99%

“…Introduction. There has been a recent growing interest in the application of game-theoretic concepts to applications in automated systems, as explored in [12,19,3,2,8,9,4,7]. Indeed, numerous problems arising in these domains can be modeled as games, and particularly as dynamic or repeated games.…”

mentioning

confidence: 99%

“…This type of solution is capable of capturing strategies for a player which anticipate and account for the reaction of other players. Some advantages of this type of solution are explored in the autonomous driving context in, e.g., [12].…”

mentioning

confidence: 99%

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The Computation of Approximate Generalized Feedback Nash Equilibria

Laine¹,

Fridovich-Keil²,

Chiu³

et al. 2021

Preprint

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We present the concept of a Generalized Feedback Nash Equilibrium (GFNE) in dynamic games, extending the Feedback Nash Equilibrium concept to games in which players are subject to state and input constraints. We formalize necessary and sufficient conditions for (local) GFNE solutions at the trajectory level, which enable the development of efficient numerical methods for their computation. Specifically, we propose a Newton-style method for finding game trajectories which satisfy the necessary conditions, which can then be checked against the sufficiency conditions. We show that the evaluation of the necessary conditions in general requires computing a series of nested, implicitly-defined derivatives, which quickly becomes intractable. To this end, we introduce an approximation to the necessary conditions which is amenable to efficient evaluation, and in turn, computation of solutions. We term the solutions to the approximate necessary conditions Generalized Feedback Quasi Nash Equilibria (GFQNE), and we introduce numerical methods for their computation. In particular, we develop a Sequential Linear-Quadratic Game approach, in which a locally approximate LQ game is solved at each iteration. The development of this method relies on the ability to compute a GFNE to inequality-and equality-constrained LQ games, and therefore specific methods for the solution of these special cases are developed in detail. We demonstrate the effectiveness of the proposed solution approach on a dynamic game arising in an autonomous driving application.

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Section: Examplementioning

confidence: 99%

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confidence: 99%

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The Computation of Approximate Generalized Feedback Nash Equilibria

Laine¹,

Fridovich-Keil²,

Chiu³

et al. 2021

Preprint

Self Cite

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“…In ref. [215] the authors take uncertainty about the intention of other agents by constructing multiple hypotheses about the objectives and constraints of other agents in the scene.…”

Section: Game Theoretic Modelsmentioning

confidence: 99%

Social Interaction‐Aware Dynamical Models and Decision‐Making for Autonomous Vehicles

Crosato,

Tian,

Shum

et al. 2023

Advanced Intelligent Systems

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Interaction‐aware autonomous driving (IAAD) is a rapidly growing field of research that focuses on the development of autonomous vehicles (AVs) that are capable of interacting safely and efficiently with human road users. This is a challenging task, as it requires the AV to be able to understand and predict the behaviour of human road users. In this literature review, the current state of IAAD research is surveyed. Commencing with an examination of terminology, attention is drawn to challenges and existing models employed for modeling the behaviour of drivers and pedestrians. Next, a comprehensive review is conducted on various techniques proposed for interaction modeling, encompassing cognitive methods, machine‐learning approaches, and game‐theoretic methods. The conclusion is reached through a discussion of potential advantages and risks associated with IAAD, along with the illumination of pivotal research inquiries necessitating future exploration.

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“…However, computational methods were historically limited to highly-structured problems such as those found in linear robust control [4,18]. Recent work on iterative linear-quadratic methods [15,24,25] extends these ideas to more general games such as those found in noncooperative robotic planning.…”

Section: B Trajectory Gamesmentioning

confidence: 99%

Learning Mixed Strategies in Trajectory Games

Peters¹,

Fridovich-Keil²,

Ferranti³

et al. 2022

Preprint

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In multi-agent settings, game theory is a natural framework for describing the strategic interactions of agents whose objectives depend upon one another's behavior. Trajectory games capture these complex effects by design. In competitive settings, this makes them a more faithful interaction model than traditional "predict then plan" approaches. However, current game-theoretic planning methods have important limitations. In this work, we propose two main contributions. First, we introduce an offline training phase which reduces the online computational burden of solving trajectory games. Second, we formulate a lifted game which allows players to optimize multiple candidate trajectories in unison and thereby construct more competitive "mixed" strategies. We validate our approach on a number of experiments using the pursuit-evasion game "tag."

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Multi-Hypothesis Interactions in Game-Theoretic Motion Planning

Cited by 13 publications

References 19 publications

The Computation of Approximate Generalized Feedback Nash Equilibria

The Computation of Approximate Generalized Feedback Nash Equilibria

Social Interaction‐Aware Dynamical Models and Decision‐Making for Autonomous Vehicles

Learning Mixed Strategies in Trajectory Games

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