Integrated Decision Making and Trajectory Planning for Autonomous Driving Under Multimodal Uncertainties: A Bayesian Game Approach

TL;DR

This paper introduces an integrated decision-making and trajectory planning framework based on Bayesian game (i.e., game of incomplete information), and a general solver based on no-regret learning is introduced to obtain a corresponding Bayesian Coarse Correlated Equilibrium.

Abstract

Modeling the interaction between traffic agents is a key issue in designing safe and non-conservative maneuvers in autonomous driving. This problem can be challenging when multi-modality and behavioral uncertainties are engaged. Existing methods either fail to plan interactively or consider unimodal behaviors that could lead to catastrophic results. In this paper, we introduce an integrated decision-making and trajectory planning framework based on Bayesian game (i.e., game of incomplete information). Human decisions inherently exhibit discrete characteristics and therefore are modeled as types of players in the game. A general solver based on no-regret learning is introduced to obtain a corresponding Bayesian Coarse Correlated Equilibrium, which captures the interaction between traffic agents in the multimodal context. With the attained equilibrium, decision-making and trajectory planning are performed simultaneously, and the resulting interactive strategy is shown to be optimal over the expectation of rivals' driving intentions. Closed-loop simulations on different traffic scenarios are performed to illustrate the generalizability and the effectiveness of the proposed framework.

Figures (7)

• Figure 1: Settings of the game of incomplete information for traffic interaction. The game is an extensive-form game containing multiple stages. In the beginning, chance players select types for all players in a chance stage (corresponding to the chance actions in the figure), where the selections are subject to distribution $p$. Then in each of the stages, all players perform a single action in turn. Eventually, the actions of players form a path leading from the root node to one of the leaf nodes, where the payoffs of all players are determined. The notation $I^n_{i,k}$ represents the $k^{th}$ information set of player $i$ at stage $n$, and $a_{I,m}$ denotes the $m^{th}$ action under information set $I$. Each of the information sets contains one or more states, such that the agent to play, under that information set, cannot distinguish between the game states contained in the information set. Therefore it will take the same action (or the same strategic profile of actions) for all the states contained in the information sets. Further, we assume that at the end of each stage except for the chance stage, all the states are distinguishable, and therefore each game state at the end of a stage constitutes an information set at the beginning of the next stage.
• Figure 2: Simulation results for Case I. In all scenarios, AV manages to merge into the main road without collision. Depending on the differentiated behaviors of HVs, AV either merges into the gap between two HVs or merges behind both HVs.
• Figure 3: Longitudinal velocities of AV in different scenarios in Case I.
• Figure 4: Simulation results for Case II. Successful unprotected left-turning is performed in all scenarios without collisions. Adaptive strategies of AV are demonstrated in these figures, which react responsively to different driving modes of HVs to ensure security and successful passing.
• Figure 5: Longitudinal velocities of AV in different scenarios in Case II.

Theorems & Definitions (11)

• Definition 1
• Definition 2
• Definition 3
• Remark 1
• Remark 2
• Theorem 1
• proof
• Theorem 2
• proof
• Remark 3