Automated Lane Merging via Game Theory and Branch Model Predictive Control

TL;DR

The paper addresses lane-merging in dense traffic with $N$ vehicles by modeling interactions via game theory and integrating motion planning with predictive control. It introduces a two-layer GT-BMPC framework: a behavior planner that forms a matrix game between the ego vehicle and a vehicle group to output multi-vehicle trajectories, and a BMPC module that uses a trajectory tree to account for multiple equilibrium strategies with belief updates over $\omega_t$. Contributions include semantic-level actions, interaction-aware forward simulation, Bayesian belief over $\omega_t$, a tailored iLQR-tree solver exploiting the trajectory-tree structure, and validation on the INTERACTION dataset showing improved safety and driving comfort. The approach enables real-time, less-conservative lane merging in interactive traffic, with potential for broader adoption in autonomous driving.

Abstract

We propose an integrated behavior and motion planning framework for the lane-merging problem. The behavior planner combines search-based planning with game theory to model vehicle interactions and plan multi-vehicle trajectories. Inspired by human drivers, we model the lane-merging problem as a gap selection process and determine the appropriate gap by solving a matrix game. Moreover, we introduce a branch model predictive control (BMPC) framework to account for the uncertain equilibrium strategies adopted by the surrounding vehicles, including Nash and Stackelberg strategies. A tailored numerical solver is developed to enhance computational efficiency by exploiting the tree structure inherent in BMPC. Finally, we validate our proposed integrated planner using real traffic data and demonstrate its effectiveness in handling interactions in dense traffic scenarios. The code is publicly available at: https://github.com/SailorBrandon/GT-BMPC.

Figures (8)

• Figure 1: Structure of the proposed game-theoretic planner. The behavior planner outputs the multi-vehicle trajectories that represent different equilibrium strategies. The BMPC planner utilizes the so-called trajectory tree to account for the potential behavior modes of the surrounding vehicles. In this example, the separate tree branches handle two distinct behavior modes (equilibrium strategies) of the interacting vehicle (pink), whereas the shared part (green) needs to accommodate both potential behavior modes.
• Figure 2: (a): The lane-merging problem: three gaps are available for the ego vehicle to choose from: Gap0, Gap1 and Gap2. The dashed red lines represent the centerlines of the lanes, and the dashed blue line represents the probing line. EV stands for the ego vehicle (blue), while SV0, SV1, SV2 and SV3 denote the surrounding vehicles. (b)-(c): Illustrate the interaction graphes when EV selects Gap1 and Gap2, respectively. The single-headed arrow indicates one-way influence, while double-headed arrows denote mutual interaction.
• Figure 3: Multi-vehicle forward simulation. $|x^l-x^f|$ and $|y^l-y^f|$ represent the longitudinal and lateral distances between the lane-changing vehicle (leader) and the interacting vehicle (follower), respectively.
• Figure 4: Trajectory tree with a horizon of $T = 2$. The tree branches out at each time step based on the behavior mode $\omega_t \in \Omega:= \{\omega^1, \omega^2\}$. A transition probability $P_i$ pertains to each branch. In this example, $\mathcal{N} = \{0,1,2,3,4,5,6\}$ and $\mathcal{L} = \{3,4,5,6\}$.
• Figure 5: Simplified trajectory tree. The tree has multiple branches exclusively at the root node, while all other nodes, except for the leaf nodes, have only one single branch.

Theorems & Definitions (2)

• Definition 1
• Definition 2