We propose an integrated behavior and motion planning framework for the automated lane-merging problem. The behavior planner combines search-based planning with game theory to model the interaction between vehicles and select multi-vehicle trajectories. Inspired by human drivers, we model the lane-merging problem as a gap selection process. To overcome the challenge of multi-modal driving behavior exhibited by the surrounding vehicles, we formulate the trajectory selection as a matrix game and compute some equilibrium solutions. In practice, however, the surrounding vehicles might deviate from the computed equilibrium trajectories. Thus, we introduce a branch model predictive control (BMPC) framework to account for the uncertain behavior modes of the surrounding vehicles. A tailored numerical solver is developed to enhance computational efficiency by leveraging 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.

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