  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.
