Automatic parking via bidirectional planning with model predictive control

This paper studies an online automatic parking control problem based on a bidirectional model predictive control (MPC) formulation that considers forward-time motion from an initial state and backward-time motion from a target state simultaneously. By incorporating the terminal condition into the MPC cost function as a soft constraint, the bidirectional formulation becomes suitable for online implementation. However, this relaxation means that the forwardtime and backward-time trajectories are not forced to coincide exactly. To compensate for this mismatch, a complete online control scheme is proposed based on the bidirectional MPC with online reversal-point determination and trajectory tracking. Numerical examples show that the proposed method can generate feasible parking maneuvers while determining the reversal point online, even when the forward-time and backward-time trajectories do not merge exactly. The results also indicate that appropriate weighting design in the MPC cost function is important for shaping vehicle behavior and naturally reproducing parking motions consistent with human driving behavior.