Phased manifold-based RRT*: An optimized motion planning approach for autonomous bow-in berthing of inland vessels

To address the issue of autonomous bow-in berthing for inland vessels under environmental influence, a phased manifold-based rapidly-exploring random tree star (PMRRT*) approach is proposed for the trajectory and posture planning (TPP). A systematic framework for bow-in berthing, employing a U-turn or alongside strategy, is developed by partitioning its procedure into collision-free berthing phase and the terminal berthing phase. In the first collision-free berthing phase, the constraint manifold is incorporated to the RRT* algorithm based on water depth, flow, vessel’s dynamics. Meanwhile, the sampling space of RRT* is extended from the configuration space to the state space, and each branch samples the vessel’s position, heading and speed, all constrained by the corresponding dynamic constraint manifolds. The second terminal berthing phase initiates when the vessel is positioned close to the berth, at which point a Bezier curve is employed to design the motion trajectory, considering the orientations of the terminal points. Then, throughout the motion, the vessel’s speed and heading are allocated based on the geometric characteristics of the motion, and an inverse proportional function is applied to regulate the vessel’s speed continuous decay. Simulational experiments with actual water depth and flow data demonstrate that the proposed PMRRT* method achieves higher berthing accuracy compared to traditional RRT*, artificial potential field, and A-star methods, the final heading error remains within 8°, meanwhile achieving the lower steering frequency and reduced heading fluctuations with acceptable computational real-time performance. Moreover, the scale-model berthing experiments in real-world tank further verify the effectiveness of the PMRRT* strategy.