Time-optimal trajectory planning for unmanned ships along a specified path based on the phase plane

This study addresses the under-explored dynamic characteristics of unmanned ships in trajectory planning by constructing a constraint space in the navigation state-phase plane. First, we employ a path-velocity decoupling approach to transform the vessel's inherently complex, multi-state dynamic model into a single-state-variable representation. This decoupling separates geometric path planning from speed scheduling, reducing computational complexity. Next, through targeted variable transformations and parameter adjustments, we introduce a path influence suppression mechanism that minimizes geometric effects on speed dynamics, yielding a simplified model with one state variable and one control input. Building on this foundation, we propose the Finite Trajectory Phase-Plane (FTP) method to derive the Maximum Feasible Velocity Curve (MFVC). By analyzing the hull's hydrodynamic forces and resistance, we establish inequality constraints in the phase plane and delineate the feasible region for velocity as a function of path position. A prescribed speed-task schedule further refines this region, enabling precise computation of the MFVC and achieving optimal path-speed matching. Finally, we validate our methodology through trajectory planning and tracking control experiments involving Lissajous figure and irregular curve. Under various curvature conditions, the FTP method successfully yields time-optimal trajectories that fully respect the ship's dynamic constraints. Experimental results confirm that the proposed approach enhances trajectory accuracy, feasibility, and practical operability for autonomous unmanned ship navigation.