Trajectory planning for autonomous surface vehicles based on linear quadratic regulator and control space sampling

• An algorithm based on state space equations, which establishes the coupled mapping between system’s kinematic states and discretized control inputs, thereby ensuring that the generated trajectories adhere to the kinematic constraints of the ASV. • A comprehensive cost function that integrates both heuristic distance guidance and control effort, enabling a balanced optimization. The proposed method achieves a theoretically grounded trade-off between global optimality and local dynamic feasibility. • A grid-based trajectory pruning mechanism that uses terminal position linear projection and minimum-cost screening, which significantly reduces computational complexity while preserving the quality of feasibility of the resulting solutions. In response to the limitations of traditional planning methods for Autonomous Surface Vehicles (ASVs), which heavily rely on predefined map representations and neglect kinematic feasibility, this paper proposes a novel kinematic trajectory planning method based on control space sampling for ASVs in complex environments. The proposed planning method integrates control space sampling, kinematic state space equation, and a multi-objective cost function to generate kinematically feasible trajectories while ensuring computational efficiency. By sampling the control input space and deriving state transition trajectories through system kinematics, the dependency on grid-based maps is eliminated and the characteristics of ASV motion are considered. A comprehensive cost function is designed to balance the global path length optimization with local state, control, and predicted cost minimization. Meanwhile, a grid-based redundancy pruning mechanism is proposed to reduce computational complexity. It is demonstrated in the feasibility study that the proposed planning method outperforms conventional methods by generating smoother trajectories with reduced control effort. Finally, a series of experimental tests based on a trial ship are conducted to verify the ability of the proposed method.