Mitigating Output Redefinition Error in Trajectory Planning for Underactuated Unmanned Surface Vehicles

Underactuated unmanned surface vehicles (USVs) lack surge-direction controllers, making it difficult to accomplish motion control tasks. To address the issue that available control inputs in the yaw direction cannot directly correspond to position error, an output redefinition method is used to shift the control object from the centroid to offset point with a small distance therefrom. This approach directly takes the point's position as the control object to avoid underactuation issues, but it introduces tracking error. This paper proposes a trajectory planning method for underactuated USVs to mitigate output redefinition error. The method translates each point of a known desired trajectory by a certain distance along its tangent direction with sideslip angle compensation, which is used to make up for the inconsistency between the USV's moving direction and the tangential direction of the desired trajectory, and finally generates a new trajectory for the offset point. This ensures the USV centroid follows the original desired trajectory when the offset point tracks the new one. Compared with direct tracking, it mitigates error due to output redefinition, enabling more accurate trajectory following. Simulation results validate the method's effectiveness.