Nonlinear Wave Equation-Based PD Control for Course Deployment of Unmanned Surface Vehicles

This paper investigates the problem of course de-ployment for multiple unmanned surface vehicles (USVs) based on the nonlinear wave equation derived from the Norrbin model. The proposed method, different from other existing course con-trollers, can accurately estimate unknown external disturbances and rapidly achieve the course deployment of multiple USVs. Firstly, the Norrbin model of unmanned ship is transformed into a second-order nonlinear wave equation error model by introducing course angle error, so that the deviation between the actual course angle and the expected course angle can be converging depending on the relative course angle information of each ship under the influence of disturbance. Secondly, based on the constructed disturbance observer, a course PD controller with anti-interference capability is designed, which can accurately estimate the disturbance and realize the course deployment from different initial course angle to the expected course angle for each ship in the large-scale unmanned ship cluster. Then, the sufficient linear matrix inequalities (LMIs) condition is derived by using the Lyapunov theory, and the stability of course deployment control of the multi-USV is demonstrated. Finally, a numerical simulation is conducted to validate the effectiveness of the proposed approach.