Optimization Strategies for Auto-Berthing of Unmanned Surface Vessels Using Differential Homeomorphism and the Gauss Pseudospectral Method

This paper designs an optimal control strategy for the auto-berthing control (ABC) problem of underactuated surface vessels. The purpose is to achieve accurate berthing of USVs in complex environments. In the traditional ABC problem of surface vessels, the underactuated characteristics of USVs complicate the control design. This underactuated phenomenon is manifested in the lack of lateral driving force on the boat, which restricts its motion to a specific direction. In order to solve the problem of the lack of lateral driving force of USVs, this paper first uses diffeomorphism transformation to transform the original nonholonomic constraint system into a chain structure. Through this transformation, the problem of the state of the vessel being restricted during motion is avoided. On this basis, this paper further describes the optimal control problem of the USV on the horizontal plane based on the kinematic and dynamic models of the USV. In order to solve the optimal control problem, this paper adopts the Gaussian pseudospectral method (GPM). By discretizing the continuous optimal control problem into a nonlinear programming problem, the computational complexity is effectively reduced and the solution efficiency is improved. The optimal navigation trajectory of the USV system and the corresponding optimal control input are then obtained. In order to verify the feasibility and effectiveness of the proposed control strategy, numerical simulation is carried out. The simulation results show that the optimal control strategy can achieve stable and accurate berthing of USVs.