Path Following of a High Speed Planing Boat Based on Gauss Pseudospectral Method

Abstract

In this paper, the problem of optimal path following for a high speed planing boat is addressed. First, a nonlinear mathematical model of the boat’s dynamics is derived and then the Serret-Frenet frame is presented to facilitate the path following control design. To satisfy the constraints on the states and the input controls of the boat's nonlinear dynamics and minimize both the cross tracking and heading error, a nonlinear optimal controller is formed. To solve the resulted nonlinear constrained optimal control problem, the Gauss pseudospectral method (GPM) is used to transcribe the optimal control problem into a nonlinear programming problem (NLP) by discretization of states and controls. The resulted NLP is then solved by a well-developed algorithm known as SNOPT. The results illustrate the effectiveness of the proposed approach to tackle the boat path following problem.