Trajectory optimization for a high speed planing boat based on Gauss pseudospectral method

In this paper, the problem of Optimal Trajectory Planning for a high speed planing boat under nonlinear equality and inequality path constraints, is addressed. First, a nonlinear mathematical model of the craft's dynamic is constructed. To solve a trajectory optimization problem, we can utilize the indirect or direct methods. In the indirect methods, the maximum principle of Pontryagin is used to transform the optimal control problem into Euler-Lagrange equations, on the other hand, in the direct methods it is necessary to transcribe the optimal control problem into a nonlinear programming problem (NLP) by discretization of states and controls. The resulted NLP can be solved by well-developed algorithms such as SNOPT. We use direct method to optimize the trajectories by solving an optimal control problem using the Gauss pseudospectral method (GPM). An example of boat berthing in a circular obstacle environment is presented to demonstrate the effectiveness of the approach for designing optimal maneuvers.