A rapid solution method for surface unmanned vessels motion planning problem based on optimal control

Abstract

Unmanned Surface Vehicle (USV) technology has been widely applied in various fields, due to the nonlinear, multiconstraint, high-dimensional nature of motion planning problems, as well as the dynamic characteristics of USV movement and the uncertainty of the environment, solving USV motion planning problems is highly complex and has an unpredictable failure rate. This paper focuses on the motion planning problem of surface USVs and studies the solution methods based on the optimal control model in modern control theory. By introducing the trapezoidal collocation method from the direct method, the optimal control formula describing the entire USV motion planning problem is fully discretized into a largescale non-linear programming problem (NLP), which is then quickly solved using an interior-point solver. In random scenario simulation experiments with different ship interaction conditions, the motion planning algorithm's solution time is within 250ms, basically meeting the practical engineering requirements. The highlights of this paper are as follows: 1. The optimal control method is used to ensure that the output control input is suitable for the USV power chassis; 2. The direct method is used to fully discretize the problem, transforming the optimal control problem, which essentially seeks the functional extremum in infinite space, into a NLP that can be quickly solved using mature mathematical tools to meet the low-latency requirements of USV working conditions; 3. The adoption of trapezoidal collocation discretization ensures that the constraints describing the control system in NLP are all first-order algebraic terms and their linear combinations, guaranteeing the low difficulty of solving NLP and effectively reducing the failure rate to within 10%.