Time optimal Zermelo’s navigation problem with moving and fixed obstacles

In this paper, we consider a time optimal Zermelo’s navigation problem (ZNP) with moving and fixed obstacles. This problem can be formulated as an optimal control problem with continuous inequality constraints and terminal state constraints. By using the control parametrization technique together with the time scaling transform, the problem is transformed into a sequence of optimal parameters selection problems with continuous inequality constraints and terminal state constraints. For each problem, an exact penalty function method is used to append all the constraints to the objective function yielding a new unconstrained optimal parameters selection problem. It is solved as a nonlinear optimization problem. Different scenarios are considered in the simulation, and the results obtained show that the proposed method is effective.