Optimal control problems for path planing of AUV using simplified models

Here we propose a simplified model for the path planning of an Autonomous Underwater Vehicle (AUV) in an horizontal plane when ocean currents are considered. The model includes kinematic equations and a simple dynamic equation. Our problem of interest is a minimum time problem with state constraints where the control appears linearly. This problem is solved numerically using the direct method. We extract various tests from the Maximum Principle that are then used to validate the numerical solution. In contrast to many other literature we apply the Maximum Principle as defined in [9].