Time optimal control of a non-linear surface vehicle subject to disturbances

The problem of an autonomous agent moving on a planar surface, such as an aerial drone or a small naval vessel can be treated as navigation between a series of points. While nominally the movement between each pair of points can be treated as a 1D projection of the movement on the vector connecting the two points, in the presence of disturbances, the full problem on the plane must be considered. The time optimal solution is now dependent on the value and direction of the disturbance which in this paper is assumed to be a constant inertial velocity of the medium (wind or current, respectively). We address the minimum time problem of movement on a 2D plane with quadratic drag, under norm state (inertial vessel velocity), and norm control (acceleration) constraints. The structure and properties of the optimal solution are found and analyzed, utilizing the Pontryagin Maximum Principle (PMP) with control and state constraints. Simulations supporting the results are provided and compared with those of the open-source academic optimal control solver Falcon.m.