Time optimal control for a non-linear planar 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 arbitrary constant disturbance the full problem on a plane must be considered. The minimum-time optimal solution is now dependent on the value and direction of the disturbance, which naturally affects the completion of the movement task. In this work, we address the problem of minimum time movement on a 2D plane with quadratic drag, under norm state (velocity), and norm control (acceleration) constraints. The structure and properties of the optimal solution of this nonlinear problem are found and analyzed. The Pontryagin Maximum Principle (PMP) with control and state constraints is utilized. Simulations encouraging the results are presented and compared with those of the academic open-source optimal control solver Falcon.m.