Optimal Feedback Guidance of a Small Aerial Vehicle in a Stochastic Wind

The navigation of a small unmanned aerial vehicle is challenging due to a large influence of wind to its kinematics. When the kinematic model is reduced to two dimensions, it has the form of the Dubins kinematic vehicle model. Consequently, this paper addresses the problem ofminimizing the expected time required to drive aDubins vehicle to a prescribed target set in the presence of a stochastically varyingwind. First, two analytically-derived control laws are presented. One control law does not consider the presence of the wind, whereas the other assumes that the wind is constant and known a priori. In the latter case it is assumed that the prevailing wind is equal to its mean value; no information about the variations of the wind speed and direction is available. Next, by employing numerical techniques from stochastic optimal control, feedback control strategies are computed. These anticipate the stochastic variation of the wind and drive the vehicle to its target set while minimizing the expected time of arrival. The analysis andnumerical simulations show that the analytically-deriveddeterministic optimal control for this problemcaptures, inmany cases, the salient features of the optimal feedback control for the stochasticwindmodel, providing support for the use of the former in the presence of light winds.On the other hand, the controllers anticipating the stochasticwind variation lead tomore robust andmore predictable trajectories than the ones obtained using feedback controllers for deterministic wind models.