(Georgia Institute of Technology, 2013)
Anderson, Ross P.; Bakolas, Efstathios; Milutinović, Dejan; Tsiotras, Panagiotis
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 of minimizing the expected time required to drive a Dubins vehicle to
a prescribed target set in the presence of a stochastically varying wind. 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 and numerical simulations show that the analytically-derived deterministic optimal control for this problem captures, in many cases, the salient features of the optimal feedback control for the stochastic wind model, providing support for
the use of the former in the presence of light winds. On the other hand, the controllers anticipating the stochastic wind
variation lead to more robust and more predictable trajectories than the ones obtained using feedback controllers for deterministic wind models.