Optimal Feedback Guidance of a Small Aerial Vehicle in the Presence of 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 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 de-

[1]  Danwei Wang,et al.  Standoff tracking control of moving target in unknown wind , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[2]  Efstathios Bakolas,et al.  Feedback Navigation in an Uncertain Flowfield and Connections with Pursuit Strategies , 2012 .

[3]  L. Dubins.  On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents , 1957 .

[4]  P. Tsiotras,et al.  Time-optimal synthesis for the Zermelo-Markov-Dubins problem: The constant wind case , 2010, Proceedings of the 2010 American Control Conference.

[5]  Craig A. Woolsey,et al.  Minimum-Time Path Planning for Unmanned Aerial Vehicles in Steady Uniform Winds , 2009 .

[6]  Timothy W. McLain,et al.  Vector Field Path Following for Miniature Air Vehicles , 2007, IEEE Transactions on Robotics.

[7]  R. Rysdyk.  Unmanned Aerial Vehicle Path Following for Target Observation in Wind , 2006 .

[8]  Dejan Milutinovic,et al.  A stochastic approach to Dubins feedback control for target tracking , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[9]  J. Hedrick,et al.  Optimal Path Planning with a Kinematic Airplane Model , 2007 .

[10]  H. Sussmann,et al.  The Markov-Dubins problem with angular acceleration control , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[11]  Efstathios Bakolas,et al.  Optimal Synthesis of the Asymmetric Sinistral/Dextral Markov–Dubins Problem , 2011, J. Optim. Theory Appl..