Feedback Guidance in Uncertain Spatiotemporal Wind Using a Vector Backstepping Algorithm

This work deals with the problem of guiding a controlled object to a given target set in a three-dimensional configuration space in the presence of wind with an uncertain spatiotemporal velocity field. The proposed guidance law uses (imperfect) measurements of the velocity of the local wind along the ensuing path of the controlled object to a given target set. No information about the velocity gradients (temporal and spatial) of the wind is assumed to be available. The development of the proposed guidance feedback law is based on the use of a backstepping algorithm that forces the controlled object to follow closely the motion of a lower-order kinematic model that is driven by a pure pursuit navigation law. In this way, the controlled object converges to its target set in finite time. Two kinematic models that describe the motion of the controlled object are considered. In the first model, the rate of change of the air velocity of the controlled object is unconstrained, whereas in the second one, it has to remain perpendicular to the air velocity at all times. Numerical simulations that are based on real wind data are presented.