  This paper presents the problem of lateral interception by a Dubins car of a
target that moves along an a priori known trajectory. This trajectory is given
by two coordinates of a planar location and one angle of a heading orientation,
every one of them is a continuous function of time. The optimal trajectory
planning problem of constructing minimum-time trajectories for a Dubins car in
the presence of a priory known time-dependent wind vector field is a special
case of the presented problem. Using the properties of the three-dimensional
reachable set of a Dubins car, it is proved that the optimal interception point
belongs to a part of an analytically described surface in the three-dimensional
space. The analytical description of the surface makes it possible to obtain 10
algebraic equations for calculating parameters of the optimal control that
implements the minimum-time lateral interception. These equations are generally
transcendental and can be simplified for particular cases of target motion
(e.g. resting target, straight-line uniform target motion). Finally, some
particular cases of the optimal lateral interception validate developments of
the paper and highlight the necessity to consider each of 10 algebraic
equations in general case.
