  This paper is concerned with a Minimum-Time Intercept Problem (MTIP), for
which a Dubins vehicle is guided from a position with a prescribed initial
orientation angle to intercept a moving target in minimum time. Some geometric
properties for the solution of the MTIP are presented, showing that the
solution path must lie in a sufficient family of 4 candidates. In addition,
necessary and sufficient conditions for optimality of each candidate are
established. When the target's velocity is constant, by employing the geometric
properties, those 4 candidates are transformed to a class of sufficiently
smooth real-valued functions. In order to compute all the 4 candidates, an
efficient and robust algorithm to find all the zeros of sufficiently smooth
real-valued functions is developed. Since the MTIP with a constant target's
velocity is equivalent to the path planning problem of Dubins vehicle in a
constant drift field, developing such an algorithm also enables efficiently
finding the shortest Dubins path in a constant drift field. Finally, some
numerical examples are presented, demonstrating and verifying the developments
of the paper.
