  Existing methods for avoiding dynamic engagement zones (EZs) and minimizing
risk leverage the calculus of variations to obtain optimal paths. While such
methods are deterministic, they scale poorly as the number of engagement zones
increases. Furthermore, optimal-control based strategies are sensitive to
initial guesses and often converge to local, rather than global, minima. This
paper presents a novel sampling-based approach to obtain a feasible flight plan
for a Dubins vehicle to reach a desired location in a bounded operating region
in the presence of a large number of engagement zones. The dynamic EZs are
coupled to the vehicle dynamics through its heading angle. Thus, the dynamic
two-dimensional obstacles in the (x,y) plane can be transformed into
three-dimensional static obstacles in a lifted (x,y,{\psi}) space. This insight
is leveraged in the formulation of a Rapidly-exploring Random Tree (RRT*)
algorithm. The algorithm is evaluated with a Monte Carlo experiment that
randomizes EZ locations to characterize the success rate and average path
length as a function of the number of EZs and as the computation time made
available to the planner is increased.
