Page 100 - Innovations in Intelligent Machines

90 I.K. Nikolos et al.

Fig. 2. A typical simulation result of the off-line path planner for a single UAV;
the horizontal section of the terrain represents the imposed upper limit to the UAV
flight. The starting position is marked with a circle

3 Off-line Path Planner for a Single UAV

The off-line path planner, discussed in detail in [23], will be briefly presented
here, in order to introduce the concept of UAV path planning using Evo-
lutionary Algorithms. The off-line planner generates collision free paths in
environments with known characteristics and flight restrictions. The derived
path line is a single continuous 3-D B-Spline curve, while the solid bound-
aries are interpreted as 3-D rough surfaces. The starting and ending control
points of the B-Spline curve are fixed. A third point close to the starting one
is also fixed, determining the initial flight direction. Between the fixed control
points, free-to-move control points determine the shape of the curve, taking
values in the constrained space. The number of the free-to-move control points
is user-defined. Their physical coordinates are the genes of the EA artificial
chromosome.
The optimization problem to be solved minimizes a set of four terms,
connected to various objectives and constraints; they are associated with the
feasibility and the length of the curve, a safety distance from the obstacles and
the UAV’s flight envelope restrictions. The objective function to be minimized
is defined as
4

f = w i f i . (8)
i=1
Term f 1 penalizes the non-feasible curves that pass through the solid
boundary. The penalty value is proportional to the number of discretized curve