IEEE - Aerospace and Electronic Systems - February 2020 - 24

Coverage Mission for UAVs Using Differential Evolution and Fast Marching Square Methods
and values r1 , r2 , and r3 are random individuals,
being r1 6¼ r2 6¼ r3 6¼ i. In this way, the mutation is
based on the randomness.
Crossover: The crossover process is used to increase
the diversity of the new generation.
Selection: The selection mechanism compares the
individuals of the cost of the trial vector and the
cost of the target vector. Here, the best result is
chosen. If the value of the trial vector cost is
smaller than the value of the target vector cost, the
result is the value of ug . On the contrary, the best
result will be the value of the individual of the population xg , maintaining in both cases this value for
the next population.

Figure 6.
Flowchart of the DE algorithm for our approach.

Mutation: The mutation process generates the donor
vector from the linear combination of different members of the population according to vgi ¼ xgr1 þ F Á
ðxgr2 À xgr3 Þ; where the parameter related to the
speed of convergence is a positive constant F = 0.8,
whose value gives a good precision of the solution,

Figure 7(a) shows the specific surface to track in the
map, and Figure 7(b) shows the resulting zigzag path after
the application of the DE algorithm to cover the whole
area of the surface with a minimum cost.
Once the zigzag path has been obtained in Figure 7(b),
an enlargement of the zigzag path is applied, obtaining
W0 matrix, as shown in Figure 7(c). Over this new
enlarged path, the FM method is now applied, obtaining
W matrix as shown in Figure 7(d). Now, the FM algorithm
is used again to plan the final path at a fixed altitude with
respect to the terrain (using p1 and p2 adjustment parameters), avoiding any obstacles found in the environment.
The resulting path is shown in Figure 7(e) and Figure 7(f)
in top and 3-D views, respectively.
As an original contribution to the FM2 algorithm, in
order to impose a fixed flight level for the UAV, W is
modified according to the parameters p1 and p2 , whose

Figure 7.
Process to obtain the path with minimum cost. (a) Surface to be covered. (b) Result from the DE algorithm. (c) Enlargement of the
zigzag path. (d) Applying FM to obtain W matrix. (e) Applying FM again to obtain the final path. (f) 3-D perspective of the resulting
path from our approach.

24

IEEE A&E SYSTEMS MAGAZINE

FEBRUARY 2020

IEEE - Aerospace and Electronic Systems - February 2020

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