IEEE - Aerospace and Electronic Systems - February 2020 - 19

the DE algorithm, choosing the most optimal one in terms
of the distance cost. Once the most optimal path is
obtained, the fast marching square (FM2 ) algorithm is
used as the planner.
The FM2 has been used for different purposes, such as
path planning with mobile vehicles [18], [19], [20] and vehicle formations in 2-D [21] and 3-D [22] environments, providing optimal trajectories in terms of smoothness and safety.
To achieve a feasible path planning for a UAV, the
inclusion of certain constraints into the FM2 is an important factor to take into account. In [23], the authors have
proven to generate paths with adaptive smoothness and
compatible with UAV kinematic restrictions, where the
paths resulting from FM2 are compared with those resulting from considering the Dubins model. Thanks to the
introduction of two adjustment parameters, the algorithm
will allow the path to fulfill both flight level and smoothness constraints so that it can be feasibly executed by a
real UAV platform without the need to implicitly include
its kinematic or dynamic model into the algorithm.
The contributions of this article are as follows. (1) We
use for the first time a combination of the DE algorithm
and the FM2 method to solve a CPP problem, keeping a
fixed flight level over the terrain. (2) The FM2 method has
been modified to introduce two adjustment parameters p1
and p2 that allow both changing the smoothness of the
path and setting the flight level in a very intuitive way
and without adding computational complexity to the
approach. (3) The generated path is optimal in terms of
the distance cost, safety, and smoothness, taking into
account the environment and running the approach only
once for the case of static environments. (4) The low
computational cost of the approach makes it suitable for
its application in real time for dynamic environments,
where moving obstacles have to be avoided. This research
can be useful in the future when applied for surveillance
and tracking tasks or monitoring (videos or overlaying
images) of a whole area with a minimum distance cost,
among other applications.
The advantages of our approach lie in the following
aspects.
Easy concept: The method is based on the natural
movement of a wave, so conceptually, it is very
FEBRUARY 2020

easy to understand. Thanks to this, the imposition of
the flight level constraint is simple to implement.
Feasible trajectories: The method provides very
smooth paths, since it is based on the propagation of
a wave, and no later optimization is required in order
to respect the kinematics of the UAV.
Fast response: As it is not necessary to include a kinematic model into the algorithm, the computational
cost is reduced considerably, allowing it even to be
executed in real time for dynamic environments.
This article is organized as follows. Section
"PROBLEM STATEMENT" introduces the problem statement, the mission to be carried out and the environment. A
summary of the methods used for this research is presented
in Section "METHOD FOR COVERAGE PATH
PLANNING." The proposed approach to cover a whole area
with a minimum distance cost and maintaining a flight level
with respect to the ground is presented in Section
"COVERAGE PATH PLANNING APPROACH." Section
"RESULTS AND DISCUSSION" presents the simulation
results from the application of the proposed approach.
Finally, the conclusions and future works are presented in
Section "CONCLUSIONS AND FUTURE WORKS".

PROBLEM STATEMENT
In this work, a mission planning for UAVs is carried out,
whose main objective is to cover a whole area in the most
optimal way in terms of the distance cost. The UAV also
keeps a fixed altitude with respect to the ground. In this
way, for certain applications such as tracking or cartography, the UAV could track a whole area and obtain images
of the terrain, maintaining a homogeneous size of the pixel
and without overlapping.
Our approach has the following inputs: an environment
map where the mission is carried out and a surface that represents the area for the CPP. The environment is represented by an open-field map with mountainous terrain,
where the surface is rather uneven, as shown in Figure 1.
This map is a 3-D grid map whose size is 118 × 87 × 40
cells. The size of each cell is equivalent to 10 × 10 × 10 m.

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IEEE - Aerospace and Electronic Systems - February 2020

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