IEEE - Aerospace and Electronic Systems - February 2020 - 20

Coverage Mission for UAVs Using Differential Evolution and Fast Marching Square Methods

Figure 1.
3-D Environment. The representation of the area to be covered by
the UAV and the zigzag path to cover the surface.

Here, it is not necessary to consider the size of the UAV,
since it is assumed to be smaller than the size of a cell.
An instance of the surface and the zigzag path for that
surface is represented in Figure 1, which is planned with a
certain width between the bands and with a determined
steering angle a. Here, the steering angle is defined as the
direction of each band with respect to the x and y axes [as
shown in Figure 2(a)], and the width between the bands
corresponds with the camera visual field of the UAV. It
has to be taken into account that the real camera footprint
must be considered when preparing the simulation environment for real applications and that camera requirements must be adequately addressed.
The execution of the path by the UAV can be affected
by its kinematics and dynamics. However, large environments are considered in general inspection cases and it is
assumed that the turns of the path are compatible with the
turning radius of the UAV and do not compromise its
dynamic stability.

The length of the trajectory resulting from the coverage
algorithm depends mainly on the steering angle. The DE
algorithm will evaluate iteratively a cost function defined
by the distance of the zigzag path, obtaining as a result the
steering angle of the path with minimum distance cost.
Then, the FM2 method is used to plan the final path according to the resulting zigzag path, avoiding any obstacles in
the environment and maintaining a certain altitude with
respect to the ground. The final path is composed of a set of
consecutive points (Q ¼ P0 ; P1 ; :::; Pn ), and its smoothness and safety distance can be modified by two adjustment
parameters used in the FM2 method. In this way, the path
could be adapted to the kinematics of the UAV.

METHOD FOR COVERAGE PATH PLANNING
Our proposal for CPP is divided into three different parts:
the Zigzag path method, the DE algorithm, and the FM2
method. Next, all these parts will be explained in detail. All
algorithms and simulations presented have been implemented and run using MATLAB R2018a software in a standard MacBook Pro with processor 2,4 GHz Intel Core i5.

ZIGZAG PATH METHOD
The area to be covered is a surface, which can be represented by an irregular form [for instance, see Figure 2(a)].
To begin the zigzag path planning in the area, the tangent
point to the surface is determined according to a certain
angle a. This angle corresponds with the steering angle of
the bands. The tangent point is found within the enclosed

Figure 2.
Process to cover all the surface with a zigzag path. (a) Area to find the tangent point. (b) First band is calculated. (c) Next band is calculated.
(d) Creation of the cut points for the arc. (e) Adaptation of the cut points for the UAV visual field. (f) Repetition of the process for the rest
of the bands.

IEEE A&E SYSTEMS MAGAZINE

FEBRUARY 2020

IEEE - Aerospace and Electronic Systems - February 2020

Table of Contents for the Digital Edition of IEEE - Aerospace and Electronic Systems - February 2020