IEEE - Aerospace and Electronic Systems - August 2022 - 22

Cooperative Control of UAVs Over an Unreliable Communication Network
Markov model has been stated in [2]. It extends the
Gilbert-Elliott model [13], [14] for varying error probabilities
using the Rice distribution. In [15], the parameters of
a channel connecting UAVs modeled by the Gilbert-Elliott
model have been derived by experiments.
This article utilizes the model from [2] to estimate the
current packet loss probability and the transmission delay
induced by the network. This estimate is considered for the
decision when it is necessary to invoke communication.
In the literature of control theory different methods
exist to overcome transmission delays and packet losses
of networks. In [16], an event-based approach has been
presented, which states a bound for the transmission delay
so that a state-feedback loop is stable despite of the
delayed information. Guinaldo [17] provided the extensions
of the event-based control loop to cope with transmission
delays and packet losses. Yoo and Johansson [18]
applied a machine learning technique to compensate random
delays. A hybrid system framework has been stated
in [19] that has incorporated communication constraints,
varying transmission intervals, and varying delays to guarantee
the stability based on Lyapunov functions. Cuenca
et al. [20] proposed a periodic event-triggered sampling
method to reduce the network utilization.
The mentioned approaches assume fixed upper bounds on
the time delay and focus on the stabilization ofsystems over an
unreliable communication network. In contrast, in this article
the time delays are estimated online. The control method uses
the idea of the classical event-based control but applies it on a
higher abstraction level to the trajectory planning task.
The control problem to be solved in this article concerns
the problem ofcollision avoidance, which has been dealt with
in literature either by planning collision-free trajectories in a
distributed way in advance, as in [21] and [22], based on
piecewise Bezier curves, or by reacting on the movement of
neighboring objects as in [23], along an artificial potential
field. Further methods are based on velocity obstacles [24]
and on sampling-based trajectory replanning [25].
These methods require the continuous knowledge of
the positions of neighboring objects. To satisfy this
assumption a high communication effort is required. In
contrast, the proposed method in this article needs information
only at discrete points in time. Moreover, no sensors,
e.g., for a distance measurement are necessary.
The method of the event-based cooperative control of
autonomous objects was introduced in [26] and extended
in [27], and has used the idea of event-based control on a
higher abstraction level. It has considered the free movement
of two objects in the 3D airspace, which were connected
by an ideal communication network. It includes
trajectory planning method to change the trajectories of the
objects online to enable them to fulfill their control aims. In
contrast, in this article the method is extended to cope with
transmission delays and packet losses induced by an unreliable
communication network. To this aim, the control unit
22
introduced in [26] is enhanced and extended by the position
prediction method stated in [28] and a delay estimator.
The rest ofthis article is organized as follows. The problem
statement and the way of solution are given in the
" Formulation ofthe Control Problems " section. The " Delay
Estimator " section states the delay estimator and the difficulties
arising from the use ofan unreliable network. The components
of the control method are given in the sections
" Prediction Unit, " " Event Generator, " and " Trajectory Planning
Unit. " The method is analyzed in " Evaluation of the
Estimation Method for an Unreliable Network " and
" Communication Flow Over an Unreliable Network "
describes the communication flow. A simulation study with
two quadrotors illustrates the method in two scenarios in the
" Simulation Results of the Control Method " section.
Finally, we provide the " Conclusion. "
FORMULATION OF THE CONTROL PROBLEMS
PROBLEM STATEMENT
The problem investigated is depicted in Figure 1 with two
quadrotors. The aim is to bring the two objects from their start
points SA;S, SA;G to their end points SB;S, SB;G while fulfilling
the conditions (1) and (2) introduced in the following. To
this aim, the control method has to satisfy the following control
aims, where the positions ofthe objects are given by
pSðtÞ¼ ð xSðtÞ ySðtÞ zSðtÞÞT;ppGðtÞ
¼ðxGðtÞ yGðtÞ zGðtÞÞT:
CONTROLAIMSOFTHEOVERALLSYSTEM
(A1) Trajectory planning and monitoring: The trajectories
wiðtÞ ofthe objectsPi, ði 2fS;GgÞ should be planned so as
to bring them from their start points SA;i to their end points
SB;i. The separation sðtÞ should satisfy the inequalities
s sðtÞ¼ jjpGðtÞ pSðtÞjj 8t
sðtÞ¼ jjpGðtÞ pSðtÞjjs
(1)
(2)
where s is a safety distance to avoid collisions between the
objects ands is a maximum separation to achieve specific
control aims (e.g., communication relay).
(A2) Trajectory following: The objects
Pi, ði 2
fS;GgÞ should follow given trajectories wiðtÞ exactly if
there are no external disturbances
wiðtÞ¼ piðtÞ;i 2fS; Gg8t:
(A3) Disturbance compensation: External disturbances
(e.g., wind) should be compensated by the objects to
ensure a smooth flight behavior.
IEEE A&E SYSTEMS MAGAZINE
AUGUST 2022
IEEE - Aerospace and Electronic Systems - August 2022

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