IEEE - Aerospace and Electronic Systems - August 2022 - 32

Cooperative Control of UAVs Over an Unreliable Communication Network
Figure 10.
Event generation ofthe give-way object for the first part ofcase 3.
consecutive packets get lost at t ¼ 5s and at t ¼ 5:4s.At
both time instants the event eG2 is generated with (14) and
the give-way object increases the distance to the stand-on
object by 2 dS, because two packets got lost. It can be seen
that the replanning manoeuvre is successful and the collision
is safely avoided. At t ¼ 5:9s the next information is
received. Event eG1 is directly invoked and the trajectory
of the give-way object is planned so that it returns to its
initial trajectory as the movement of the stand-on object
allows this.
CASE 3: SATISFACTION OF THE MAXIMUM
SEPARATION WITH A CERTAIN PROBABILITY
The trajectories of the quadrotors in the xy-plane are
shown in Figure 10 for the third case.
The stand-on object changes its trajectory from the
dashed line to the solid line after t ¼ 2s.At t ¼ 5s and at
t ¼ 5:4s two consecutive packets get lost. Hence, the
event eG2 is generated twice, which leads the give-way
object to increase the distance to the stand-on object by
2 dS. It can be seen that the maximum separation cannot
be satisfied any more due to the change of the trajectory of
the give-way object. The trajectory replanning has to be
performed due to the lack of information from the standon
object to ensure requirement (1). It is necessary,
because the collision avoidance has a higher priority than
keeping the maximum separation between the objects.
Hence, the maximum separation is violated for a short
time span. After receiving the next data from the stand-on
object at time t ¼ 5:9, event eG1 is generated and the
give-way object changes its trajectory so as to fulfill both
requirements (1) and (2) again and to reach its given
destination.
32
Figure 11.
Event generation of the give-way object for the second part of
Case 3.
As the stand-on object changes its trajectory at the
same time instant under the same circumstances from the
dashed line to the dot-dashed line the maximum separation
between the objects is fulfilled at any time as illustrated in
Figure 11. In particular, requirement (2) is satisfied despite
the give-way object increases the distance to the stand-on
object by 2 dS due to the lack of information. This is possible,
because the stand-on object moves on a trajectory that
keeps it close to the give-way object. At time t ¼ 6:1s the
second condition of (13) is violated. The give-way object
notices this fact at t ¼ 5:9s when it receives the current
information of the stand-on object. The event eG1 is generated
but the trajectory remains unchanged, because the
give-way object already moves with its maximum speed
and no violation of requirement (2) threatens.
DISCUSSION OF THE SIMULATION RESULTS
The three cases show that in the control method the occurrence
of packet losses need to be considered to achieve
the control aims. Both requirements of control aim (A1)
can be always fulfilled if no packet losses occur. In contrast,
in the presence of packet losses the collision-free
movement is guaranteed if packet losses are considered,
while the fulfillment of the maximum separation depends
on the movement of the stand-on object. Due to the lack
of information caused by the packet losses, the give-way
object generates the event eG2 to guarantee requirement
(1) even though this causes a violation of requirement (2).
A comparison of the model used in this article to estimate
the time delay with the classical Gilbert-Elliott
model shows that the root squared mean error of the estimate
is significantly smaller [2]. Hence, the used model is
suitable for the invocation of communication and the
unnecessary invocation of event eG2 can be avoided. The
IEEE A&E SYSTEMS MAGAZINE
AUGUST 2022
IEEE - Aerospace and Electronic Systems - August 2022

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