IEEE - Aerospace and Electronic Systems - August 2022 - 26

Cooperative Control of UAVs Over an Unreliable Communication Network
ySðt; tr;k; tkÞ, and
zSðt; tr;k; tkÞ, and its radii
rS;xðt; tr;k; tkÞ, rS;yðt; tr;k; tkÞ, and rS;zðt; tr;k; tkÞ
depend on the position and the speed at the communication
time instant tc;k and incorporate
the current time delay tk [28]. The set
PS;dðtc;k;tc;k; tkÞ is generated using (10) as well,
which includes the movement of the stand-on
object during the current time delay tk.
The prediction unit of the stand-on object just receives
the request RGðtc;kÞ (12) of the give-way object and
passes it to its event generator.
EVENT GENERATOR
The event generator ofthe give-way object acts as a supervisor.
It sends an acknowledgment (ACK) message to the
stand-on object whenever new information SSðtc;kÞ has
been successfully received. It monitors the minimum and
maximum possible distances
distminðwGðtÞ; PSðt; tr;k; tkÞÞ
¼ minpSðtÞ2PSðt;tr;k;tkÞðjjwGðtÞ pSðtÞjjÞ
distmaxðwGðtÞ; PSðt; tr;k; tkÞÞ
¼ maxpSðtÞ2PSðt;tr;k;tkÞðjjwGðtÞ pSðtÞjjÞ
between the current position of the give-way object and
the set PSðt; tr;k; tkÞ of predicted positions of the stand-on
object. In addition, the distance
distðwGðtÞ;wwSðtÞÞ¼jjwGðtÞ wSðtÞjj;t tk
between the trajectories of the two objects is checked
whenever the trajectory of the stand-on object or the trajectory
of the give-way object changed. The replanning of
the trajectory of the give-way object is triggered in case of
a possible violation of the control aim (A1). A new estimate
of the time delay is invoked whenever the estimate
gets too uncertain. The generation of the following four
events is necessary to satisfy the control aim by using an
unreliable communication network.
Communication event eG0: Communication to the
stand-on object is invoked whenever the condition
eG0 :
(
distminðwGðtÞ; PSðt; tr;k; tkÞÞ ¼ s þeG þedðdð~tiÞÞ
_ distmaxðwGðtÞ; PSðt; tr;k; tkÞÞ ¼seGedðdð~tiÞÞ
(11)
eS0 :
is fulfilled and the objects are so close to one another that a
violation of control aim (A1) is possible. The thresholdeG
depends on the dynamics of the objects, while the threshold
edðdð~tiÞÞ depends on the estimated time delay as
edðdð~tiÞÞ ¼ vS;max ~tmaxðdð~tiÞÞ
26
and describes the maximum distance the stand-on object
can cover during the time interval of length ~tmaxðdð~tiÞÞ.
As a reaction, the request
RGðtc;kÞ¼
T
tc;k
tc;kþ1
~tmaxðdðtkÞÞ
.. .
~tmaxðdðtkþ1ÞÞ .. .
(12)
is sent to the stand-on object, which should send its data at
each communication time instant autonomously without
any further request. The request contains sufficiently
many future communication time instants tc;kþj, ðj ¼
1; ... ;NÞ and the time delays ~tmaxðdðtkþjÞÞ, which are
estimated to occur at the predicted event time instants tkþj
by an evaluation of the distance between the trajectories
of the objects at these time instants.
Reactive event eG1: The planning of a reactive trajectory
wG;rðtÞ of the give-way object introduced in the next
section is triggered to keep the control aim (A1) satisfied
if the condition
eG1 :
distðwGðtÞ;wwSðtÞÞ s þ 2eG
_ distðwGðtÞ;wwSðtÞÞs 2eG
(13)
is fulfilled.
Packet loss event eG2: The collision avoidance should
be guaranteed despite the statistical uncertainty of the estimated
time delay since tk > ~tmaxðdð~tiÞÞ can occur.
Hence, to handle this statistical uncertainty and to derive a
deterministic reaction that ensures the collision avoidance,
the event eG2 is invoked if the condition
eG2 : tk ¼ t tc;kþj > ~tmaxðdð~tiÞÞ;j ¼ 0; 1; ... ;N
(14)
is fulfilled. As a result the planning of an avoidance trajectory
wG;aðtÞ is triggered as stated in the next section to
satisfy the control aim even if information is missing.
Estimation event eG3: A new estimate of the time
delay is invoked whenever the condition
eG3 : jdð~tiÞ dðtÞj ¼d
(15)
is satisfied showing that the distance between the objects
has changed significantly so that the former estimate is no
longer valid.
The event generator of the stand-on object acts as a
supervisor as well. At time t ¼ 0 the event generator communicates
its data SSð0Þ to the give-way object. After that
it generates the event eS0 with condition
reception of RGðtc;kÞ
_ t ¼ tc;kþj;j ¼ 0; 1; .. . ;N
and sends the data SSðtc;kÞ as a matrix whenever a new
request is received or the next time instant in RGðtc;kÞ
(12) is reached. As the data can get lost, the event generator
expects an ACK message from the give-way object
after the time delay 2~tmaxðdðtkÞÞ after sending its data.
IEEE A&E SYSTEMS MAGAZINE
AUGUST 2022
IEEE - Aerospace and Electronic Systems - August 2022

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