IEEE - Aerospace and Electronic Systems - August 2022 - 24

Cooperative Control of UAVs Over an Unreliable Communication Network
effort, the data RGðtc;kÞ and SSðtc;kÞ are only transmitted at
discrete time instants. In the following, the tasks ofthe components
of the control unit of the give-way object are summarized,
which are stated in detail in the following sections.
The delay estimator generates a statistical estimate
~tmaxðdð~tiÞÞ of the current time delay tk ofthe communication
network at discrete time instants [Problem (I)]. It
reacts on the event eG3 and uses the distance dð~tiÞ at the
discrete time instant ~ti (dashed lines in Figure 3).
The prediction unit receives the communicated data
SSðtc;kÞ of the stand-on object and generates continuously
an inclusion PSðt; tr;k; tkÞ of the position of the stand-on
object. Furthermore, an inclusion PS;dðtc;k;tc;k; tkÞ of the
position of the stand-on object during the current time
delay tk of the communication link is generated [Problem
(II)]. After reception of the data SSðtc;kÞ it is continuously
available. The prediction unit transfers the data SSðtc;kÞ
and the sets PSðt; tr;k; tkÞ, PS;dðtc;k;tc;k; tkÞ continuously
to the event generator and the data SSðtc;kÞ to the trajectory
planning unit (solid lines in Figure 3).
The event generator supervizes the fulfillment of the
control aims. It uses the estimated time delay ~tmaxðdð~tiÞÞ,
current position pGðtÞ of the give-way object, and matrix
WGðtÞ, which contains the trajectory and the first four
derivatives of the trajectory to invoke communication by
generating an event eG0 and by sending a request RGðtc;kÞ
that is later defined in (12) [Problem (III)]. It triggers a
new time delay estimation whenever a threshold is violated
by generating the event eG3 at the discrete time
instant
t~i. Furthermore, based on the received data
SSðtc;kÞ, it determines the current time delay tk and it
decides when it is necessary to change the trajectory of
the give-way object by generating the events eG1 or eG2 at
the discrete time instant tk (dashed lines in Figure 3).
The replanning ofthe trajectory is performed by the trajectory
planning unit based on the data SSðtc;kÞ [Problem
(IV)]. The unit is split into theplanning task section and the
planning algorithm section, which generates the matrix
WGðtÞ, which is continuously forwarded to the controller
C
G and the event generator (solid line in Figure 3).
DELAY ESTIMATOR
CONSEQUENCES OF AN UNRELIABLE NETWORK
In order to explain the difficulties resulting from delayed
information transfers and packet losses, and the necessity to
introduce a delay estimator, first the control method for a
network without time delays ðtk ¼ 0Þ is considered as illustrated
in Figure 4 (left). At a time instant tk the current position
ofthe stand-on object is communicated to the give-way
object. Based on this position the prediction of the future
movement of the stand-on object is generated and the distance
between the objects is checked for a violation of(A1).
24
Figure 4.
Control method with instantaneous communication (left) and
delayed communication (right).
An unreliable communication network requires severe
extensions of this approach for the following reasons.
The received information is outdated by the current
time delay tk, while the stand-on object continues
moving during this time span. Hence, the object is
not at the communicated position pSðtkÞ but at the
unknown position pSðtk þ tkÞ, which is in an area
around pSðtkÞ. As a result, communication has to be
invoked earlier about the time delay tk at tc;k ¼
tk tk. An estimate of the time delay is generated
by the delay estimator to ensure that data can be
received before or at the time instant tk if no packet
losses occur. During the time delay the stand-on
object can change its movement. Its current position
becomes uncertain but remains in the gray area
PS;dðtc;k;tc;k; tkÞ in Figure 4 (right) due to its
dynamical limitations. For the prediction of the
future movement ðt>tkÞ and the determination of
the distance between the objects, the movement of
the stand-on object during the time delay tk needs
to be taken into account.
As the current time delay tk can be larger than the
estimated mean time delay ~tmaxðdð~tiÞÞ introduced
in the following, a packet is considered to be lost if
tk > ~tmaxðdð~tiÞÞ applies. In case of a packet loss,
the give-way object does not receive information
from the stand-on object and its movement becomes
more uncertain as illustrated by the red area in
Figure 4 (right). Hence, the stand-on object can
approach the give-way object without notice. New
information can be received earliest after the time
span 2 tk as described in the " Evaluation of the Estimation
Method for an Unreliable Network " section.
A suitable method for the give-way object has to be
found to plan its trajectory so as to guarantee the
collision avoidance despite the uncertainty.
In the rest of this article two different notations for the
time instants are used. ~ti denotes the time instants at which
a new estimate of the delay estimator is triggered and tk
denotes the time instants at which communication is
invoked or the trajectory of the give-way object needs to
be changed.
IEEE A&E SYSTEMS MAGAZINE
AUGUST 2022
IEEE - Aerospace and Electronic Systems - August 2022

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