IEEE - Aerospace and Electronic Systems - August 2022 - 23

Schwung and Lunze
The control method is supposed to respect the following
constraints:
(C1) Network topology: There is no coordinator or forwarding
unit in the network but all control and estimation
algorithms have to work with local information.
(C2) Communication: The communication link
between the objects should only be invoked if the uncertainty
of the local information exceeds a threshold.
(C3) Computation: The computation power onboard the
objects is limited and causes bounded computational delays.
Due to the complexity ofthe control problem, this article
focusses on a method which enables the objects to satisfy
control aim (A1). To this aim, both objects plan their trajectories
locally, while only the give-way object is responsible
to plan its trajectory so as to satisfy the requirements (1) and
(2). The conditions can be partly contradictory. As the collision
avoidance is of superior importance, requirement (1)
has to be guaranteed all the time, while requirement (2) is
allowed to be violated for short time spans. Control aims
(A2) and (A3) are fulfilled by both quadrotors locally by utilizing
the controllers C
S and C
G, which were derived in [1].
The following assumptions are made.
Assumption 1. The speeds vSðtÞ and vGðtÞ ofPS and
PG are bounded
jjvGðtÞjj vG;max; and vS;max vG;max:
Assumption 2. The objects are only able to measure
their ownposition, speed, and acceleration.
Assumption 3. The meanpacket lossprobability ofthe
channel is boundedfrom above by pe;max. The statistics
ofthe wireless channel are constant as long as the difference
ofthe current distance dðtÞ between the objects
and the distance dð~tiÞ at the last time instant ~ti at which
the statistics were estimateddoes not exceedd
djdð~tiÞ dðtÞj;i ¼ 1; 2; ...
Assumption 1 is required, because the give-way object
is responsible to satisfy the control aim (A1). In order to
be able to adjust the distance between the objects, it must
have a higher dynamic compared to the stand-on object.
Assumption 2 limits the use of sensors for a distance measurement,
so that the required information can only be
obtained through communication. Assumption 3 follows
from the fact that the properties of the communication
channel depend on the distance between the objects.
WAY OF SOLUTION
The planning method for a trajectory to bring the objects
from their start points to their end points is identical for
both objects. As the give-way object is in addition responsible
to satisfy conditions (1) and (2), in the rest of this
AUGUST 2022
Figure 3.
Structure of the control unit AG coupled with the delay estimator
DG of the give-way object.
article the control method for the give-way object is
described in more detail. In order to satisfy control aim
(A1) the give-way object has to solve the following four
problems.
I) Estimate the current quality-of-service (QoS) properties
of the communication channel, which vary
with the relative movement of the objects.
II) Estimate the future positions of the stand-on object,
when the trajectory becomes uncertain over time.
III) Use an event-based method to invoke communication
only when it is necessary and to trigger a
change of the trajectory by incorporating the estimated
QoS properties of the channel.
IV) Plan the trajectory to satisfy control aim (A1) while
fulfilling dynamic constraints on the rotor speeds
u ui ¼ n2
iu; i ¼ 1; ... ; 4
(3)
as well as on the angles around the x-axis and the
y-axis of the quadrotor
f fðtÞf; # #ðtÞ#:
(4)
This article focusses on the solution to Problem (III)
and uses the delay estimator described in [29] to solve
Problem (I). A position estimation method solving Problem
(II) has been stated in [28]. The trajectory planning
method to solve Problem (IV) is given in [26].
Both objects use the control unit, as shown in Figure 3.
Its working principle applies the idea ofevent-based control,
where signals are only sent ifan uncertainty threshold is violated.
Solid arrows depict a continuous signal transmission
in the figure while the dashed arrows represent an eventbased
signal transfer. In order to reduce the communication
IEEE A&E SYSTEMS MAGAZINE
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IEEE - Aerospace and Electronic Systems - August 2022

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