The Magazine of IEEE-Eta Kappa Nu October 2017 - 19

Connectivity in Networked Unmanned Aerial Vehicles

Fig. 2: Target tracking for 3-6 UAVs with different target trajectories.

position and orientation to keep the target centered in
the UAVs formation. All UAV dynamics are governed by
a simple point-mass dynamic model for two degrees of
freedom systems [19], and assumed to fly at a constant
altitude on a 2D plane. The developed controller, formally
defined in Subsection III-B, successfully tracks a target
with different trajectories with a varying number of UAVs,
as shown in Figure 2. The thick red line shows the target
trajectory, the dashed line between UAVs is the polygon
created for the desired connectivity, and the thin multicolored lines represent the UAV trajectories.
B.

Formation Control

The formation controller on each UAV makes decisions
on position and orientation of the UAV based on
the states of its own UAV and the neighboring UAVs.
The controller is designed using the second order
i is the acceleration of UAV
i  Mi ui, where p
system p
i, Mi captures the UAV dynamics, and ui is the control
input. The input to the system is then described by a
proportional and derivative controller given as [4]

ui

Mi1
 jN w ij
i

w

j Ni

ij









 pi  1 pˆ i  pˆ j   2 p i  p j  ,



(1)

where input, ui, is a vector containing the ith UAVs
control inputs: acceleration and yaw rate. Vector pˆ i
represents the estimated position of UAV i, while α1 and
α2 are controller gains. Each UAV determines its control
inputs by comparing its position error and velocity, (pˆ , p
), with the position and velocity of other UAVs within
its communication range. Controller weights, wij, are
determined by the graph edge weights and are carefully
chosen so that more control effort is applied to UAVs
that are further away, providing support in improving
the time-varying connectivity. When the relative position
error, ( pˆ i - pˆ j ), and relative velocity, (p i  p j), converge
THE BRIDGE // Issue 3 2017

Fig. 3: Change in Fiedler value with varying damping
coefficient.

to zero, then the multi-UAV network reaches the desired
formation or position consensus.
Necessary theories with supported simulations [19],
show the proportional gains, α1, have influence in the rate
of formation convergence. Interestingly, the derivative
control gains, α2, have influence in the slope of the
achieved connectivity profile, which is exploited in our
work for regulating connectivity covered in Subsection
III-C. Bounds are determined for the controller gains to
ensure a positive connectivity measure for all time during
the formation process, and can be found in [19]. Figure
3 shows how connectivity profiles are smoother with
an increase in the derivative control gain values while
keeping the proportional gain fixed. Consequently, the
total number of rises and valleys on UAV paths diminish,
and UAVs attain a fluid path toward the desired positions
for surrounding a mobile target.
C. Desired Connectivity

The problem of achieving a desired connectivity while
making formation can be treated as an optimal control
problem, where optimal control gains 1* (t ) and  2* (t ) are
iteratively selected in time by minimizing a connectivity
tracking error function, given by
E *  t 

min

1ij , 2 ij S ( t )

2

E  t  2  t  Δt   2d  t  Δt   ,
(2)
19



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http://www.brightcopy.net/allen/brid/113-3
http://www.brightcopy.net/allen/brid/113-2
http://www.brightcopy.net/allen/brid/113-1
http://www.brightcopy.net/allen/brid/112-3
http://www.brightcopy.net/allen/brid/112-2
http://www.brightcopy.net/allen/brid/112-1
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