The Magazine of IEEE-Eta Kappa Nu October 2017 - 20

FEATURE
where λ2(t) and 2d  t  are the achieved and desired
Fiedler values determined from the graph Laplacian,
Ln+1, respectively. E(t) represents the connectivity
tracking error calculated one time step forward, and
E*(t) is the minimum error. At each time instant, future
desired and achievable Fiedler values are determined
from a range of controller gains α1 and α2. The gains
used to find E*(t) are chosen as the optimal gains 1* (t )
and  2*  t .
To follow a desired connectivity profile, we apply identical
time-varying gain values for all UAVs [18]. Constraints
for the optimal gain search are posed carefully in
concern with the feasibility of the proposed algorithm.
At every time instant t, our proposed algorithm finds
the current optimal gain values in a 2D search space
in the neighborhood of the gain values determined at
the previous time instant. This gain selection scheme
avoids jumps in the time-varying gain profiles, and saves
in invested control effort.
In simulations, we considered a specific desired
connectivity profile where the Fiedler value increases
exponentially at the initial stage, and then decreases
at the same rate to finally settle on a specific Fiedler
value. Such a connectivity profile is chosen to mimic
a typical scenario where the multi-UAV group attains
adequate information exchange capability at the early
stage of a cooperative mission, and then gradually
converges to a desired formation. Figure 4 shows a
sample run of connectivity tracking using the controller
in Equation (1) [18].

IV. Future Work
When the task of multiple cooperative robots is formation,
exploration, or area coverage, it is required that some level
of communication in the network must be maintained.
There exists, however, multiple formations that result
in the same connectivity. Finding alternate formations
that provide the same connectivity profile gives a group
of UAVs flexibility in adding or breaking communication
links, thus increasing its operational capabilities. Such
capabilities could be useful in avoiding certain areas or
obstacles by readjusting the formation accordingly and
still maintain a specific level of connectivity.

V. Conclusion
Distributed controllers for driving multiple UAVs to
a formation surrounding a mobile target while also
preserving the time-varying network connectivity are
20

Fig. 4: Results of the network connectivity tracking over time.

becoming essential for multiple cooperative UAVs. We
show one such controller that maintains the connectivity
and enables UAVs to fly in varying formations using
optimal gain tuning techniques. We expect that much
efforts by researchers in the UAV community will further
advance our knowledge of connectivity and formation in
the near future.

VI. References
[1] D. Jones, "Power line inspection-a UAV concept," in
Autonomous Systems, 2005. The IEE Forum on (Ref. No.
2005/11271), 2005.
[2] J. Katrasnik, F. Pernus and B. Likar, "A survey of mobile
robots for distribution power line inspection," IEEE
Transactions on Power Delivery, vol. 25, no. 1, pp. 485493, 2010.
[3] Z. Li, Y. Liu, R. Hayward, J. Zhang and J. Cai, "Knowledgebased power line detection for UAV surveillance and
inspection systems," in Image and Vision Computing
New Zealand, 2008. IVCNZ 2008. 23rd International
Conference, 2008.
[4] M. E. Campbell and W. W. Whitacre, "Cooperative tracking
using vision measurements on seascan UAVs," IEEE
Transactions on Control Systems Technology, vol. 15, no.
4, pp. 613-626, 2007.
[5] M. Flint, M. Polycarpou and E. Fernandez-Gaucherand,
"Cooperative control for multiple autonomous UAV's
searching for targets," in Decision and Control, 2002,
Proceedings of the 41st IEEE Conference on, 2002.
[6] J. Tisdale, A. Ryan, Z. Kim, D. Tornqvist and J. K. Hedrick,
"A multiple UAV system for vision-based search and
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Table of Contents for the Digital Edition of The Magazine of IEEE-Eta Kappa Nu October 2017