IEEE Robotics & Automation Magazine - September 2012 - 78

and analyzed them using power spectral density. The data
are presented in Table 1. In all four cases, data show less
energy for the load displacement while tracking the
optimal trajectory. The table shows the simulation results
too. Videos of simulations and experiments can be found
at [31].

Figure 7. The Hummingbird quadrotor transporting a
suspended load through obstacles. (Photo courtesy of the
students of MARHES lab, University of New Mexico.)

In the second set of experiments, we try to mimic
swing-free trajectory tracking in cluttered environments,
motivated in the first section by simulations presented in
Figure 3. We built a maze of obstacles shown in Figure 7.
The quadrotor is flying above the obstacles while carrying
the suspended load (the same load used for the first experiment) through narrow corridors. First, the quadrotor was
tracking an initial three-dimensional (3-D) trajectory with
cubic profile with respect to time. Then, using the dynamic
programming-based algorithm, we have computed a 3-D
trajectory with an optimal swing-free profile with respect
to time. The experimental data, including quadrotor position, are shown in Figure 6.
Since it is hard to analyze raw experimental data just by
visual inspection, we use the tools from signal processing,
computing the power spectral density for each signal.
Before processing, we extracted the part of the signal that
corresponds to the swing-free behavior. Power spectral
density describes how the power of a signal is distributed
with frequency [see Figure 6(c)]. By taking the integral of
the power spectral density, we compute the total power
for each signal. We repeated the experiment in four trials

Table 1. Total power Ptot
of the load-displacement signals.

Conclusions
The ability to safely and efficiently manipulate and transport loads using UAVs is an extremely useful capability in
many civilian and military applications ranging from
search and rescue missions, humanitarian relief operations, and automated construction. In this article, we
describe a number of key methodologies that enable
micro UAVs to transport loads while satisfying mission
constraints. Due to the small-scale, limited power, and
limited resources of micro UAVs, we are faced with a new
set of challenges that need to be addressed to make UAVs
commonplace. Static controllers are not sufficient to
handle changes in the CoG of the vehicle. The proposed
adaptive control for changes in the CoG alleviates this need
by providing a provable adaptation rule to compensate for
the changes in the quadrotor's CoG. If (practical) swingfree motion is required, the dynamic programming
approach described in this article is a viable solution to
tackle this issue. Finally, to better understand the advantages and limitations of the proposed approaches, systematic experimental studies on a hardware test bed are
mandatory. To this end, we outlined our multi-UAV
robotic test bed and demonstrated its capabilities to validate advanced control algorithms, networking protocols,
and cooperative behaviors that would make stable and
agile UAV manipulation and transportation using micro
UAVs a reality.
Acknowledgments
Partial support was provided by NSF grant ECCS 1027775
and by DOE URPR (University Research Program in
Robotics) grant DE-FG52-04NA25590.
References
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Experimental
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Ptot Init.
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Ptot Opt.
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Trial 1

31.0634

26:7398

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Trial 3

Trial 4

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[4] S. Bouabdallah, P. Murrieri, and R. Siegwart, "Design and
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IEEE ROBOTICS & AUTOMATION MAGAZINE

SEPTEMBER 2012

http://www.honeywell.com/News/Pages/Honeywell

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2012