IEEE Robotics & Automation Magazine - December 2022 - 55

dc-based solutions. Then we just need to compare the noise
of the signals. To this end, the standard deviation of the
receiver's signal Vi when the robot is stationary is calculated
as the signal's noise indoors in our laboratory. Then we have
that the noise of the signal under the ac-based solution is
about 2-10 µV, while the noise of the signal under the dcbased
solution is about 1-3 mV [13]. That is, in terms of the
SNR, the ac-based solution improves the dc-based solution
by two to three orders of magnitude, thereby significantly
improving the quality of the signal and further improving
the detectable range of the emitter.
Electric-Emitter Architectures
Although our ac-based solution has successfully improved the
detectable range compared with that of the dc-based solution,
the detectable range of a single emitter is always limited. To
enable the small underwater robots to locate in a large-scale
environment, we further construct distributed electric-emitter
architectures and show three typical architectures in Figure 3.
To construct such architectures, first of all, we need to
decide on the configurations, including the positions and
orientations of the emitters. For ease of expression, we
assume that each of the three typical architectures shown
in Figure 3 is distributed in a rectangular form that has M
rows and N columns, i.e., MN emitters in total. Specifically,
in Architecture 1, every two emitters occupy the same
position in an orthogonal form, while in Architectures 2
and 3, the emitters are uniformly distributed so that the
distances between each pair of adjacent emitters are equal.
Besides, each pair of the adjacent emitters is orthogonal in
Architecture 2, while all of the emitters are parallel in
Architecture 3. It is worth emphasizing that the rectangular
form of configurations we choose is just for ease of
expression and comparison. In real applications, one can
construct various configurations and even space them in a
sparse configuration (see our discussions in the section
" Real-World Applications " ).
Having a configuration of the emitters, it is more important
to assign different frequencies to different emitters appropriately.
In this way, by detecting the frequency of the signals
it receives, the robot can tell which emitters the signals come
from, and then it superimposes the known pose information
of the corresponding emitters and obtains its own global
localization information. To this end, a simple idea is to assign
a unique frequency to each emitter. However, doing so would
obviously waste too many frequency-band resources, especially
when the architecture is large. To solve this problem, we
apply the technique of multifrequency signals; that is, each
emitter generates a signal whose frequency is a combination
of multiple frequencies, while the frequency combinations of
the emitters in the architecture are different. Obviously, with
the help of the multifrequency technique, the frequency-band
resources can be greatly conserved.
For our three typical architectures in Figure 3, we apply the
dual-frequency technique to the MN emitters distributed in a
rectangular form of M rows and N columns. For the emitter
(i, j) lying in the ith row and jth column, its dual frequency
f,ij
combines the two frequencies fi
distinguish the MN emitters.
need ()
row and
f .j
col
MN+ different frequencies to enable the robots to
Biomimetic Electric Sense-Based Localization
On the basis of our proposed hardware solution, we design
localization approaches based on the biomimetic electric
sense. To this end, we first build a theoretical model of the
electric field generated by the electric emitter. Then, we construct
three modules, including the dynamic-model module,
the IMU module, and the electric sense module, each of
which separately estimates the position and/or the orientation
of the robot. Finally, by selectively fusing these modules, we
propose three localization methods.
Model of the Electric Field
We first model the electric field generated by an emitter under
the nonboundary case in a 3D environment, where the electric
potential V s^h is calculated by
V^ hs =
2 11 c +--
`
,,
Rd
V
-
s
xy z
0 11
j sr sr
e
where =^h is a position in the coordinate system
is the distance
( ,,)x 00 and
·
2 denotes the
attached to the emitter, V0 is the voltage of the emitter, R is
the radius of the emitter's electrode, de
between the emitter's two electrodes, and r =++
r =--
22
m ,
(1)
Now, we only
( ,,)x 00 are the positions of the positive and negative
electrodes of the emitter, respectively.
Euclidean distance. Then, based on the preceding model for
the nonboundary case, repeatedly using the mirror method
[16], we build the theoretical model of the electric field for
the six-plane boundary case corresponding to our experimental
environment [i.e., the pool shown in Figure 6(b)].
For more details about the model for the six-plane boundary
case, refer to [13].
According to the theoretical model of the electric field
generated by an emitter, we are able to obtain the pose information
(including the position and the orientation) of the
robot from its receiver's three independent measurements
,
Vi ,,.
i 12 3=
Furthermore, we discuss the relationship among the
physical parameters of the hardware and the receiver's measurements
(),
V i ,,, where sr
irs =123
the receiver to the emitter in a 3D environment, and ()dis sr
denotes the distance from the receiver to the emitter. Specifically,
one can see that the measurement ()V sir
tive correlation with the voltage of the emitter V0, the radius
of the emitter's electrode R, and the distance between the
emitter's two electrodes de, respectively. In particular, when
the distance de
dR5e
2 ), the measurement ()V sir
proportional to V0, R, and de, respectively. Also, the receiver's
measurement ()V sir
has a positive correlation with the
distance between the receiver's electrodes dr, and this
DECEMBER 2022 * IEEE ROBOTICS & AUTOMATION MAGAZINE *
55
is the relative pose of
has a posiis
five times larger than the radius R (i.e.,
is approximately directly
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