IEEE Robotics & Automation Magazine - December 2022 - 63

measurements ()V sir are calculated by the theoretical
^h=
of the receiver's signal Vi, where
is denoted as
Vrms is the root mean square of the receiver's voltage on the
quadrature method, and the signal's noise Vnoise
the standard deviation of the receiver's signal Vi when the
robot is stationary. Thus, the signal's noise is about 2-10 µV,
whose median is 5 µV.
Taking these previous calculations, we can obtain the
receiver's measurements Vi and its SNR at every pose sr
the receiver relative to the emitter. Since ()V sir
tive correlation with the distance ()dis sr
has a negafrom
the receiver
to the emitter, one can check that, for a given voltage threshold
V
,thr
the set of positions at which VV
rmsthr
rmsthr
=
region whose boundary line (also called the equipotential
line) consists of the positions at which
VV . To provide
an intuitive demonstration, we select four pairs of the
typical voltage threshold Vthr
and its SNR as (0.5 mV,
40 dB), (0.25 mV, 34 dB), (0.1 mV, 26 dB), and (0.05 mV,
20 dB) and draw the corresponding boundary lines in Figure
11. It is shown that each boundary line is an approximate
ellipse. The extreme values of the distances from the
emitter's center to each boundary line are denoted as Dmin
and
D ,max and their values are also shown in Figure 11. That
is, if it is required that the receiver's signal is valid when its
SNR exceeds 20 dB, the emitter's maximum detectable range
is around 2.32-2.76 m. Actually, we have conducted testing
experiments and found that the receiver's signal with an
SNR of 20 dB is enough for localization.
To sum up, for the electric sense-based hardware with the
physical parameters of V0 = 5 V, R = 0.75 cm, de = 10 cm, and
dr = 20 cm, its emitters' maximum
detectable range is around 2.32-2.76 m.
Until now, we have evaluated the
detectable range of a single emitter. We
believe that the detectable range is not
small compared with the physical
parameters of the hardware.
Moreover, we discuss how to in -
3
2
1
crease the detectable range. From the
theoretical model of the electric field,
one can see that the receiver's measurement
Vi has a positive correlation with
four physical parameters separately,
including the voltage of the emitter V0,
the radius of the emitter's electrode R,
the distance between the emitter's two
electrodes de, and the distance between
the receiver's electrodes dr. Considering
that high voltages could pose a
variety of risks (e.g., to aquatic animals),
we can increase the receiver's
measurement and thus improve the
detectable range by easily increasing
one or more of the other three physical
parameters, R, de, and dr.
Emitter
−1
−2
−3
−4
−3
−2
−1
X (m)
Figure 11. A schematic diagram of the distribution of electric field intensity for a single
emitter. The yellow (respectively, blue) area represents the high (respectively, low)
electric field intensity. The black lines denote the equipotential lines under the different
voltage thresholds Vthr
and the corresponding SNR.
DECEMBER 2022 * IEEE ROBOTICS & AUTOMATION MAGAZINE *
63
0.25 mV, 34 dB,
1.32-1.66 m
0.5 mV, 40 dB, 1.02-1.32 m
Vthr, SNR, Dmin-Dmax
12 34
$ will form a
model of the electric field. Then we calculate the SNR
:log VV20 10 rmsnoise
of
Electric-Emitter Architectures
Now we gain insight into what contributes to the performance
differences among the three typical electric-emitter
architectures, Architecture 1, Architecture 2, and Architecture 3.
First of all, we mention that the emitter density of the three
architectures is identical, and each emitter has the same physical
parameters (i.e., the voltage of the emitter V0, the radius of
the emitter's electrode R, and the distance between the emitter's
two electrodes de). Therefore, a comparison of the three
architectures is essentially a comparison of the uniformity of
the distribution of the electric field, including the uniformity
of the intensity and the uniformity of the direction.
Ideally, our expectation is that the electric field intensity is
equal everywhere in space, so that the localization accuracy of
the robot in different spatial positions will be relatively constant.
However, the emitter's physical properties have already
determined the nonuniformity of its generated physical field
(i.e., electric field intensity), as shown in Figure 11. Meanwhile,
the architecture of the emitters, including both the
position and the orientation of each emitter, will further affect
the uniformity of the electric field intensity. Therefore, our
expectation becomes making the area above a certain voltage
threshold as large as possible (e.g., the yellow area in Figure
3). On the other hand, the uniformity of the electric field
direction is affected by the orientation of each emitter in the
architecture. If a robot can obtain a certain strength of the signal
in more orientations, the robustness of its localization will
be increased compared with the case when the signal is
obtained in only one orientation.
Following the previous discussions, using the theoretical
model of the electric field, we calculate the spatial distribution
0.05 mV, 20 dB, 2.32-2.76 m
0.1 mV, 26 dB, 1.82-2.22 m
Y (m)

IEEE Robotics & Automation Magazine - December 2022

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