To integrate the source localization with this movement
strategy for a mobile platform, microphones were positioned
on top of the robotic dog, as shown in Figure 2b. The path
planning strategy is shown in Figure 8a. Initially, the robotic
dog records the first measurement at the starting point. Next,
it performs a sweep of the environment by rotating around a
fixed point in 15° increments to identify the direction of the
source. Following this, the robotic dog moves horizontally
toward the estimated source, either to the left or right. At the
new position, a second data point is collected, and the source
location is estimated. It is important to note that we assume
the source is always in front of the robot.
To assess the effectiveness of this strategy, we conducted
two experiments. In the first experiment, the robot took an
initial sample at a starting point and then collected two addi-
tional samples at random locations within a grid, maintaining
a consistent orientation throughout. Using the gathered data,
the hyperbolic equation (Equation 7) was solved to estimate
the source location.
In the second experiment, the robot first captured an initial
sample and then began rotating to gather data. When the
TDOA reached zero, the robot identified the source direction.
With the initial sample and direction established, the robot
moved horizontally to a new position to obtain a second TDOA
for source location estimation. It’s important to note that the
robot maintained the same orientation when taking the second
TDOA as it did for the first, as shown in Figure 9. Additionally,
the robotic dog’s rotational and translational movements
were executed manually rather than autonomously, with
the minimum step size for rotation being 15°. Figure 9 shows
the robotic dog’s motion trajectory for random and strategic
walking.
20
–2
–1
0
1
2
40 60 80 100 120 140 160
Direction θ (degrees)
180°
210° 330°
300° 240°
150°
120°
30°
60°
90°
0.8
0.6
0.4
0.2
1
270°
0°
Amplitude (v)
Leakage
TDOA trend
Leakage
Figure 7. Angle using robotic arm versus (a) variation of time difference
of arrival (TDOA) and (b) amplitude variation.
Record of the first measurement
Find sound source direction of arrival (DOA)
While (TDOA ≠ 0)
keep rotating about Z axis
if (TDOA =0)
DOA =current microphone orientation (θ)
If (0 DOA 90)
motion direction =right
If (90 DOA 180)
motion direction =left
Else
either direction is fine
If TDOA 0
motion direction =right
If T DOA 0
motion direction =left
Else
either direction is fine
Lateral motion direction
Lateral motion direction
Record of the second measurement
Record of the second measurement
Record of the first measurement
Estimate the source location
Estimate the source location
Figure 8. (a) Proposed path planning algorithm and (b) updated path planning algorithm for the robotic dog.
A P R I L 2 0 2 5 • M AT E R I A L S E V A L U AT I O N 57
TDOA
(s
×10–4)

Figure 10 illustrates how the TDOA changes as the robotic
dog rotates about the Z-axis from 0° to 180°, taking measure-
ments every 15°. The expected angle for the TDOA to reach
zero is 63.4°, but the results show that this occurs around
80°, with an approximate error of 15°. The authors attribute
this discrepancy to several factors. Firstly, the robotic dog
may not rotate exactly 15° each time, and secondly, unlike
the robotic arm, the dog’s axis of rotation is not fixed. As the
dog rotates, it tends to shift slightly, leading to changes in its
position. Therefore, the maximum obtainable resolution of
15°, combined with the rotation inaccuracies and the inability
to maintain a consistent position while rotating, results in the
non-smooth behavior observed in Figure 10.
Despite the imperfect direction, the information still aids
the robot in selecting the next location to obtain the second
TDOA necessary for localization. With the understanding that
horizontal movement is more effective, the robot correctly
decides to move right rather than left to capture the second
TDOA. Figure 9 compares the localization results between
random walking and the proposed method.
When moving randomly and taking three measurements,
the error in distance is around 17 cm, which aligns with our
expectation based on the expected error when the robot takes
three random positions. In contrast, the strategic movement
reduces this error to ~11 cm.
While the algorithm presented in Figure 8a is functional,
a closer analysis reveals that the robot does not need to rotate
about the Z-axis in its initial position to determine the next
location. Assuming the sound source is in front of the robot,
the sign of the TDOA (positive or negative) can directly guide
the robot’s lateral motion. Specifically, a positive TDOA indi-
cates the robot should move to the right, while a negative
TDOA suggests moving to the left. This update simplifies the
algorithm by removing the need for rotational steps, thereby
reducing uncertainties related to microphone positions, robot
rotation angles, and the resolution of rotation step sizes.
The simplified and more efficient algorithm is presented in
Figure 8b.
While the results demonstrate promising applications for
mobile robots, including robotic dogs, several issues need to
ME
|
LEAKLOCALIZATION
(1)
(1)
(2)
(2)
(3)
X
Y
Δy =1 m
Δx =1 m
(3)
Source
0 0.5 –0.5 –0.5
0
0.5
1
1.5
2
2.5
X (m)
3
3.5
4
4.5
5
1 1.5 2 2.5 3 3.5 4
Source
0 0.5 –0.5 –0.5
0
0.5
1
1.5
2
2.5
X (m)
3
3.5
4
4.5
5
1 1.5 2 2.5 3 3.5 4
Leakage
Estimated
location
Leak position
Estimated location: strategic motion
Strategic motion hyperbolas
Leak position
Estimated location: strategic motion
Strategic motion hyperbolas
Leakage
Estimated
location
Δy =1 m
Δx =1 m
0.0
394 4 5
0.0
394 4 5
0.06174
0.06
1 74
0
0.001715
–0.001715
Figure 9. (a) Random
walk trajectory and
(b) strategic motion
trajectory of the
robotic dog.
0
0
–1
–2
1
2
20 40 60 80 100
Direction θ (degrees)
120 140 160 180
Original data
Smoothed data
Expected angle of zero TDOA
Figure 10. TDOA variation as the robotic dog rotates from 0° to 180°.
58
M AT E R I A L S E V A L U AT I O N • A P R I L 2 0 2 5
Y
(m)
Y
(m)
TDOA
(s
×
10–4)