IEEE Robotics & Automation Magazine - December 2022 - 121

Therefore, we have obtained the relationship between the
resultant force F and contact position of the whisker. The
resultant force on the whiskers can be calculated from the
sensor's output. The specific process is as follows.
The forces when the whisker sensor contacts an object are
detailed in Figure 3(b). The lengths of the center connector
and slender sensing beam are a2
and ,l respectively. When an
external force acts on the whisker, the center connector provides
support reactions, including force and torque, to keep
the whisker relatively stable. Analyzing one pair of sensing
beams, we find that the left part is under pressure and generates
support reaction ,SP
which represents force and torque,
whereas the right part is under tension and generates support
reaction .ST
conditions, we can calculate the value of deflection vx
ii 8^ MF Lx Fx
x
x
vx dx
x
== -+ -
== -+ -
#
#
x
EI
M d
x
1
EI
xv h
1
EI 8
2
1
xv h
11
2
1
v
^ MF Lx Fx .11 (7)
23B
6
1
v
The four piezoresistors are all distributed at the end of the
cantilever beams [Figure 1(b)]. The amount of change in the
resistance of each piezoresistor is related to the transverse and
longitudinal stresses. Because the transverse stress is very
small, it can be ignored here. Hence, the voltage output
caused by the change in the piezoresistors' resistance can be
determined as
vVcc
=
out
(( ))(( ))
()
21 21
1
+- -+
rv
rv
r
ll
l
kk
k
`
w
M
j
23 (8)
.
5 mm
The preceding expression gives the relationship between the
voltage output and torque M caused by the contact force. As a
result, the position sc
of the contact point can be determined
by simultaneously solving (5) and (8). The trajectory of the
contact points over a continuous period of scanning time can
be calculated by recording the sensor's output when the whisker
scans a certain object, and the trajectory can be then processed
to reconstruct the contour of the contact object.
Experiments
Experimental Setup
The experimental setup is shown in Figure 4. To carry out a
series of passive scanning experiments for both texture discrimination
and contour reconstruction, the whisker sensor is
moved by a robotic rat platform that is 210 mm in length,
60 mm in width, and 75 mm in height, with a weight of 465 g.
The robotic rat has 7 DoF in total: the rear wheels that represent
the hind legs have two active DoFs for movement on the
horizontal plane, the hip has 1 DoF for pitch, and there are 2
DoFs for pitch and yaw on both the head and waist. Given the
high-DoF configuration, the motion model of the robotic rat is
divided into a mobile model that is mainly responsible for
plane locomotion and a behavioral chain that is subdivided
Figure 4. The physical prototype of the robotic rat equipped with
the proposed whisker sensor presented in this work.
2B
rotation angle xi at any position of the whisker, as follows:
,
According to the force balance under quasistatic
and
into actions on the pitch and yaw chains and responsible for
action and behavior. Taking advantage of the robotic rat's yaw
and pitch motions, we conduct texture and contour identification
experiments in the vertical and horizontal planes, respectively,
so that the two experiments do not affect each other.
Performance of Texture Discrimination
In the texture discrimination experiment, the vibrations
caused by the motor and movement of the robotic rat cannot
be ignored. To minimize the impact of these noise sources
and imitate the sniffing behavior of rats, the texture discrimination
experiments use 1 DoF of the hip joint to make a
pitching motion in the vertical direction. Namely, we control
the robotic rat's hip joint to lift the rat's head up and down
regularly so that the whisker's tip touches and scans the target
texture surface, after which the whisker sensor's output is collected
for a target region. This set of actions means that the
original position of the whisker sensor is not changed. The
trajectory of the whisker sensor over one period is presented
in Figure 5. It can be seen that the starting and ending points
Whisker Sensor
Highest Point
Starting (Ending) Point
Trajectory of Whisker Sensor
Texture Collection Process
Posture Recovery Process
Figure 5. The robotic rat's motion for texture discrimination.
DECEMBER 2022 * IEEE ROBOTICS & AUTOMATION MAGAZINE *
121
IEEE Robotics & Automation Magazine - December 2022

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