IEEE Robotics & Automation Magazine - December 2022 - 120

deformation of the whisker sensor. Specifically, by applying
EBB theory, we can get force and torque changes at the base
of the sensor. By designing the Wheatstone bridge at the
base of the sensor, the force and torque change can be
obtained by the measurement of the resistance change of the
piezoresistance. With the theoretical support stated in the
preceding, the contact position can be recorded through
single point calculation, and we can obtain the trajectory of
the contact points by
driving the robotic rat to
move in a straight line at
a constant velocity and
reconstructing the contour
of the object.
The essential assumptions
of the whisker sensor's
mechanical model
are taken from [17]. First,
the experiment is restricted
to an xy-plane. The
robotic rat is driven to
move along the x-axis,
and the whisker sensor
always points to the posimicrosize
crossbeams of the whisker sensor. This means that
excessive contact force will directly lead to the breakage of
the connection between the whisker shaft and sensor base,
while plastic deformation of the whisker shaft will not occur
in the process of normal contact with obstacles. Finally, the
behavior of the whisker shaft in contact with an obstacle follows
Hooke's law. As a result, EBB theory for large deflection
is applicable.
The scanning process is presented in Figure 3(a). The
Lost feature information
and low reconstruction
accuracy will occur if
the states of contact
change from tip contact to
tangential contact.
tive y-axis direction when there is no deformation. Second,
the robotic rat moves at a relatively slow velocity so that the
experiment can be considered a quasistatic problem. Besides,
the whisker shaft is assumed to be a slim, bending rod with a
fixed length L, constant second moment of area Iz
, and constant
Young's modulus E. In addition, the whisker shaft with
nylon material has a high elastic modulus and is glued to the
y
First Contact
Snap-Off
Object Contor
Contact Points
base of the sensor moves along the x-axis from left to right,
which drives the whisker to scan a fixed object sample in a
fixed distance. As a result, information about a certain part
of the object's contour can be obtained by calculating a
series of positions from the first contact to the snap-off of
the whisker sensor, as indicated by the red line in the figure.
In this study, two objects with distinct contours (a semicircular
shape with positive curvature and rectangular shape
with zero curvature) were used in the contour reconstruction
experiments.
To obtain the position of the contact point through the
sensor's output signal, we first analyze the functional relationship
between the position and external force acting on
the whisker. The whisker shaft is treated as a bending
beam according to EBB theory, as illustrated in Figure
3(b). One end of the whisker is clamped at the center of
the sensor's four-beam structure, which moves at a constant
velocity. The contact point is defined as (, ),sx ycc c
which is acted on by support force and friction. Furthermore,
ci denotes the angle between the tangent of the contact
surface and the y direction and represents the extent of
the deformation; α is the angle between the tangent of the
contact surface and x direction, which can be obtained by
the expression
friction. As the sensor moves forward in the positive x
direction, the position of the contact point and value of the
deflection angle change.
For the ease of calculation, we decompose the resultant
υ0
x
(a)
θc
α
F
y
sc (xc, yc)
SA
sc
θ
υ0
s
x
(b)
Figure 3. The whisker sensor scanning and modeling process. (a)
The scanning process with straight-line motion. (b) The model of
the whisker sensor and force analysis of the center connector.
120 * IEEE ROBOTICS & AUTOMATION MAGAZINE * DECEMBER 2022
SP
R1
l
Sensing Beam
R2
SP′
c
Sensing Unit
SW ST
2a
force contributed by the support and friction into component
forces in the x and y directions. According to the definition of
curvature, the value k of the deformed whisker at any position
can be calculated based on the decomposed forces.
According to the boundary condition, when
iic ,= the curvature
of the whisker at the contact point can obtained. Thus,
the contact point can be determined, as follows:
s == ic
;
x
y
c
c
E
K=+ -+ia ia
z
EI
2
coscos
c
R
T
S
S
S
S
#
#
ic
cos
sin
K
K
i di
i di
V
X
W
W
W
W
,
F (( )( )) .
can be expressed as follows:
(( )( ))
L
=+ -+
i
#0
c
2F coscos
EIz
c
(5)
The relationship between the two unknowns ci and F
-1
ia ia di.
(6)
arctan ,n where n denotes the coefficient of
IEEE Robotics & Automation Magazine - December 2022

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