Mechanics and Morphological Compensation Strategy for
Trimmed Soft Whisker Sensor
Nhan Huu Nguyen and Van Anh Ho*
November 8, 2020

Abstract
Recent studies have been inspired by natural whiskers for a proposal of tactile sensing system to augment the sensory ability of autonomous robots. Here, we propose a novel artificial soft whisker sensor
that is not only flexible but adapts and compensates for being trimmed or broken during operation. In
this morphological compensation designed from an analytical model of the whisker, our sensing device
actively adjusts its morphology to regain sensitivity close to that of its original form (before being broken). To serve this purpose, the body of the whisker comprises a silicon-rubber truncated cone with an air
chamber inside as the medulla layer, which is inflated to achieve rigidity. A small strain gauge is attachedto the outer wall of the chamber for recording strain variation upon contact of the whisker. The chamber wall is reinforced by two inextensible nylon fibers wound around it to ensure morphology change
occurs only in the measuring direction of the strain gauge by compressing or releasing pressurized air
contained in the chamber. We investigated an analytical model for the regulation of whisker sensitivity
by changing the chamber morphology. Experimental results showed good agreement with the numericalresults of performance by an intact whisker in normal mode, as well as in compensation mode. Finally,
adaptive functionality was tested in two separate scenarios for thorough evaluation: 1) A short whisker(65 mm) compensating for a longer one (70 mm), combined with a special case (self-compensation) and2) vice versa. Preliminary results showed good feasibility of the idea and efficiency of the analyticalmodel in the compensation process, in which, the compensator in the typical scenario performed with
20.385% average compensation error. Implementation of the concept in the present study fulfills theconcept of morphological computation in soft robotics and paves the way towards accomplishment of anactive sensing system that overcomes a critical event (broken whisker) based on optimized morphological compensation.

* School of Materials Science, Japan Advanced Institute of Science and Technology (JAIST), 1-1 Asahidai, Nomi, Ishikawa,
923-1292 Japan, email: nhnhan@jaist.ac.jp and van-ho@jaist.ac.jp (corresponding author).

0

1Introduction

Due to frequent burrowing and inhabiting in dark narrow spaces, rats elaborately control their muscularwhiskers to make rhythmic back-and-forth swing for environment exploration [1]. Whisker-obstacle contacts cause the whisker to bend stimulating mechanoreceptive neurons in follicle complex [2]. Many scientists in biology and psychology have been inspired by how rodents utilize tactile sensation to accomplish
tasks including localization [3] and texture discrimination [4]. Additionally, constructing a biomimetic
whisker-based sensor could facilitate not only research of natural behavior in rodent sensing but also a proposal of bio-inspired solutions for sensing capability in mobile robots, especially ones operating in complex
and dangerous terrains that are inaccessible for humans such as collapsed tunnel, building or rooms filledwith gas or smoke, and so on.

Figure 1: Illustration of the proposed whisker sensory system that was integrated into a mobile robot. This
whisker can actively change the morphology of the integrated chamber upon pressurization to adapt to thecritical circumstance of its morphology (being trimmed, broken, or partly damaged) during operation. (A)The integrated chamber is pressurized at a pre-determined value in compensation mode, when the whisker
was broken. (B) Chamber in normal mode (without any damage).
Recently, autonomous robots have been a focus of the engineering and research community for theirability to operate independently in unstable and hazardous conditions [5]. To achieve this ability, sensory
systems of robots require both competencies in sensing ability and flexibility in responding to contingencies.
However, adaptability of sensing components had not been considered as a crucial feature, especially for
artificial vibrissae systems whose whisker tips are frequently eroded, trimmed, or broken (see Fig. 1). In
order to deal with such events (e.g. broken sensor whiskers), autonomous robots normally have to stop
their operation, then be manually repaired or replaced the broken sensing components. To overcome thislimitation, effort must be paid to on-site solutions, especially development of control algorithms, that can1counter problems of broken components at high levels of uncertainty [6]. In this paper, we suggest an
approach that utilizes a morphological computation technique, which can be referred in [7], to offload thecomplexity of the control system and take over the adaptive function. Inspired by how rodents adjust thecapacity arrangement of ”barrels” in their primary somatosensory cortex in adaption to broken whisker, andthe dependence of mechanical properties on the medulla layer of the whisker [1], we introduce an intriguing
prototype of a soft artificial whisker sensor that can actively vary its sensitivity with change in chambermorphology (similar to the medulla layer), changing the chamber morphology, including geometrical andmechanical specs such as shape and softness, as illustrated in Fig. 1(A). The ultimate goal is to enable
autonomous robots to maintain sensibility despite a broken sensory system and remain functioning until thenext maintenance. To support this idea, the morphology of the inner chamber of the whisker is actuated bypressurized air to change the tension of the outermost layer where a strain gauge is bonded as a receptor.
Although there are no sensing receptors on the outer surface of a rodent’s whisker, there are many reports ofinsect antennae with sensing components along their length [8]. On top of that, as far as the authors know,
no study has previously employed the rodent ability to compensate for a trimmed bio-whisker in a robotic
system. Our study demonstrates the advantage of soft materials over rigid materials for artificial whiskers
and the importance of researching the influence of whisker morphology in tactile perception.

2

Related Works

2.1

Bio-inspired active vibrissal sensor in robotics

Haptic sensing through touch offers enormous potential to robots in assessing their surrounding environment, including interaction with human beings. There has been a great deal of research regarding proposalsof new tactile sensing systems based on a variety of touch phenomena. Vibrissae sensory systems are typicalexamples that were inspired by the tactile discriminatory abilities of natural animals. The first implementation by Russell et al. [9] involved a continuum rigid wire to extract contact location, shape and contour
information regarding a target object through contact interaction. Tactile responses were collected by a simple mechanical system comprising a servo-potentiometer and springs. In the following years, a series ofstudies focused on the application of biomimetic whiskers in robotics. Kaneko et al. [10] established thefirst idea of investigating the correlation between the curvature of a flexible wire and tactile information. The
term rotational compliance introduced in this work was also used as a fundamental hypothesis to explain
how rats convert perceptible mechanical signals received during the sensing process into perceivable tactile
information [11]. Ahn and Kim [12] proposed another example of a bio-whisker system integrated into the
Koala robot platform. A Hall-effect magnetic sensor was used to measure the protraction angle in order todetect contact location as well as the texture of the object. Researchers in [2] designed an artificial follicle
containing four pairs of strain gauges that functioned as mechanoreceptors at the follicle-sinus complex.
By collecting and analyzing a set of three different mechanical components related to bending moments
and axial force along the length of the whisker, the location of the whisker-object contact point in threedimension working space could be determined. Anderson et al. [13] suggested an efficient solution to the
problem of discriminating sensory responses caused by self-active movement based on the SCRATCHbot
robotic platform. More recently, TacWhiskers was proposed in [14], wherein a vision-based vibrissal sensor
utilizes a camera to capture the deformation of inner nodular pins upon interactions with obstacles. Besides
inspiration from land mammals, systems inspired by whiskers of aquatic animals have been proposed suchas flow-whisker sensor [15]. One system mimicked the seal’s hunting ability of using its whiskers to track
vortices left by moving prey [16]. A similar effort inspired by seal whiskers was introduced by Zhu et2al. [17], which was able to work on the land (exploring an obstacle and its surface) as well as underwater(detecting water flow direction and velocity).
In general, most of these whisker sensors focus on embedding sensing components into the base, similar to the follicle-sinus complex in mammals, where external impacts along the length are transferred tothe base [2][18]. Such models were considered efficient copies of rodent’s natural behavior in environment
exploration and were proven successful in performance of sensing and navigation tasks by robotic systems.
Nevertheless, consideration of systems that can adapt to change the mechanical properties (elasticity, stiffness, moment of inertia) with variation in geometry of the whisker is still limited. The novelty of our study
lies in the intriguing inspiration from bio-whisker’s structure analysis and plasticity in the neural circuits tocreate advantageous adaptability for the artificial whisker sensory system.

2.2

Morphological computation and soft active tactile sensing

Morphological computation is a method that exploits the structure, material characteristics and dynamics ofa flexible body during interaction with its environment and thus outsource relevant computational function
to the “body” rather than assign it to “central nervous system” [19]. This concept has been widely applied
to the design of bio-inspired robots and related applications, especially in soft robotics. Hauser et al. [20]exploited static feedback generated from a muscle-skeleton system (equivalent to a mass-spring system) togenerate periodic locomotion. Nakajima et al. [21] proposed a soft arm inspired by the octopus, and demonstrated the high-dimensional non-linearity system could be partially emulated by employing the dynamics
of a physical body.
Recently, the demand for improving the interaction of robots with humans and the surrounding environments has been growing. Since soft-bodied robots are inherently soft and deformable, it is expected that they
can not only efficiently accommodate their environment but actively change their own morphology to realize
various sensing tasks. For example, Ho et al. [22] introduced a simple active sensing platform Wrin’Tac
which mimicked water-induced wrinkles on a human finger by extended periods in a wet environment. They
argued that changing morphology of the contact surface would give benefit in varying the stimuli perceived
from the environment, and allow the agent to actively select the sensing modality. Similarly, Qi et al. [23],also inspired by human wrinkles, addressed the idea of forming wrinkles to localize the sliding movement
on a soft path, as well as discriminate a surface profile. Further research highlighted the potential of using
embodiment to explain the behavior of a robot [24] and gave some clues to understand theoretically how anorgan’s morphology defines the agent’s behavior.
Regarding the whisker sensor, most recent studies have used steel or aluminum wires to fabricate suchdevices. However, such materials may experience unexpected oscillation of the whole structure duringstrong external interactions. Moreover, there is little work considering the medulla layer, which plays animportant role in the mechanical properties of the vibrissae [25][26], in designing robotic whiskers. Here,
we propose a design of soft whisker sensor with novel inclusion of the medulla layer, which plays a crucialrole in variation of whisker sensitivity upon morphological change. The main contributions of this paper
can be summarized as follows:
1) Proposal of a novel structure sensory system mimicking the geometry of a rodent whisker with theability to compensate if broken/trimmed or eroded during operation.
2) Construction of a detailed analytical model to describe and compute morphological deformation.
Through this model, we can predict the required chamber morphology for the compensation process, namely
a morphological compensation strategy.
3) A suggestion of a new platform for soft tactile sensing systems that can actively change its morphology in order to facilitate desired responses.
33

Idea and Fabrication of Soft Whisker Sensing System

3.1

Idea
A

B

Central Nervous System

Control System

C
Zone A

Stress

Tactile Compensation
Mechanism
Off-loading
Bio-Whisker’s body

Artificial Whisker’s body
Tactile Compensation Mechanism

Sensory System

Internal
Actuator Stimulation Sensory System(Air chamber)(Strain gauge)

MedullaCortex and Cuticule

Zone B

StrainControl Commands
Feedback Signals

External Stimulation(Environment)

Figure 2: (A) An illustration diagram of how lost tactile information is compensated using a neuron compensation mechanism in rodent’s brains [27] in comparison with (B) the information flows of our morphologybased compensation method which assigns the compensation tasks to the whisker’s body. (C) The typicalstress-strain curve for silicon-rubber material.
Mammalian vibrissae are of interest not only to biologists but also to neuroscientists, thanks to theirexquisite features. In this landscape, a question that arises is: How does a rodent cope when a whisker
is trimmed? Many studies in biology and neuroscience have tackled this question and characterized thecontribution of whiskers to sensorimotor development by trimming collective whiskers of rats and observing
their behavioral adjustments [28], as well as the structural dynamics of neocortical neurons when thoserats grew up [29]. A. Holtmaat and K. Svoboda [27] reported a noticed phenomenon which demonstrated
how a rodent’s central nervous system (i.e., brain) adapts to a broken whisker by adjusting neural region(known as the barrel cortex), where sensory signals are transferred from the snout so that the broken whisker(with decreased sensitivity) would be functionally replaced by its neighboring intact whiskers that appear
to be more sensitive as compensators. In short, rodent’s compensation mechanism of tactile sensing isaccomplished at the central nervous system as illustrated in Fig. 2(A). Assuming that such mechanism was
implemented in a robotic system, then the control system integrated with data-based learning techniquesshould be exploited to address the scenario of losing tactile information due to broken structure. However,this implementation generally requests the controller to share its limited resources for computation tasks
when the whisker was broken (see Fig. 2(A)). In order to reduce such computation burden in biomimetic
system, in this study, we approached differently by assigning the adaption process from the central system
to the whisker’s body (i.e., the chamber) itself as inspired by the proposal of morphological computation[19]. More specifically, as demonstrated in Fig. 2(B), actively actuating the air chamber is expected tochange not only the whisker’s geometry but also its mechanical characteristic. By doing so, the sensitivity
4yA
Region 1

D1

c
d1

x
L1

y
y

xss e

dm
t

Region 2
x

d2

d1

r

D2 D2 Dm

α

D2 Dm

x

β

Lm

l

L2

La

Region 3l
Scaled Region 2

L2

y

d3

D3

x
L3

B

Stair-type intersectionyRegion 1

D1

c
d1

x
L1

y

q

y

xssq edmqRegion 2t

Air pressure Q

q

D

x

q
2

d2

q
2

D Dm

x
q
m

q

l

d2

L
Laq

q

L2

L2

y

q

Region 3

d2
D3

x
L2

Figure 3: The design and dimensions of the artificial whisker for each region: A) Before pressurization. B)
After pressurization. Note that, the structure of the whisker after air pressurization process and most of thechanged variables belong to the region 2. See Table. 1 for details.
of the sensing element (i.e., strain gauge) could be controlled in the way of compensating for incorrect tactile
signals during interaction with the surrounding environment. In addition, it allows the decentralization of
the control system from the central (brain) to the local one (body), thus ideally reducing computation burden
at central level.
In term of the whisker body, the internal structure plays a critical role in transferring tactile signals
to mechanoreceptors. According to Lucianna et al. in [1], a bio-whisker has three separate layers: cortex,
cuticle and medulla (see Fig. 2(A) and (B)). In which, the medulla layer, which tapers from the base towards
the tip, is the so f test layer of the whisker. This suggests a whisker could produce different levels of elasticity
as reflected in Young0 s modulus E (explained in the next section) by re-shaping the medulla layer, such thatperceived signals induced by an external contact would be adjusted as expected due to the heterogeneous
structure. The design of a proposed artificial whisker based on this hypothesis is introduced in the following
sections.
Although the concept of “compensation” in nature vary among species, it is worthwhile investigating
5

Table 1: Artificial whisker parameters (see Fig. 3)
Parameter Value (mm) Parameter Value (mm)
D1
18
L2
178
D 2 = d1
17.8
L3
165
D 3 = d2
16.5
L2
148
D2
14.8
Lm
120
Dm
12
xss
6
d2
13.5
c
2
d3
11
t
3
dm
10.5
l
15
L1
180
e
2
this function in a robotic device. As suggested by Solomon et al. [30], the contact distance is generalized
for any whisker by following equation: Contact distance = a × La , where a is the contact ratio. Based on
this assumption, we propose a compensation concept: with the same contact ratio a, the tactile information
perceived by intact whiskers in an array (either longer or shorter) is supposed to be as close to the broken one
as possible. At the same time, for a sole whisker which requires a self-calibration procedure, compensation
will be activated to obtain updated sensitivity (in the broken case) that is close to the original one. These
cases will be discussed in Section 5.

3.2

Sillicon-rubber characterization

Thanks to the softness of silicon-rubber, the morphology of a soft structure is actively changed by the
integration of a simple pneumatic actuator. It is worth noting that the response of a soft material to stresshighly depends on the applied strain, and the stress-strain relationship may vary significantly as illustrated
in Fig. 2(C). More importantly, the linear theory of elasticity is only valid for a very small deformation that
corresponds to zone A of the stress-strain curve, which obeys Hooke’s law, and is characterized by a constantYoung’s modulus. As stress increases slowly with high deformation in zone B, it is expected that the applied
Young’s modulus in this region reduces, which may result in a change of the soft body morphology. This
characteristic is applied in our method to achieve the changeable morphology of an artificial whisker.

3.3

Design and fabrication of artificial whisker

To achieve the soft changeable morphology in our device, we replicated the shape of a linearly-tapered
natural whisker using silicon rubber and introduced a unique occurrence of the medulla chamber inside thewhisker as illustrated in Fig. 2(B). The proposed whisker was divided into three separate regions to facilitate
construction of the analytical model: cap (region 1), chamber (region 2), and whisker body (region 3) (seeFig. 3). Firstly, the chamber (region 2) is tapered at an equivalent degree of taper as the outer layer, i.e., t(thickness) remains constant. Second, a thin cap (region 1) covers the chamber to prevent air leakage andto house a cylindrical hose that feeds pressurized air in or out. Third, a strain gauge is fixed to the top(outside wall) of the chamber with the sensitive direction toward x-axis. To prevent all unwanted influencesof chamber expansion in other directions but x-direction to the strain gauge, two inextensible fibers (Nylon
nano-filament of diameter φ = 0.38 mm) are wrapped helically with angles α and β around the chamber as
illustrated in Fig 3(A). Bishop-Moser et al. [31] suggested that α and β should be larger than 54.7◦ and234.7◦ respectively, in order to constrain mobility in all directions but the axial translation in x-direction.
6

Figure 4: (A) Fabrication procedure consisting of 4 consecutive steps: Step 1: Mold the inner layer of thewhisker body using the core molds set I. Step 2: remove the body’s mold but leave the medulla mold tohold the shape of the chamber, then wrap slightly with the nylon fiber. Step 3: Coat an outer skin to keep
the reinforced fiber in place with the core mold set II. Step 4: remove the body and the head mold then dip
the big end into a thin layer of Dragon Skin 30 inside the combination of cap mold and an air hose. (B) The
whisker encounters the contact force P, then the change in form of the whisker and the mechanical signal
generated in the strain gauge will be analyzed. (C) Schematic analyzing the internal force exerted in eachcross-section along the length of region 2
Thus, to meet this requirement, we designed the helical path to have the pitch r = 3 mm. All essential
parameters for the analytical model and visualization are presented in Table 1 and Fig. 3, respectively .
The fabrication procedure is summarized in Fig 4(A). We used silicone-rubber Dragon Skin 00-30(Smooth-on Inc., PA, USA) to make the soft whisker body. Molds were designed using 3D-CAD software (Solidworks) and fabricated in a 3D printer (Zortrax M200, Zortrax, Olsztyn, Poland). Two different
sets of core molds were used in sequence due to the complicated design. First, core molds of set I wereused to form the double-helical trench to make ease for wrapping the inextensible fibers in the next step.
Then, set II was used to obtain all the dimensions of the outer layer as designed in Table 1. Both setsshared the same medulla mold which was not removed until finishing step 3. The model was then set on acap mold with a cylindrical air hose (outer diameter 2 mm) and a thin layer of Dragon skin 30 was used tocreate the cap. Finally, a strain gauge was bonded by glue at the designate site xss and covered by a thinlayer of silicone glue to enhance its robustness against external loads. The strain gauge used in this paper is

7

KFGS-2-120-C1-11 L1M2R with gauge factor GF = 2.21 ± 1%, grid length e = 2 mm and was bonded withadhesive glue CC-3A, both from Kyowa Electronic Instrument Co. (Japan). The fabrication procedure wascompleted by fitting the model to the base and the curing process was implemented at a warm temperature
with help from the vacuum dryer AVO-200NB-CR for getting rid of all possible bubbles.

4

Analytical Model for Normal and Compensation Mode

As aforementioned, a typical whisker-like sensing system accomplished various tactile exploration tasks
that happened on the whisker length. However, in the present study, we particularly focused on contact
localization ability, i.e., specifying where contact occurs along the body of the whisker. Therefore, we aimed
to propose an analytical solution to tackle this issue, as well as a platform for a morphological compensation
strategy. For the sake of simplicity, the following assumptions were made:• All possible interactions will be assumed to exert only in region 3 of the whisker body to minimize
estimation error due to high rotational stiffness. In practice, this hypothesis is biologically relevantto the fact that rats tend to make whisker-environment collisions near the tip to avoid the increasing
spike rate of some cells in follicle when contact is close to the snout [32].
• Lateral slip at the contact location is neglected.
• Deformation of the whisker is within the measurable range and principle measuring plane of the strain
gauge.
• A single-point contact is solely considered.

4.1

Normal mode

We attempted to construct a model for prediction of the strain gauge output upon contact with the external
environment, which depends on the geometry, location of applied force, and deformation of the proposed
whisker. Especially, the correlation between the morphology of the whisker model and the medulla chamber
is of particular interest with an intrinsic effect on the response of the sensor system. Therefore, an effective
analytical model was not only necessary to assess our idea, but also applicable for operation in a robotic
system. When the whisker encounters an obstacle, the contact force exerted at a location along the body
generates a bending moment as illustrated in Fig 4(B). We focused on expressing the ratio of the interpreted
tactile signal (or the mechanical strain) to whisker deflection at the contact point. This approach is oneof two fundamentally different methods for performing tactile perception extraction employed by [10][12].
However, such effort used classical beam theory Euler-Bernoulli which is only applicable for a beam that hasa homogeneous cross-section and material property (Young’s modulus). As a result, for our non-uniform
whisker design, we employed Castigliano’s theorem [33] that relates to strain energy generated at eachsection of the whisker body. In short, by assessing the strain energy stored in a soft structure during its
deformation, the displacement of the contact point is identified. Firstly, the principle of conservation ofenergy is given by:
ZaLa

U = ∑ Wi =
0

8

M(x)2
dx,
2Ei Ii (x)(1)

where U denotes the strain energy, Wi is total work done by internal forces, M(x) is bending momentinternally generated in the whisker body, Ii (x) and Ei (i = 1, 2, 3) represent the second moment of crosssection area and Young’s modulus for each region, respectively. The product EI is named flexural rigidity
since it is a measure of bending resistance. I1 (x), I3 (x) and M(x) are calculated as following equations:
πd1 4 (x) πD1 4 (L1 − x)4,=64
64L1 4(2)

πd3 4 (x)π D3 4=(L1 − x + l)4 ,64
64 L3 4(3)

I1 (x) =I3 (x) =M(x) = P(aLa − x),(4)where di (x) is the diameter of the cross-sectional area at position x from the base. In regards to the term I2 (x),44m (x))
the expression for second moment of section area for region 2 is supposed to be: I2 (x) = π(d2 (x)−d.
64
Nevertheless, we realized that it is a challenge to solve Equation 1 with explicit output. To deal with thisissue, an approximation approach by considering region 2 as a thin tube was applied. For instance, let us
consider the big end of region 2, we assumed that D2 ≈ D2 ≈ Dm and t = D2 − Dm . The formulation of
second moment of area for this cross-section I2 (x) is derived as follows:


π
π
π 3
I2 (x) =D42 − D4m =D22 + D2m (D2 + Dm ) (D2 − Dm ) ≈ D2 t
(5)
64
64
8
Then, the generalized formulation of I2 (x) can be re-written as:
3

I2 (x) = π33d2 (x)
π D2t=
L2 − x + c t.
3
8
8 L2

(6)

According to Castigliano’s theorem, displacement δn (x) at the contact spot is equal to the partial derivativeof the total strain energy with respect to contact force:∂Uδn (aLa ) =
=
∂P

Zc
0

M(x) M(x)dx +E1 I1 (x) ∂ P

Zlc

M(x) M(x)dx +E2 I2 (x) ∂ P

ZaLal

M(x) M(x)dx
E3 I3 (x) ∂ P(7)

In normal mode, Young’s modulus is constant for the whole whisker’s body E1 = E2 = E3 = E. Then, weget:
64PL1 4⇔ δn (aLa ) =EπD1 4Zc
0(aLa − x)2(L1 − x)4

dx +

8PL2

3

EπtD2
δn (aLa ) =

Zl

3
c

P
(δ1 + δ2 + δ3 ) ,
Eπ

where

ZaLa

(aLa − x)2
64PL3 4(aLa − x)2dx
3 dx +EπD3 4(L3 − x + l)4
L2 − x + c
l

(8)

(9)

"
#
64L1 4 L1 2 + L1 aLa − 3L1 c + (aLa )2 − 3aLa c + 3c2 L1 2 + L1 aLa + (aLa )2
δ1 =
−
(10)
D1 4
3L1 3
3(L1 − c)3
" 



#

3
L2 − aLa + c 3L2 + aLa − c
L2 − aLa + c 3L2 + aLa + 3c − 4l
8L2
L2
δ2 =
+
−
ln
3
2
2
L2 + c − ltD2
2L22(L2 + c − l)
(11)
9

δ3 =

64L3 4(aLa − l)3.
D3 4 3L3 3 (L3 − aLa + l)

(12)Consequently, Equation 8 denotes the dependence of contact deflection δn (aLa ) on the contact location aLa ,contact force P, geometrical parameters of the whisker’s body and material characteristic E. In which, thedetermination of Young’s modulus E is a difficult task. In this circumstance, we attempted to describe theratio of the strain generated in the outer layer, which is linearly proportional to contact force and material
stiffness, to the curvature of the whisker.
Hooke’s law is applied to construct the relationship between bending stress σ and the strain εn measured
by the sensing element as follows:σyM(x)εn = =,(13)
E
EI2 (x)where y is radius of the outermost layer of the chamber’s wall where the strain is measured:



1 D2
y=
L2 − x + c + t .
2 L2
Let us substitute y, M(x) and I2 (x) into Eq. 13 to get the final form:h i
ss +e D2
3 xZ
3
L
−
x
+
c
+ t (aLa − x)
2
4PL2
4PL2
L2
εn =
dx
=
κ,
3
3
3
EπtD2 xEπtD2L2 − x + c

(14)

(15)

ss

where, xss and e are location and measuring grid length of the strain gauge as shown in Fig. 3(A), and:h ixZ
ss +e D2L−x+c
+ t (aLa − x)
2
L2
κ=
dx
(16)
3
L2 − x + c
xss

Combining Equation 9 and 15 yields:
εn
κ
4L2 3
=
= fn (aLa ) ⇔ εn = fn (aLa ) × δn (aLa ).
δn (aLa ) tD2 3 δ1 + δ2 + δ3

(17)Equation 17 implies that the tactile signal in the form of mechanical strain relies on the geometry, thelocation of the stimuli source and the deformation of the whisker (candidates for contact force P and Young’s
modulus E). Validation of the above model was examined by experimental results discussed later.

4.2

Compensation mode

The proposed whisker is able to employ the compensation mode when it was trimmed or broken along
its body. In this mode, the air pressure inside the medulla chamber is varied, bringing change in chambermorphology, which results in an adjustable output of the strain gauge (attached to the chamber outside wall).
For the accomplishment of this purpose, the analytical model must predict outputs of the sensing element(strain gauge) for different dimensions of chamber morphology (see Fig. 3(B)). Let us introduce variable∆l(x) representing the axial deformation at any cross-sectional area of the chamber when the inner pressurechanges. With this notation, ∆l(l) is the total axial deformation of the chamber, which is directly measured
by a laser sensor (discussed in the experiment section). The ultimate aim is to obtain the new configurationof the whisker model after pressurization with respect to ∆l(l). For ease of modeling, several assumptions
were made as follows:10• Possible deformation upon pressurization of the chamber was assumed to be in region 2. As a result,the morphology region 1 and region 3 remains unchanged under any pressure value. Extension in thelength of region 2 may only be caused by pressure force Q (represented by black arrows in Fig. 4(C))
in the x-direction because of reinforced fibers.
• The diameter at each end of the chamber does not change during air pressurization. Region 2, in
general, and the chamber, in particular, remain linear-tapered upon pressurization.
• The intersection of region 2 and region 3 was stair-like type as illustrated in Fig. 3(B), instead of afillet shoulder.
• Thickness t q , corresponding to the pressure Q in the chamber, was considered to remain a linear distribution across region 2. Thus, t q is calculated as the average value of thickness at two arbitrary
cross-sectional areas near two ends of region 2 (we chose t q (2.5) and t q (l)). We estimated the approximation error rate was about 7.3% according to the highest examined pressure (discussed further
in the experiment section).
The estimation equation for t q (x) is derived by using the ratio of transverse strain to axial strain which issimply represented by the Poisson’s ratio coefficient υ, and calculated as follows:∆R2 (x)υ∆l(l)R2 (x)R2 (x)
υ = ∆l(l)⇔ ∆R2 (x) = ∆t(x) =
l −c
l−c

(18)

⇒ t q (x) = t − ∆t(x).

(19)

Poisson’s ratio of a typical silicone-rubber material was estimated in a tension experiment as approximately
equal to 0.5 [34], in this study, we chose the value of 0.49. Then, thickness t q applying along region 2 iscalculated as:t q (2.5) + t q (l)
,
(20)
tq =
2
where, t q (2.5) and t q (l) are thickness of the cross-section at x = 2.5 mm and x = l, respectively. The next
variable we need to identify is ∆l(x). We applied elastic mechanic theory to derive the axial deformation∆l(x) by the expression below:
F∆l(x) =
E2

Zx
c

1
dx,
A(x)

(21)

in which, F is an internal force generated on the cross-section area at x (indicated by red arrows in Fig. 4(C))
with area A(x). They are calculated by:
πdm 2
F =Q
,
(22)
4
A(x) =

πd2 2 (x) πdm 2 (x) πD2 2
πDm 2
2
−
=
(L
−
x
+
c)
−
(Lm − x + c)2 .
2
4
4
4L2 2
4Lm 2

(23)

Re-writing Equation 16, we obtain followed relation:
Qdm 2 L2 2 Lm 2∆l(x) =
E2

Zx

1

c

D2 Lm (L2 − x + c) − Dm 2 L2 2 (Lm − x + c)2
2

2

2

11

.

(24)

Original Param.
D2
d2

Table 2: Re-identification of whisker’s structure
Param. after pressurization Original Param. Param. after pressurization
D2 q = Dm + t qll q = l + ∆l(l)d2 q = dm + t q
La
La q = La + ∆l(l)qq

L2 q = DD2 q(l−d−c)
q

L2

2

xss q = xss + ∆l(xss )xss

2

By combination of above derived equations, relation of ∆l(x) w.r.t ∆l(l) can be obtained as follows:
Rx

1
2

2

2

2

2

2

D2 Lm (L2 −x+c) −Dm L2 (Lm −x+c)∆l(l).
∆l(x) = cl
R
1
2
2
2
2
2 2
c D2 Lm (L2 −x+c) −Dm L2 (Lm −x+c)(25)

Consequently, Table 2 shows all changed parameters for re-constructing the original analytical model introduced in the previous section, and their new approximation equations. Otherwise, as discussed in section
3.2, Young’s modulus of region 2 (E2 ) is expected to vary corresponding to the change in chamber morphology with pressurization. Hereafter, this variation is described by variable k2 with the following relation:
E2q = k2 E2 = k2 E. With new configuration as specified above, we finish re-constructing the analytical model
for compensation mode by adjusting Equation 10 - 12 as:"#2
2
64L1 4 L1 2 + L1 aLaq − 3L1 c + (aLaq ) − 3aLaq c + 3c2 L1 2 + L1 aLaq + (aLaq )
q
δ1 =
−
(26)
D1 4
3L1 3
3(L1 − c)3

 



!  q
q3
q
L2 − aLaq + c 3L2q + aLaq − c
L2q − aLaq + c 3L2q + aLaq + 3c − 4l q
L
8L
2

+
−
δ2q = q 2 q 3 ln
2qk2t D2L2 + c − l q
2L2q 22(L2q + c − l q )
(27)
3

δ3q =

64L3 4(aLaq − l q )D3 4 3L3 3 (L3 − aLaq + l q )(28)

as well as Equation 15:εc =4PL2q 3k2 Eπt q Dq2 3q
xss +e



Z

q
xss





q
q
L2 − x + c + t
aLaq − xq
L2
4PL2q 3
dx =
κ q,

3
k2 Eπt q Dq2 3
q
L2 − x + cqD2

where:
q

κq =

xZ
ss +e
q

xss







q
q
aLaq − x
L2 − x + c + t
q
L2
dx

3
q
L2 − x + c

(29)

q

D2

(30)

Finally, the final equation to compute the numerical strain in the compensation mode is:
3

4L2q
εc
κq
= fc (aLaq ) ⇔ εc = fc (aLaq ) × δ (aLaq ).
q =q
δ (aLa ) k t q Dq 3 δ1 + δ2q + δ3q
2

2

12

(31)

5

Eperimental Results

5.1

Experiment design

Figure 5: Experimental setup: (A) Block diagram of the experimental setup. (B) Experimental prototypes
1 and 2 have the identical dimensions as listed in Table 1 except the actual length La1 = 70 mm and La2 =65 mm, respectively. (C) Experimental setup includes the data acquisition system, sensors (pressure sensor
and distance sensor) and power supply.
To evaluate the reliability of the proposed sensing system, an experimental setup was designed as illustrated in Fig. 5. It comprised an artificial whisker and an obstacle (with a rigid, sharp edge), fixed onto two
linear motorized stages (PG750-L05AG-UA, Suruga Seiki, Japan) perpendicular to each other. They were
driven precisely at a resolution of 2 µm by a stepping motor controller (DS102, Suruga Seiki, Japan). The
X linear stage was used to ensure the contact was exerted at the desired distance from the base, whereas the
Y linear stage drove the obstacle back and forth for expected deflection with velocity v = 0.5 mm/s. In thisresearch, we examined two prototypes of artificial whisker with equivalent structure parameters as listed inTable 1 but different length: La1 = 70 mm and La2 = 65 mm, to represent an intact and trimmed whisker. The
strain output was measured by an instrument EDX-15A connected with a bridge box UI-54A-120 and sent
to the computer for post-processing by data acquisition program DCS-100A (these devices are from Kyowa,
13Electronic Instrument Co., Japan). The sampling rate for the data recording system was set at 100 Hz. To
acquire information on pressure value and axial deformation of the chamber in the compensation mode, adigital pressure sensor ISE20A-R-M (SMC Co., Japan) and an analog laser sensor IL-030 integrated withamplifier IL-1050 (KEYENCE Co., Japan) were employed. The sensor head of the laser was fixed in a
mounting bracket so that the laser light from the transmitter was coincident to the centerline of the whisker.
Moreover, to ensure the laser light absorption or excessive reflection did not affect the measurement, a black
layer of silicone covered the free end of the whisker. All analog signals from these devices were recorded
by a microprocessor (Arduino MEGA 2560) and transmitted to the computer. Finally, Matlab R2019a wasused for data analysis.

5.2

Procedure for Young’s modulus estimation

In this section, a static test to observe the variation of the material property of region 2 (E2 ) under increased
air pressure in the chamber was conducted. In details, we evaluated the response of the strain gauge generated by expansion in the x-direction of the chamber to compute the value of k2 (E2q = k2 E2 = k2 E). Notethat sensitivity adjustment relied on the change in morphology of the chamber, while a typical response of
an individual sensing element did not remarkably change. At first, the signal of strain gauge generated byaxial stress during air pressurization can be derived as follows:∆lss Qdm 2 L2 2 Lm 2
εa =
=
e
eE2q

xZ
ss +e

1
2

xss

D2o 2 Lm 2 (L2o − x + c) − Dm 2 L2 2 (Lm − x + c)2

,

(32)

where ∆lss represents for the axial deformation at the area where the strain gauge is bonded and εa is themeasured strain. Then, Young’s modulus of region 2 is computed by regressing strain output εa and pressureQ:
Qdm 2 L2 2 Lm 2
E2q =
eεa

xZ
ss +e

1
D2o Lm (L2o − x + c) − Dm 2 L2 2 (Lm − x + c)2
2

xss

2

2

.

(33)

We regulated pressure Q within the range 0.002 ÷ 0.2 MPa and repeatedly recorded the response of the strain
gauge five times. The examined range of Q is decided to avoid exceeding Zone B (see Fig. 6(C)), whichmight increase the error of the estimation method for Young’s modulus (see Section 5.2), or permanently
ruin the original structure. The results are plotted in Fig. 6(A). Output in µm/m from the measuring device
read
is converted by the equation: ε = εGF
× 10−3 , where: εread is read from the software and GF stands forthe gauge factor provided by the vendor (GF = 2.21 ± 1%). Then, by substituting the mean values ofrecorded strain for each trial into Equation 33, we can derive the variation of E2q in Fig. 6(B). Fig. 6(B)illustrates a significant decreasing trend of Young’s modulus corresponding to the increase of pressure inside
the chamber as expected. Note that at very low chamber pressures of the chamber (Q1 = 0.002 MPa andQ2 = 0.005 MPa), i.e., with small deformations of the chamber, the value of E2q slightly falls which reminds
us about the early stage of the strain-stress curve (zone A in Fig. 2(C)). Thus, we may set Young’s modulus
corresponding to pressure value Q1 = 0.002 MPa as the initial Young’s modulus E for the whole whisker.
The value of k2 , then, can be directly calculated and plotted in Fig. 6(C) (note that E2q = k2 E2 ). Finally,
for application to the entire examined range of pressure, we used Matlab’s curve fitting tool to find out thebest-fit equation as mentioned in Fig. 6(C).
In conclusion, the results prove our concept that variation of the inner pressure would lead to morphological change (including softness and shape) of the whisker, as well as the response of the strain gauge.
This was exploited to implement the broken whisker compensation strategy in the next section.
14

Strain gauge output

0.2

0.15

0.1

0.05

BB

1.7

Young’s modulus E! (N/mm")

εa

A 0.25

1.6

0
0

0.04

0.08

0.12

0.16

E2
Q1

1

1.4

1.3

q

Q1 = 0.002Mpa →E2 =1.6148 N/mm"q
1.2 Q2 = 0.005Mpa →E2 =1.6094 N/mm"
1.1

0.2

0

0.04

0.08

D 3.5

0.16

0.2

Measurement data
Fitting line

3
2.5

Δl(l) (mm)

0.9

k!

0.12

Pressure (MPa)

Measurement data
Fitting line

0.95

Q2

1.5

Pressure (MPa)

C

q

0.85

0.8

2
1.5
1

0.75

Fitting equation: k = -1.337Q+0.9958
R-square: 0.9862

0.5

Fitting function: Δl(l) = 18.92Q-0.1249
R-square: 0.9949

0

0.7
0

0.04

0.08

0.12

0.16

0

0.2

0.04

0.08

0.12

0.16

0.2

Pressure (MPa)

Pressure (MPa)Figure 6: Variation of material characteristics with respect to a range of pressure Q: (A) Sensor signals
with standard deviation due to the axial elongation of the chamber were recorded in five times. (B) Young’s
modulus E2q estimation result in which, at low pressures, E2q shows insignificant variability. (C) The corresponding value of k2 and the approximate function depends on the pressure Q. (D) Deformation of thewhisker model in x-direction measured by the distance sensor

5.3

Validation of the analytical model

In this section, we report an experimental method for validation of the proposed analytical model for twomodes (normal and compensation) and demonstration of the feasibility of using the model to predict anappropriate chamber morphology for the compensation process (of a broken whisker). Measurement of
the strain gauge response with different value of pressure in the chamber (Q = 0 MPa for normal modeand Q = [0, 0.002, 0.05, 0.1, 0.15, 0.2] MPa for compensation mode) were recorded, then compared to
the numerical ones derived from the analytical model. All experiments were conducted within the strain
gauge’s sensing range. Before each trial, change in length ∆l(l) corresponding to an input air pressure of
the chamber was measured by a laser sensor. Figure 6(D) shows the obtained result and the fitting functionof ∆l(l) w.r.t Q.
First, we validated the proposed model for the normal mode (Q = 0) using prototype 1 (original whisker
length La1 = 70 mm as illustrated in Fig. 5(B)). In this experiment, X and Y linear stages drove the whisker
and the obstacle, respectively, to make contact at different locations a = 0.45 ÷ 1 in steps of 0.05 along
the body of the whisker, and in a range of deflection δ (aLa ) = 0 ÷ 6 mm. Measurement of strain gauge
output was synchronized with contact onset. The investigated ranges of contact location and deflection were
15

0.2

Numerical result

0.16

Strain gauge output

Experimental result, Q = 0 MPa
0.12

0.08

0.04

0
0.5

Sca
led 0.6
contact 0.7
dis

tanc0.8
ea

0.9
1

1

0

2

3

4

5

6

Deflection (mm)Figure 7: Numerical solution versus experimental result in normal mode (Q = 0 MPa)chosen based on the observation that rodents tend to make subsequent touches (after an unexpected collision)in locations far from the base (along the whisker), as the whisker sweeps over an obstacle without requiring
large deflection [35]. Furthermore, any measuring inaccuracy due to exceeding the sensor threshold could
be prevented. The results are analyzed and plotted in Fig .7. The output of the strain gauge, shown in
Fig. 7, has a quite small variance in amplitude in comparison with the numerical result, demonstrating thefeasibility of the analytical model for normal mode.
Regarding the model in the compensation mode, a similar procedure was applied with different valuesof compressed air Q in the chamber, and the results are presented for the entire range of contact location anddeflection (see Fig. 8). At first glance, both graphs share a similar trend compared to the normal mode resultsin Fig. 7, which highlights an increase in strain amplitude with pressure Q increase under the same interaction conditions (location and deflection). It can be explained by Fig. 6(B) where the value of E2q reveals arapid decrease at high value of compressed air in the chamber, resulting in larger mechanical strain on thechamber’s wall. Results in Fig. 8 also implies that, by variation of inner pressure, the sensitivity of the strain
gauge could be actively adjusted, which supports our original idea on the morphological change that leads
to a change of sensor output and sensitivity. The blow-ups reveal that the strain output at Q = 0.002 MPa isnearly coincident to that of Q = 0 MPa. Hence, it is acceptable to take the value of E2q corresponding to thepressure Q = 0.002 as the initial value of the chamber’s inner pressure. Accordingly, it is sufficient to keep
the whisker’s medulla chamber with a small value of pressure, to be more resilient to change from normal tocompensation mode upon being trimmed. Based on this evaluation, the proposed whisker and the analyticalmodel can be used as a body and brain for selection of suitable morphology to the response of different
sensing tasks, especially for a compensating broken whisker.
In the next section, two case studies are examined which could emulate the compensation process inspired by rodents, and demonstrate the applicability of the proposed whisker sensor to a robotic system forclarification of the efficiency of the analytical model.

16Numerical Results
0.25

Q = 0 MPa
Q = 0.002 MPa

Strain gauge output

0.2

Q = 0.05 MPa

0.15

Q = 0.1 MPa
Q = 0.15 MPa

0.1

Q = 0.2 MPa

0.05

0
0.5

Scal 0.6
ed c 0.7
onta
ct lo 0.8 0.9
catio
na

1

1

0

2

3

4

5

6

Deflection (mm)Experimental Results
0.25

Q = 0 MPa

Strain gauge output

0.2

Q = 0.002 MPa
Q = 0.05 MPa

0.15

Q = 0.1 MPa
Q = 0.15 MPa

0.1

Q = 0.2 MPa
0.05
0
0.5

Sca 0.6led
con 0.7tact
loc 0.8
atio 0.9
na

1

0

2

1

3

4

5

6

Deflection (mm)Figure 8: Numerical solution versus experimental result in the compensation mode: The gradient of thestrain output gets higher as the input of air pressure increases.

5.4

Compensation experiment

In this section, two study cases regarding a broken whisker compensated by its neighboring shorter whisker(Case 1) as well as longer whisker (Case 2), are introduced in evaluation of the suggested compensation
strategy for broken whiskers. While these cases are inspired by the natural behaviors of rodents, anothersub-case of Case 1, which is more appropriate for a robotic system, is also investigated:• Case 1: A short whisker compensates for a neighboring long whisker. In this case, the experimental
Prototype 2 (65 mm in length, see Fig. 5(B)) plays the role of compensator, and the Prototype 1(70 mm in length) plays the role of target. This also includes a sub-case when a broken whisker (theshort one) compensates for itself after being trimmed from its original (long) state.
• Case 2: A long whisker compensates for a neighboring broken (shorter) whisker. In this case, theexperimental Prototype 1 (70 mm in length, see Fig. 5(B)) plays a role of compensator, and the17Prototype 2 (65 mm in length) plays a role of target.
The compensation technique is based on the proposed analytical model for calculation of an appropriate
value of chamber pressure Q so that the updated sensitivity of the compensator is close to that of the target
one. The experiment procedure can be summarized in the following steps:• First, we selected the initial air pressure Q1 = Q2 = 0.1 MPa for prototypes 1 and 2. Then, we estimated the geometrical structure and the material characteristics caused by morphology change byusing equations mentioned in section 4.2 and parameters listed in Table 2.
• Second, from the analytical model for the compensation mode in section 4.2, in order to obtain at thesimilar response of the strain gauge for the compensator and target (i.e., εc1 and εc1 , respectively), a
suitable value k2 that satisfied the concept of compensation was estimated by the following equation:qqqq
εc1 = εc2 ⇔ fc (aLa1) × δc (aLa1) = fc (aLa2) × δc (aLa2
).

(34)

In this evaluation, we chose the input of contact location a = 1 (at the tip of the whiskers) and deflecq
tion δ (aLai) = 1 mm.
• Third, we substituted the value of k2 from the previous step to the relation equation between k2 andpressure Q to determine the necessary amount of air to be compressed into the chamber.
• Finally, the strain gauge output was recorded under different interaction conditions (a = 0.45 ÷ 1 andqδ (aLai) = 0 ÷ 6 mm (i = 1, 2) in steps of 0.05 and 0.1 mm, respectively) for each whisker model andis represented by blue circle markers (the original compensator), red square markers (the target) andblack plus markers (the tuned compensator) for comparison as illustrated in Fig. 9.
5.4.1

Case 1:In this scenario, the compensator (prototype 2) attempted to adjust its sensitivity (i.e., change pressure valueQ) to match that of the target whisker (prototype 1). Substituting the required variables to solve Eq. 34,
reveals the desired value of air pressure is Qq2 = 0.048 MPa resulting with k2 = 1.5033. Simultaneously,
experimental outputs of the strain gauge were recorded as shown in Fig. 9(A). One can observe that bydecreasing the pressure from the initial value to Qq2 = 0.048 MPa, the response of the compensator decreases
significantly (from blue circle markers to black cross markers) towards the target (red square markers) overthe entire range of contact distance and deflection, regardless a small deviation. This result guarantees
the compensator is able to perform similar responses in comparison with those of the target whisker, bysolely changing pressure Q. We also conducted a special case for this scenario, called self-compensation.
Specifically, prototype 1 was trimmed by 5 mm (i.e., length change from 70 mm to a value La1 = 65 mm),then compressed air was discharged at the calculated value of 0.048 MPa. The tactile perception of prototype
1 was re-measured and compared to its own performance before being trimmed. The compensation result,as shown in Fig. 9(B), reveals that it is possible to adjust the sensitivity of the whisker so that it performs
similarly to its own previous state (before being trimmed).
5.4.2

Case 2:In this case, the compensator (length La1 = 70 mm) was set to adjust its sensitivity to match the sensing
performance of the neighboring target whisker (being trimmed with length La2 = 65 mm). In order to
18

A

B

0.25
0.25

Prototype 1, Q = 0.1 MPa

Prototype 1, Q = 0.1 MPa
Prototype 2, Q = 0.1 MPa
Prototype 2, Q = 0.048 MPa

Trimmed Prototype 1, Q = 0.1 MPa
Trimmed Prototype 1, Q = 0.048 MPa

0.2

0.15

Strain gauge output

Strain gauge output

0.2

0.1

0.05

0.15

0.1

0.05

0
0
0.4

-0.05
0.4
Sc
a 0.5

led
co 0.6
nt 0.7act d 0.8
ist 0.9
an
ce
a

1

0

1

2

3

6

5

4

Sc 0.5ale
d c 0.6
on 0.7tac
t d 0.8
ist
an 0.9ceam)Deflection (m

1

1

0

2

3

4

5

6

(mm)
Deflection

C
0.25

Prototype 2, Q = 0.1 MPa

Strain gauge output

0.2

Prototype 1, Q = 0.1 MPa
Prototype 1, Q = 0.192 MPa

0.15
0.1

0.05
0
-0.05
0.4

Sc
ale 0.5
d c 0.6
on 0.7tac
t d 0.8
ist 0.9
an
ce
a

1

0

1

2

3

4

5

6

m)
Deflection (mFigure 9: Compensation test results. Graphs in (A) and (B) are obtained strain signal at various condition ofcontact location ratio and deflection of Case 1 (short whisker compensates for the neighboring long whisker)
and its sub-case (Shelf-compensation: a trimmed whisker compensates to itself), respectively: while graphin (C) is the result for Case 2 (long whisker compensates for a neighboring broken (shorter) whisker)
accomplish this situation, the estimated value of k2 and air pressure Qq1 were approximately 0.7365 and0.192 MPa, respectively. Then, the response of the compensator whisker under various contact locations
and deflections was recorded and illustrated in Fig. 9(C). One can see that by increasing chamber pressure
from its initial value to the estimated one (0.192 MPa), the compensated response of the compensator (black
plus markers) set to leave its original response (blue circle markers) toward and match the response of thetarget whisker (red square markers). Again, by a change in chamber morphology (by internal pressure),whisker sensing performance can be actively adjusted, demonstrating morphological compensation in tactile
sensing.
In conclusion, by evaluation of two showcases on morphological compensation, despite a small difference among calculated and experimental values, the proposed whisker could actively adjust its sensitivity tomatch sensing performance of itself (or a neighboring whisker) when the body length shortened (trimmed
or broken). At the same time, the proposed whisker design and compensation strategy can be exploited todevelop an active robotic whiskers that can actively change their sensitivity to match various sensing tasks,19

or even to compensate itself when it is accidentally broken.

6

Discussion

6.1

Artificial whisker design with changeable morphology

The design of our artificial whisker was inspired by the structure of a rodent whisker but has some differences. The performance of the sensing element (strain gauge) is highly dependent on the morphology of thechamber layer, which differs from a natural whisker in proportion (as illustrated in Fig. 2(A) and (B)). In
detail, the conical-shaped medulla of a natural whisker extends further towards the tip than the chamber in
our artificial whisker, which provides different levels of elasticity. Generally, we kept the chamber’s length
at around 15÷25% of the overall length for two main reasons. First, the area of the small end of the chamber
was kept as large as possible to produce more internal force F with a little compressed air Q (see Fig. 4(C)).
Second, we tried to avoid physical interaction between the chamber body (region 2) and the surrounding
environment, which might result in complications in deriving the numerical solutions. Also, the damaged
zone (broken, trimmed) must not be within the length of the region 2, otherwise, the calculations for theartificial whisker become invalid.
On the other hand, the precision of the morphology analysis relies on the stable expansion of the chamberin the direction of measurement by the strain gauge, thanks to the reinforcement fiber. However, in experimental trials, a slight bend of the chamber was observed at high inner pressure. Due to this observation, theresulting strain output shown in Fig. 6(A) may include not only pure axial translation. However, this may
little affect whisker performance as long as the screw pitch r (see Fig. 3(A)) of the helical path is sufficiently
small. Also, we ignored any possible impact of the nylon fiber in the analytical model and evaluation test of
the material characteristics, even though they were assembled without twisting or tightening.

6.2

Applicability: Haptic sensing system for autonomous robots

A changeable morphology whisker is considered appropriate for embodied intelligence [20] and behavior
adaptivity. Our aim was to provide an efficient solution to active sensing which allows us to actively reconfigure the sensing components to fulfill specific purposes or adapt to critical uncertainty (e.g. partlybroken state). In this discussion, we recommend two types of application configurations for our whiskerbased system:

Type 1: An array of whiskers
An array of whiskers is capable of tactile exploration since all whisker tips lie in a plane, such that, an
obstacle will be swept over by multiple whiskers to obtain rich information. This case deploys the biologicalcompensation procedure discussed in Section 3.1 which is summarized as follows: the broken whisker will
be completely and functionally replaced by its neighboring whiskers in an array of whiskers. Furthermore,whiskers in this system would require the ability to compensate for either longer (Case 1) or shorter (Case2) which were validated by two experiment cases in Section 5.4. Hence, stability is highly required for bothworking states. We will demonstrate how this configuration hardly meets such criteria in the next section.

20

Type 2: A single whisker
For a sole whisker system (or more than one located independently), in order to deal with unexpected
situations (e.g. broken or trimmed whisker), it needs to be able to self-calibrate its performance. The
experimental results, discussed in the previous section (Fig. 9(B)), demonstrate the potential of our whisker
system for such application. Obviously, only air decompression is sufficient in this case. Nevertheless, therobot must be able to acquire feedback about the new configuration of the whisker after trimming to selectan appropriate chamber morphology for exact compensation. This feature will be further examined in thenext study. Furthermore, along with the investigation of sensing ability, we target this sensing device as a
new communication protocol that a mobile robot can use to send a message to their allies in a swarm throughtouching, whereas the content of the message depends on the morphology of the chamber.

6.3

Reliability of the analysis model

In this paper, a numerical model of strain energy stored in each section of an artificial whisker body was
introduced to analyze the consequences of morphology change if its internal chamber is changed. The
convenience of this approach lies in the independent expression of the material characteristic for each region
which is significantly important for the non-uniform structure proposed in this study. Nevertheless, due tothe fact that the inherent relationship between the actuation and the morphological (including geometricaland material) properties were approximated (by equations as introduced in Section 4 and 5), we might beunable to obtain an explicit solution for Equation 34. Among those equations, the expression of the second
moment of cross-section area for region 2, which is approximated by Equation 6, is considered to be a major
factor. We compared the approximated expression I2 (x) with an exact one, then calculated the maximum
approximation error which ranged from 4.7% to 11.51% with chamber width (see Fig. 3) from 33% to 50%of the outer radius of the large end. Thus, to minimize any error in the analytical model, the value of t should
be set as small as possible with regard to the possibility of the fabrication process.
On the other hand, quasi-static tests to observe responses of the embedded sensing element under different contact conditions were conducted with a wide range of chamber morphology. Comparison results in
Section 5.2 and 5.3 show consistency with the hypothesis we made at the beginning of this study. The firstagreement is related to the decreasing trend of Young’s modulus E2 when the air pressure in the chamberincreases (as illustrated in Fig. 6(B)) which conforms to the stress-strain curve (see Fig. 2(C)). The second
agreement is that the experimental results of the analytical model could predict the overall performanceof the system. Thus, the model could be utilized to serve as a brain to actively control the whisker bodydepending on various tasks such as adaptive functions.
Although the performance of the whisker prototypes in compensation mode (see Fig.9) tended to agreewith the hypothesis, some challenges still remain. Some errors in the measurement data may have arisen
during analog-to-digital conversion by the microprocessor system, or the proposed analytical model itself
does not fully consider all potential factors affecting system performance. For overall evaluation, we examined how the parameters of actual length La and air pressure Q influenced the compensator performancein the compensation mode. Moreover, we evaluated how accuracy of the proposed model changed in compensation mode, when the whisker was trimmed at different locations. An experimental procedure similar
to that introduced in Section 5.4 was conducted on the compensator whisker with the length varied from
65 mm to 69 mm in Case 1, and 66 mm to 70 mm in Case 2. Under each condition of trimmed whisker, thedesired inner pressure Q was estimated from the model and applied to the chamber. Then, the difference
between the strain signal of compensator whisker and its target one after implementing the compensation

21

A

B

80

a = 0.45

a = 0.7

Compensation error (%)

60

60

60

50

50

40

40

30

1~2

2~3

3~4

4~5

Deflection range (mm)

0

5~6

0~1

1~2

2~3

4~5

1~2

2~3

Compensation error (%)

Compensation error (%)

Compensation error (%)

20

10
3~4

4~5

5~6

0

La = 69 mm, Q = 0.18 MPa

40

La = 68 mm, Q = 0.165 MPa

30

La = 67 mm, Q = 0.146 MPa
La = 66 mm, Q = 0.124 MPa

20

10Deflection range (mm)

La = 70 mm, Q = 0.192 MPa

50

30

20

5~6

60

40

30

4~5

a=1

70

50

40

3~4

Deflection range (mm)F

a = 0.7

70

50

2~3

0~1

80

60

1~2

0

E

a = 0.45

0~1

La = 66 mm, Q = 0.063 MPa
La = 65 mm, Q = 0.048 MPa

5~6

80

60

0

3~4

Deflection range (mm)

D
80
70

La = 67 mm, Q = 0.075 MPa

10

10
0~1

La = 68 mm, Q = 0.086 MPa

40

20

20

10

La = 69 mm, Q = 0.094 MPa

50

30

30

20

a=1

70

Compensation error (%)

70

Compensation error (%)

70

0

C
80

80

10
0~1

1~2

2~3

3~4

4~5

Deflection range (mm)

5~6

0

0~1

1~2

2~3

3~4

4~5

Deflection range (mm)5~6Figure 10: Compensation error analysis for Case 1 (A)-(C) and Case 2 (D)-(F) with different actual length(La ) and chamber pressure (Qq ) of compensator. The contact location ratio a was varied from 0.45 (contact
location is near the tip of the chamber), 0.7 (contact location is near the center of the trimmed whisker),and 1 (contact location is at the tip of the trimmed whisker); while the pressure Qq was estimated from theanalytical model. Error was calculated based on experimental results as shown in Eq. 35.
was computed through Equation 35.
Compensation error(%) =εac − εt× 100,
εbc − εt(35)

where εac , εbc and εt are tactile responses of compensators after and before compensation process and its
target, respectively. In short, the smaller the compensation error is, the more accurate the compensation
process is.
Figure 10 compares the average compensation error with respect to a specific range of deflection at threedifferent contact locations, i.e., the contact location ratio a was varied from 0.45 (contact location is near thetip of the chamber), 0.7 (contact location is near the center of the trimmed whisker), and 1 (contact location
is at the tip of the trimmed whisker). Generally, the error of Case 1 (Fig. 10A-C) was rather consistentunder most conditions of length and pressure; and smaller than most conditions of error of Case 2 (Fig.
10D-F), especially when contact occurred near the tip of the chamber (i.e., a = 0.45). The factors affecting
the overall accuracy of Case 2 can be characterized as below:• Figure 10(D) illustrates that, at the early stage of whisker bending (very small deflection), the larger
the value of the chamber inner pressure, the larger the compensation error. This can be explained by
the fact that at high pressure, the chamber is stretched resulting in a significant increase of tension of
the chamber wall which requires greater contact force even with small deflection. As a result, the outersurface of region 2 experienced a local deformation at the interacted region, leading to an amount ofstrain output absorbed.
• Whereas, at higher deflection ranges, the bending stress increases enormously producing larger mechanical strain output complying with the stress-strain curve in Fig. 2(C). Thus, the compensation
22

error decreases dramatically which can be observed more clearly for the high-pressure cases (e.g.
blue and orange columns). As can be seen from Fig. 10(E)-(F), the influence of such factors described above was no longer significant due to the inversely proportional relation between contact
location and contact force.
For other cases (Fig. 10(A)-(C)), the results were consistent with the above arguments. Generally, the greatest error occurred with contact close to the base (a = 0.45). However, there was no remarkable differencecompared with the other contact location since the air compressed in the chamber was relatively small for
all testers.
According to above investigation, we conclude that, with the morphology of the artificial whisker suggested by the analytical model, the compensator in Case 1 accomplished the compensation task with morestability and lower overall average error (20.385%) for the whole range of contact locations and deflections,compared to Case 2 (36.1837%). This suggests it is better to configure the proposed device according totype 2, whose chamber pressure is always lower than the initial value in compensation mode, rather thantype 1.

6.4

Affecting factors of compensable range

In the proposed whisker sensory system, the largest compensable range of a shortened whisker is considered
as a fundamental feature of the compensation ability. This feature is also understood as the maximum andminimum level of tactile perception that a whisker can actively adjust to accomplish compensation tasks
with an acceptable accuracy rate. According to the compensation principle clarified in Section 3.1 and 4,
this range is strongly dependent on the morphological transformation of the chamber. In this study, wetested two scenarios (see Section 5.4) with trimmed length up to 5 mm. However, it should be noted that the
proposed compensation process also works for a wider range. To tackle this issue, the value of the initial airpressure Qi (i = 1; 2) assigned in the experiment Section 5.4 need to be altered to 0.2 MPa for Case 1 and 0
MPa for Case 2, respectively. As a result, the changeable range of air pressure inside the chamber, which is
proportional to the morphological transformation level, will be increased accordingly.
Nevertheless, increasing the adjustable range of the compressed air inside the chamber to claim a better
compensation range is not always advantageous due to a higher resulted compensation error (as pointed out
in Section 6.3). Furthermore, in such attempt, the air regulating system needs a more power-consuming
and bulkier compressor which is not suitable especially for a small-scale robotic system. An alternative
approach is to optimize the geometrical variables of the whisker body especially the chamber such as thechamber length l, the thickness t and outer diameters of each region (see Fig. 3) to achieve the maximum
compensable range (upon application’s demand) with a small value of compressed air. Since such approachrequires more thorough investigation on the correlation among influencing elements to the compensation
range, thus, it remains in our future work as a comprehensive fulfillment of the idea of morphology-based
tactile compensation.

7

Conclusion

The novelty of this artificial vibrissa sensing device is the variable morphology of the medulla-like chamber
actively controlled by an external pneumatic actuator to accomplish the re-calibration task for the tactile
perception of a broken or trimmed whisker. In the compensation mode, all potentially deformable parameters were considered in the analytical model and estimated with respect to the inner pressure of the chamber.
Additionally, various experiments confirmed that the material characteristic reflected in the term Young’s
23

modulus E was strongly dependent on the morphology of the chamber. This indicates the sensitivity of thesensing element (strain gauge) can be controlled by using the analytical model. Also, the feasibility andvariability of the proposed device were investigated through two separate experimental cases, in which, case
1 (a short whisker compensating for a longer one or self-compensation) outperformed its counterpart with
only 20.385% compensation error. Furthermore, to our knowledge, this is the first whisker design for arobotic system that incorporates the medulla layer to achieve tactile perception.
In future work, we will explore new methods to optimize the design and increase its precision rate. The
analytical model based on the morphological computation technique will be investigated more thoroughly
to exploit this idea for other applications such as a failure warning system. In addition, the efficiency of thissensory system will be verified by integrating it into a robotic system.

Acknowledgements
This work was partially supported by the Doctoral Research Fellowship of JAIST and partially by JSPS
Grant-in-aid for Scientific Research KAKENHI number 18H01406. The authors would like to thank Mr. Le
Dinh Minh Nhat for his support in setting up the data acquisition system.

References[1] F. A. Lucianna, A. L. Albarracin, S. M. Vrech, F. D. Farfán, and C. J. Felice, “The mathematicalwhisker: A review of numerical models of the rat’s vibrissa biomechanics,” Journal of Biomechanics,
vol. 49, no. 10, pp. 2007–2014, 2016.
[2] Emnett, Hannah etal. “A Novel Whisker Sensor Used for 3D Contact Point Determination and Contour
Extraction.” Robotics: Science and Systems, 2018.
[3] M. Salman and M. J. Pearson, “Advancing whisker based navigation through the implementation of
Bio-Inspired whisking strategies,” in 2016 IEEE International Conference on Robotics and Biomimetics (ROBIO), 2016, pp. 767–773.
[4] J. C. Sullivan et al., “Tactile discrimination using active whisker sensors,” IEEE Sens. J., vol. 12, no.
2, pp. 350–362, 2012.
[5] M. J. Pearson, B. Mitchinson, J. Charles Sullivan, A. G. Pipe, and T. J. Prescott, “Biomimetic vibrissal
sensing for robots,” Philos. Trans. R. Soc. B Biol. Sci., vol. 366, no. 1581, pp. 3085–3096, 2011.
[6] F. Iida and R. Tedrake, “Minimalistic control of a compass gait robot in rough terrain,” in 2009 IEEE
International Conference on Robotics and Automation, 2009, pp. 1985–1990.
[7] R. Pfeifer and G. Gómez, “Morphological Computation – Connecting Brain, Body, and Environment
BT - Creating Brain-Like Intelligence: From Basic Principles to Complex Intelligent Systems,” B.
Sendhoff, E. Körner, O. Sporns, H. Ritter, and K. Doya, Eds. Berlin, Heidelberg: Springer Berlin
Heidelberg, 2009, pp. 66–83.
[8] M. I. Zhukovskaya and A. D. Polyanovsky, “Biogenic Amines in Insect Antennae,” Front. Syst. Neurosci., vol. 11, p. 45, Jun. 2017.

24

[9] A. Russell and A. W. Jaury, “Object Location and Recognition using Whisker Sensors”, Australas.
Conf. Robot. Autom. Proc., 2003.
[10] M. Kaneko, N. Kanayama, and T. Tsuji, “Active antenna for contact sensing,” IEEE Trans. Robot.
Autom., vol. 14, no. 2, pp. 278–291, 1998.
[11] L. Pammer etal., “The mechanical variables underlying object localization along the axis of thewhisker,” J. Neurosci., vol. 33, no. 16, pp. 6726–6741, 2013.
[12] S. Ahn and D. E. Kim, “Radial distance estimation with tapered whisker sensors,” Sensors (Switzerland), vol. 17, no. 7, 2017.
[13] S. R. Anderson, M. J. Pearson, A. Pipe, T. Prescott, P. Dean, and J. Porrill, “Adaptive cancelation ofself-generated sensory signals in a whisking robot,” IEEE Trans. Robot., vol. 26, no. 6, pp. 1065–1076,
2010.
[14] N. F. Lepora, M. Pearson, and L. Cramphorn, “TacWhiskers: Biomimetic Optical Tactile Whiskered
Robots,” IEEE Int. Conf. Intell. Robot. Syst., no. i, pp. 7628–7634, 2018.
[15] W. Deer and P. E. I. Pounds, “Lightweight Whiskers for Contact, Pre-Contact, and Fluid Velocity
Sensing,” IEEE Robot. Autom. Lett., vol. 4, no. 2, pp. 1978–1984, 2019.
[16] J. Z. Gul, K. Y. Su, and K. H. Choi, “Fully 3D Printed Multi-Material Soft Bio-Inspired Whisker
Sensor for Underwater-Induced Vortex Detection,” Soft Robot., vol. 5, no. 2, pp. 122–132, 2018.
[17] L. Zhu, L. Zeng, X. Chen, X. Luo, and X. Li, “A bioinspired touching sensor for amphibious mobile
robots,” Adv. Robot., vol. 29, no. 22, pp. 1437–1452, 2015.
[18] F. Fries and P. Alvarado, “Whisker-like sensors with soft resistive follicles,” 2017 IEEE Int. Conf.
Robot. Biomimetics, ROBIO 2017, vol. 2018-January, pp. 2038–2043, 2018.
[19] R. Füchslin et al., “Morphological Computation and Morphological Control: Steps Toward a Formal
Theory and Applications,” Artif. Life, vol. 19, Nov. 2012.
[20] H. Hauser, A. J. Ijspeert, R. M. Füchslin, R. Pfeifer, and W. Maass, “The role of feedback in morphological computation with compliant bodies,” Biol. Cybern., vol. 106, no. 10, pp. 595–613, 2012.
[21] K. Nakajima, H. Hauser, R. Kang, E. Guglielmino, D. Caldwell, and R. Pfeifer, “A soft body as areservoir: case studies in a dynamic model of octopus-inspired soft robotic arm ,” Frontiers in Computational Neuroscience , vol. 7. p. 91, 2013.
[22] V. A. Ho, H. Yamashita, Z. Wang, S. Hirai, and K. Shibuya, “Wrin’Tac: Tactile Sensing System With
Wrinkle’s Morphological Change”, IEEE Transaction on Industrial, vol. 13, no. 5, pp. 2496–2506,
2017.
[23] Q. Qi, S. Hirai, and V. A. Ho, “Wrinkled Soft Sensor With Variable Afferent Morphology,” IEEE
Robot. Autom. Lett., vol. 4, no. 2, pp. 1908–1915, 2019.
[24] H. X. Trinh, V. A. Ho, and K. Shibuya, “Computational model for tactile sensing system with wrinkle’s
morphological change,” Adv. Robot., vol. 32, no. 21, pp. 1135–1150, 2018.

25

[25] H. M. Belli, A. E. T. Yang, C. S. Bresee, and M. J. Z. Hartmann, “Variations in vibrissal geometry
across the rat mystacial pad: Base diameter, medulla, and taper,” J. Neurophysiol., vol. 117, no. 4, pp.
1807–1820, 2017.
[26] B. W. Quist, R. A. Faruqi, and M. J. Z. Hartmann, “Variation in Young’s modulus along the length of
a rat vibrissa,” J. Biomech., vol. 44, no. 16, pp. 2775–2781, 2011.
[27] A. Holtmaat and K. Svoboda, “Experience-dependent structural synaptic plasticity in the mammalianbrain,” Nat. Rev. Neurosci., vol. 10, no. 9, pp. 647–658, 2009.
[28] H. Arakawa and R. S. Erzurumlu, “Role of whiskers in sensorimotor development of C57BL/6 mice,”
Behav. Brain Res., vol. 287, pp. 146–155, 2015.
[29] M. Armstrong-James, M. E. Diamond, and F. F. Ebner, “An innocuous bias in whisker use in adultrats modifies receptive fields of barrel cortex neurons,” J. Neurosci., vol. 14, no. 11 II, pp. 6978–6991,
1994.
[30] J. H. Solomon and M. J. Z. Hartmann, “Radial distance determination in the rat vibrissal system andthe effects of Weber’s law,” Philos. Trans. R. Soc. B Biol. Sci., vol. 366, no. 1581, pp. 3049–3057,
2011.
[31] J. Bishop-Moser, G. Krishnan, C. Kim, and S. Kota, “Design of soft robotic actuators using fluid-filled
fiber-reinforced elastomeric enclosures in parallel combinations,” IEEE/RSJ International Conferenceon Intelligent Robots and Systems, 2012, pp. 4264–4269.
[32] M. Szwed, K. Bagdasarian, B. Blumenfeld, O. Barak, D. Derdikman, and E. Ahissar, “Responses ofTrigeminal Ganglion Neurons to the Radial Distance of Contact During Active Vibrissal Touch,” J.
Neurophysiol., vol. 95, no. 2, pp. 791–802, Feb. 2006.
[33] E. J. HEARN, “CHAPTER 11 - STRAIN ENERGY,” E. J. B. T.-M. of M. 1 (Third E. HEARN, Ed.
Oxford: Butterworth-Heinemann, 1997, pp. 254–296.
[34] Properties: Silicone Rubber. AZoM.com, 27 Feb. 2020, www.azom.com/properties.aspx?ArticleID=920.
[35] M. Srinivas and L. M. Patnaik, ”Genetic algorithms: a survey,” in Computer, vol. 27, no. 6, pp. 17-26,
June 1994, doi: 10.1109/2.294849.

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