A Method to use Nonlinear Dynamics in a Whisker Sensor for Terrain
Identiﬁcation by Mobile Robots
Zhenhua Yu 1, S.M.Hadi Sadati2, Hasitha Wegiriya3, Peter Childs 4,Thrishantha Nanayakkara5,
Abstract— This paper shows analytical and experimental
evidence of using the vibration dynamics of a compliant whisker
for accurate terrain classiﬁcation during steady state motion
of a mobile robot. A Hall effect sensor was used to measure
whisker vibrations due to perturbations from the ground.
Analytical results predict that the whisker vibrations will have
one dominant frequency at the vertical perturbation frequency
of the mobile robot and one with distinct frequency components.
These frequency components may come from bifurcation of
vibration frequency due to nonlinear interaction dynamics at
steady state. Experimental results also exhibit distinct dominant
frequency components unique to the speed of the robot and the
terrain roughness. This nonlinear dynamic feature is used in a
deep multi-layer perceptron neural network to classify terrains.
We achieved 85.6% prediction success rate for seven ﬂat terrain
surfaces with different textures.
Index Terms— Robotic whiskers, Surface identiﬁcation,
multi-layer perceptron, Modal analysis.
Terrain surface identiﬁcation is an important function
for mobile robots moving and performing tasks in ex-
treme,unstructured environments . By identifying different
terrain surfaces, mobile robots could better perceive the
surrounding environment information and decide the optimal
next move. For example, they can avoid less favorable terrain
types such as soft sand, and use the identiﬁcation information
for mapping and localization objects. Although many sensors
such as cameras are used for object recognition, whiskered
tactile perception can potentially provide a robust, and eco-
nomical solution for these problems, especially in extreme
(e.g. dark, foggy) environments.
Over the years, vision , lidar , sound , iner-
tial measurement units , and tactile sensors  have
been studied for surface identiﬁcation. Vision-based meth-
ods combined with deep learning have become a research
hotspot and signiﬁcant scientiﬁc and technological devel-
opments made. However, vision-based methods can have
*This work was supported in part by the Engineering and Physical
Sciences Research Council (EPSRC) RoboPatient project under Grant
EP/T00603X/1, MOTION project under Grant EP/N03211X/2, Grant
EP/N029003/1, and supported in part by China Scholarship Council.
1Zhenhua Yu is with Dyson School of Design Engineering, Imperial
College London, SW7 2DB London, UK firstname.lastname@example.org
2S.M.H. Sadati is with the Department of Surgical and Interventional
Engineering, King’s College London, London WC2R 2LS, U.K
3H. Wegiriya is with the Faculty of Natural and Mathematical Sciences,
King’s College London, London, WC2R 2LS, UK .
4P.Childs is with Dyson School of Design Engineering, Imperial College
London, Dyson Building, 25 Exhibition Road, London, SW7 2DB, UK.
5T. Nanayakkara is with Dyson School of Design Engineering, Imperial
College London, Dyson Building, 25 Exhibition Road, London, SW7 2DB,
Fig. 1. Proposed mobile robot equipped with a bioinspired whisker sensor
mounted on a 4-DOF servo fusion rotating platform.
a high probability of failure because of the similar visual
appearance of different terrains or objects. Moreover, visual
accuracy is severely impaired by environmental conditions
such as fog, smoke, low light levels, high-brightness and
high-temperature. Recognition and classiﬁcation methods for
different objects based on lidar data have been popularly
used in autonomous cars, but its accuracy will drop in sandy
applications and dusty scenes. For an IMU installed on the
mobile robot body, a challenge is that they cannot predict
the terrain and object types in advance before the robot has
contact. For example, when the robot detects a change in
terrain from concrete to soft sand based on inertial signals,
the wheels may have already come into contact with the sand.
This can lead to dangerous consequences. Therefore, it is
important to ﬁnd robust sensing modes for the environment
to achieve terrain identiﬁcation under extreme unstructured
environments and the whisker sensor is a choice worth
Artiﬁcial Whiskers sensors have been demonstrated in
several studies that are a particularly high-efﬁciency method
for animals such as rats and sea lions which can use them to
navigate in the dark and perceive environmental information
and features without vision .
This has motivated researchers to design and construct
whiskers for applications such as navigation , obstacle
avoidance , object detection , size measurement ,
shape recognization , and surface information . For
example, in , Zurek showed that static antennae can
act as locomotory guides which can compensate for visual
methods to determine the location and distance of obstacles
during fast locomotion. By rotating the whisker against a
sequence of contact points of the object and collecting
torque information, Solomon and Hartmann put forward a
method to obtain an object’s 3D contour information .
In 2020, authors of  showed that a novel variable stiffness
controllable multi-modal whisker sensor can capture different
vibration frequencies by controlling whisking speed and the
stiffness of the follicle. In all these cases, experimental
results prove that the whisker sensors can effectively com-
pensate for the shortcomings of vision sensors in an extreme
In the work reported here, we designed and constructed a
novel whisker tactile sensor to achieve terrain identiﬁcation
for a mobile robot platform (Fig. 1). Reservoir computing
,  is used in the whisker sensor to map slight
changes in the ground perturbations to distinct steady state
frequency components. This paper ﬁrstly shows that the
steady state response of nonlinear vibration dynamics can
be used to classify terrain textures even on ﬂat terrain. The
remainder of this paper is organized as follows: Section II
introduces the design and construction of the whiskers tactile
sensor, and the experimental system including the Raspberry
robot, whiskered tactile sensor. The whisker sensor vibration
characteristics and modal analysis are studied in Section
III. Section IV reports the whisker vibration data collection
and feature extraction as well as algorithm framework based
on multi-layer perceptron. Section V presents the results
and analysis of terrain identiﬁcation experiments . Finally,
Section VI concludes this paper’s contribution and discuss
the future work.
II. SYS TEM DESIGN & PRELIMINARY ANALYS IS
A. Bioinspired Whisker Sensor Design
The proposed whiskered tactile sensor uses SS49E linear
Hall sensors that are orthogonally mounted on one side
of a silicone rubber sensor holder base and spring beam
on the other side. The structure is shown in Figure 2. A
neodymium permanent magnet is embedded inside the spring
beam that is made of high-carbon steel, with the free length:
60 mm, wire diameter: 1 mm, outside diameter: 10 mm, and
inside diameter: 8 mm respectively. Tapered silicone rubber
is installed on the tip of the spring in order to accurately
capture the vibration of the surface . The components and
materials cost of this whiskered tactile sensor totalled less
than $5 based on one-off non-discounted prices. The low
cost construction of this novel sensor provides an advantage
to many existing surface identiﬁcation sensors
B. Sensor Characterization & Working Principle
The whisker sensor is installed on the 4-DOF servo fusion
rotating platform for orientation control of the whisker,
which keeps the whisker sensor at a horizontal orientation all
the time for clarity. When the robot traverses different terrain,
external vibrations are applied to the whiskered spring shaft,
and the shaft deforms also inducing the same vibrations
on the magnet inside. This causes a continuous magnetic
ﬂux change near the linear hall effect sensor. Consequently,
the hall effect sensor generates continuous low-frequency
Fig. 2. The bioinspired whisker sensor.
Fig. 3. Schematic diagram of the robot whisker system ﬂow framework
electrical voltage signals. The sensitivity of this whiskered
tactile sensor relies on the vibration of the whiskered spring
beam and the silicone rubber tip.
C. Experimental Setup Design & Procedure
The experiment is conducted by a four-wheel mobile
robot. The wheeled unit and electronic system are shown
in Fig.1. The robot is 270 mm in length, 150 mm in height
and 130 mm in width, 1.4 kg in mass, with the diameter and
width of the wheels are 70 mm and 30 mm respectively. The
robot car could traverse through the coarse ground at a speed
of up to 1.3 m/s, With a power supply of 5 V.
The robot system consists of a whiskered tactile sensor
orthogonal ﬁxed in a 4-DOF servo fusion rotating platform,
controlled by a Raspberry Pi 4 B.The whiskered tactile
sensor has its own ampliﬁer, and the raw voltage signals
are sent to an ADS1115 analog to digital converter.
The AD converters, servo motor driver as well as the
4-DOF rotating platform are connected to a Raspberry Pi
4B. The sensor data collection, robot’s motion and rotating
platform’s movement are synchronized controlled by the
Raspberry Pi 4B . All data are recorded in the raspberry pi
on-board ﬂash memory, and then transferred to a computer
(1.60 GHz, 8 GB RAM) via Bluetooth for processing. Fig.3
shows the system ﬂow framework.
III. PRELIMINARY THEORETICAL STUDY
The sensor vibration characteristics are studied as a proof-
of-concept for the idea presented.
A. Cantilever Beam Vibration with Base Excitation
The sensor is modelled as an equivalent cantilever beam
with uniform mass under base excitation (Fig. 2). The steady
state response of such system for sinusoidal base excitation
yb=hbsin(ωbt)can be found based on the derivations in
 as a summation over the beam ﬁrst ﬁve mode shapes in
Yi(x) = sin(βi·x)−sinh(βi·x)−...
αi=sin(Di) + sinh(Di)
cos(Di) + cosh(Di),βi=Di
qi(t) = 1
Qi(t) = Zl
where y(x,t)is the beam displacement at any length
xand time t,hband ωb=2πfare the base ex-
citation amplitude in [m] and frequency in [rad/s],
fis the base excitation frequency in [Hz], D=
[1.8751,4.6941,7.8548,10.9955,14.137]is a set of
constants related to a cantilever beam mode shapes ,
and ζ=0.04 is the modal damping based on stainless steel
material. The equivalent beam has a length lsimilar to
the coil spring axial length lc=l=60 [mm] and cross-
section area asimilar to the spring wire cross-section area
w, where rw=0.5 [mm] is the wire radius. The
beam unit length density is ρ=Cρwwhere ρw=8050
[Kg/m3] is the wire material (stainless steel) density, and
C=lw/(np)is a correction factor to account for the coil
shape based on the spring wire pitch p=ls/n, overall length
lw=np(2πr)2+p2, and spring number of coils n=13.
We may assume that the beam bending modulus E I is
equivalent to the spring wire torsional modulus GwJw, where
Gw=Ew/3=70 [GPa] is the wire material (stainless steel)
shear modulus, and Jw=πr4
w/4 is the wire cross-section 2nd
moment of area.
B. Sensor Modal Analysis
The simulation results for the sensor lateral displacement
ys=y(xs,t), where xs=5 [mm] is the sensor distance from
the beam base, and the signal FFT (Fast Fourier Transform)
analysis in response to different excitation parameters (hb=
0.1&0.3 [mm] and fb=100&300 [Hz]) are plotted in
Fig. 4. Distinctively, different signal proﬁles and dominant
frequency are observed for different excitation frequencies
(i.e. due to ground texture). The signals’ ﬁrst two dominant
frequencies are 100 (same as excitation) & 140 [Hz] and 120
& 300 (same as excitation) [Hz] respectively.
Fig. 5 shows the sensor maximum displacement ys−max
in [m] and dominant modal frequency fs−max in [Hz] for
different excitation frequency fband amplitude hbvalues.
Distinct regions are observed for the values of fs−max as a
function of fband independent of hb. This shows that it
0 200 400 600 800 1000
0 200 400 600 800 1000
0 200 400 600 800 1000
0 0.005 0.01 0.015
hb = 0.0003 [m], fb = 300 [Hz]
0 0.01 0.02 0.03 0.04 0.05
hb = 0.0003 [m], fb = 100 [Hz]
0 0.01 0.02 0.03 0.04 0.05
hb = 0.0001 [m], fb = 100 [Hz]
Fig. 4. Sensor displacement y(steady-state oscillations for ﬁve base exci-
tation cycles) and FFT analysis due to various base excitation frequencies
fband amplitudes hb.
hb [m] 10-3
Fig. 5. Sensor displacement maximum value ys−max and dominant modal
frequency fs−max vs. base excitation height hband frequency fb.
is possible to successfully classify the excitation frequency
fb(i.e. the regions with different different growth patterns)
based on the sensor signal dominant frequency fs−max.ys−max
is affected by both the fband hbdespite its distinct maximum
values around fb=100 [Hz] and rapid growth for higher
values of fb. As a result, the sensor signal amplitude ys−max
is not solely enough to determine valid information about
the base excitation. However, by classifying the excitation
frequency fbbased on the sensor signal modal analysis, the
sensor signal amplitude ys−max has enough information to
determine the excitation amplitude hb(i.e. ground proﬁle
height). Sudden changes in the slope of ys−max vs. fbfor
fb≈500 [Hz] show that sharper changes in the sensor signal
should be anticipated as a result of proﬁle texture variations
for a higher frequency base excitation (e.g. rough train).
The above analysis indicates that the sensor signal can
provide enough information for classifying the sensor base
excitation (ground proﬁle) if an appropriate method is em-
ployed to effectively handle the real-world uncertainties.
Such a method is discussed later in this paper.
IV. DATA PRO CES SIN G AND D EEP NEURAL NETWORK
The entire terrain surface identiﬁcation and recognition
process are divided into three phases: 1) whisker-based off-
line data collection and processing; 2) off-line training based
Fig. 6. Diagram of whisker vibration data collection and procession
on machine learning; 3) whisker-based online surface clas-
siﬁcation and recognition. The whisker should be designed
properly and the classiﬁcation models need to be trained off-
line accurately, in order to achieve a higher success rate for
identifying similar terrain surfaces.
A. Data Feature Extraction
The whiskered robot needs to collect enough whiskered
tactile sensor vibration information for model training by
traversing different terrain surfaces several times. The operat-
ing frequency of whiskered tactile sensor during experiments
is 200 Hz, and the tactile vibration data which is collected by
the whiskered sensor was pre-processed and then segmented
for accelerating the model training speed. Every segmented
vector corresponds to one-second of data from the whiskered
tactile sensor , so a 1 ∗200 labeled surface vector x1∗200
Where Siis the different terrains surfaces and
i=1,2,3,4,5,6,7 corresponds to ﬂat, cement, brick , carpet,
soft-grass, sand and asphalt terrain surface respectively.
The raw vibration data is subsequently converted from the
time domain to frequency domain . The ﬁrst stage of data
procession is standardized, and every vibration vector unit
is normalized to a unit vector whose standard deviation is 1
and the mean value is 0.
Then, the tactile vibration vector unit x1∗200
formed from the time-domain to the frequency domain x1∗200
through a Fast Fourier Transformation. The Fast Fourier
transformation has been proven efﬁcient and capable of clas-
sifying the difference between multiple terrains in Section
III and it signiﬁcantly enhances the Fourier transform speed
when compared to other Fourier transform methods.
B. Network Architecture
As shown in Figure 7, a , deep neural network with seven-
layers based on multi-layer perceptron is built to achieve
the different terrain surfaces identiﬁcation. The activation
functions of the ﬁrst ﬁve layers are Rectiﬁed Linear Units,
and the Soft-max function is introduced to better identify
surface types. The cross-entropy loss function activation can
be applied to evaluate the deviation matrix between the
predicted and actual value.
Fig. 7. Overview of Deep Multi-Layer Perceptron Neural Network Pipeline.
For different terrains, this project collects 5 minutes of
tactile vibration data Xraw for model training and terrain
surfaces classiﬁcation. These data are pre-processed and
divided into 300 terrain feature vector unit x(i,f)based on
above data feature extraction method. All the data are labeled
and connected as a terrain feature class vector X(i,f).
During the training and classiﬁcation period, 75 % data
Xtrain are randomly selected from the Xffor model training,
and the remaining 25% data Xtest are used to test the
performance of network. The input layer of this network
consists of 200 neurons which corresponds to the dimension
of the surfaces feature vector unit x1∗200
(i,f), and the output
layer includes 7 neurons, corresponding to the seven different
terrain surface types considered here. All layers of the
network are fully connected. After the training is completed,
this network is used to classify the remaining 25% testing
vectors data Xtest and it returns an estimation of the terrain
type. By trial and error, all the network’s training parameters
were updated, but it is impossible to make it optimal.
To verify the reliability and robustness of the afore-
mentioned whiskered tactile sensors and sensor vibration
characteristics analysis based on reservoir computing, surface
identiﬁcation experiments were conducted on seven different
terrains at the same speed. Then, the inﬂuence of the mobile
robot running speed on the whiskered tactile sensor’s iden-
tiﬁcation capability has also been analyzed and discussed
from nonlinear dynamic resonance perspectives based on the
theory presented in Section III.
A. Terrain Surfaces Identiﬁcation
Based on the above methods, the whiskered robot was
controlled by a Raspberry Pi 4 system to move on 7 different
terrain surfaces: brick, cement, ﬂat terrain, carpet, soft-grass,
sand and a soft-soil surface respectively. All raw collected-
data are pre-processed and the deep multi-layer perceptron
neural network is pre-trained ofﬂine properly. Part of the
sample experiment terrain surface and its corresponding
vibration data are given in Figure 8.
This experiment collects 5 minutes of vibration data for
each terrain surface. By randomly extracting 75 % data Xtrain
from the terrain tactile vibration database as the training
Fig. 8. Comparison of two example terrain surface(top two:soft-grass;the
bottom two:brick) and corresponding raw vibration data. The time window
of this vibration voltage data is 5 seconds
EXP ER IM EN TS PARAMETER SET TI NG - 3 00 S ET S (T RA IN IN G DATA:
75%; TES T DATA 25% )
Robot Velocity 0.2 m/s
Sampling Frequency 200 Hz
Time-window 1 sec
Fig. 9. Prediction rate of seven terrains surface
data, and the rest 25% of data Xtest were used to test the
performance of this network. The experimental parameters
are set as shown in Table I. In all, 20 random experiments
were conducted to avoid accidental errors caused by random
As can be seen from the Figure 9, the predicted classiﬁca-
tion success rates for ﬂat terrain, carpet, cement, soft-grass,
brick, sand and softsoil terrain surface are 87.3%, 83.6%,
Fig. 10. Confusion matrix of seven terrain prediction success rate
79.2%, 91.3%, 85.4%, 86.6%, and 85.8% respectively. The
experimental results indicate that the whiskered tactile sensor
and the deep multi-layer perception neural network have
good recognition and identiﬁcation capabilities of different
terrains, with an average success rate of about 85.6%.The
results shows that the steady state response of nonlinear
vibration dynamics of whisker sensor can be used to classify
Based on the confusion matrix in Figure 10, this network
has high identiﬁcation and classiﬁcation success rate for
ﬂat and soft grass terrain surface because they have distinct
vibration features based on their vibration signals. However,
there is a high confusion rate between the ﬂat surface and
the brick surface which can be explained by the similar gap
between the two adjacent units. In the case of the cement
terrain, this could have a complicated surface including
features such as gaps, a smooth or rugged surface which
make the network more challenging to classify it from others.
Combined with the simulation results in Section III, the
results indicate that robot’s base excitation vibration am-
plitude (i.e. ground proﬁle height) affects the sensitivity of
whisker sensor , and the sensor signal can provide enough
information for classifying the sensor base excitation (terrain
proﬁle) by employing deep multi-layer perceptron neural
B. Different Speed Experiments
The result of the previous section indicates that the
whiskered tactile sensor and the proposed deep multi-layer
perceptron neural network reported in this paper has good
classiﬁcation and identiﬁcation capabilities on seven terrains
Siat a constant velocity 0.2 m/s. The inﬂuence of different
speeds on the sensor and model prediction accuracy has been
analyzed. Data collection was performed at speeds of 0.1
m/s, 0.15m/s, 0.2m/s, 0.25 m/s and 0.3 m/s respectively.
All parameters during this experiment are the same as in
the previous section. The identiﬁcation accuracy results are
shown in Table II.
IDE NT IFI CATI ON AC CU RAC Y OF SE VE N TERRAIN SU RFAC ES AT
DI FFE RE NT S PE ED S
0.10m/s 87.6% 78.8% 82.3% 88% 84.8% 86.9% 74.8%
0.15m/s86% 85.2% 88.6% 83.2% 82% 93.2% 82%
0.20m/s87.3% 83.6% 79.2% 91.3% 85.4% 86.6% 85.8%
0.25m/s90.6% 93% 90.3% 81.3% 89.1% 79.3% 91%
0.30m/s92.5% 78.5% 82.2% 85.5% 92.5% 84.2% 78.5%
Fig. 11. Identiﬁcation Accuracy of Seven Terrain Surfaces at different
speeds.The colour of blue, orange,yellow, purple and green represent the
speed of 0.1 m/s, 0.15 m/s, 0.2 m/s, 0.25 m/s and 0.3 m/s respectively.
Looking at Figure 11 and Figure 12, it can be seen that this
system has good identiﬁcation accuracy for seven terrains
surface at different speeds. The average prediction accuracy
of the seven terrains at different speeds are: 83.31%, 85,74%,
85.60%, 87.8%, and 84.84%. Therefore, speed has no con-
Fig. 12. Average prediction accuracy of seven terrains at different speeds
sistent effect on identiﬁcation success rate. However, there
are still some details here that can be used as a reference
to improve the identiﬁcation accuracy. Firstly, the average
identiﬁcation accuracy at a speed of v = 0.25 m/s is higher
than the other four operating states reaching 87.8%, which
indicates that the speed of mobile robot has inﬂuence on
identiﬁcation accuracy. This may be caused by the dynamic
resonance of the nonlinear experiment system. The spring
beam and the robots car achieve a better resonance effect
at 0.25m/s, which makes the spring vibration more obvious.
Since the sensitivity of the sensor depends on the vibration of
the spring, it has a better classiﬁcation effect at this speed.
This also echoes the simulation results of the Section III,
indicating that robot’s base excitation vibration frequency
affects the whisker tactile sensor sensitivity. Moreover, a
nonlinear system has multiple resonance frequencies, this can
also explain why good results are also achieved at the speed
0.15m/s but relatively poor at 0.2m/s.
Secondly, the accuracy of distinguishing between the brick
and ﬂat terrain surfaces increases when the robot speed
increases. Combined with modal analysis in Section III, these
results indicate that terrain surface proﬁle amplitude and
robots vibration frequency affects the sensor sensitivity in
the same way. But, the surface amplitude is the dominant
factor in affecting the sensor displacement for low frequency
Whiskers, vestibular system, and the cochlear are three
examples of compliant mechanical systems in biological
counterparts that solve realtime perception problems using
nonlinear vibration dynamics. Work done on such reservoir
computing systems show that even periodic sinusoidal exter-
nal perturbations can lead to complex steady state dynamics
in the compliant mechanical system including period bifur-
cation and frequency separation at local sites. This paper
shows for the ﬁrst time that the steady state response of
nonlinear vibration dynamics can be used to classify textures
even on ﬂat terrain. We also show that a mobile robot can
use speed control to move the perturbation frequencies to
elicit unique frequency domain responses in a whisker to help
terrain classiﬁcation. Experiment results show that the novel
whiskered sensor and the deep multi-layer perceptron neural
network have good recognition and identiﬁcation capabilities
of different terrain surfaces for mobile robots.
In the future, it will be interesting to investigate how
realtime stiffness control of the whisker can be used as a
control parameter to elicit steady state vibration frequency
components unique to the texture and low frequency geo-
metric features of a given terrain.
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