Design of a Vibrotactile Display via a Rigid Surface
Yon Visell and Jeremy R. Cooperstock
McGill University, Centre for Intelligent Machines and CIRMMT, Montreal, Canada
A BSTRACTThis paper describes the analysis, optimized redesign and evaluation of a high fidelity vibrotactile interface integrated in a rigid
surface. The main application of the embodiment described here isvibrotactile display of virtual ground surface material properties for
immersive environments, although the design principles are general. The device consists of a light, composite plate mounted on anelastic suspension, with integrated force sensors. It is actuated by asingle voice coil motor. The structural dynamics of the device were
optimized, within constraints imposed by the requirements of userinteraction, and corrected via digital inverse filtering, in order to enable accurate simulation of virtual ground materials. Measurementsof the resulting display demonstrate that it is capable of accurately
reproducing forces of more than 40 N across a usable frequency
band from 50 Hz to 750 Hz.
Keywords: Vibrotactile display design, Vibrotactile rendering,
Foot interfaces
1 I NTRODUCTION
Vibrotactile display devices consist of palpable interfaces that arecapable of vibrating at frequencies salient to human tactile perception, but are not necessarily capable of static force display [35]. Advantages of such displays include their low cost, power efficiency,
and capability of rendering transient or textural effects accurately,at high temporal resolution, when suitable actuators are used.
1.1 Vibrotactile augmentation of floor surfaces
The work presented here concerns the design of a vibrotactile display device integrated in a rigid panel. The specific embodiment
involved is an augmented floor panel designed to enable vibrotactile interaction with ground surfaces. Potential applications of sucha device include the simulation of ground textures for virtual andaugmented reality simulation [39] or telepresence (e.g., for remoteplanetary simulation), the rendering of abstract effects or other ecological cues for rehabilitation, or the presentation of tactile feedback to accompany the operation of virtual foot controls, control
surfaces, or other interfaces [40]. This device constitutes a redesignand optimization of an interface that was introduced in earlier workby the authors [36]. The goal was to systematically improve its fidelity. One motivation for doing so is to avoid artifacts that canaffect realism and prevent careful control of stimuli in experiments
involving human vibrotactile perception. The main artifacts alleviated by the redesign are due to selective variations in the device
frequency response within the range of human vibrotactile sensitivity. We have also attempted to provide enough documentationthat the device, or others like it, may be produced by researchers
or practitioners interested in vibrotactile display via rigid surfaces.
The sections that follow present the device concept, its mechanicaland electronic structure, the optimizations that were undertaken to
improve its dynamic response, and an analysis of the results.
1.2 Background
The fidelity of a haptic device depends on the selection and arrangement of electronic components, and on its structural design, as haslong been emphasized in the research literature on force-feedback
displays. Many of the analogous questions for the design of vibrotactile (VT) displays have received less attention. The vibrotactile
augmentation of touch surfaces has been widely investigated for
HCI applications [24, 11, 23], although design issues affecting theirperceptual transparency have often been neglected. A few examples demonstrating optimized vibrotactile device engineering [41]or software compensation of their dynamics [18] do, nonetheless,exist. Issues related to sensor and actuator selection are covered inrecent reviews of haptic hardware prototyping [13], while the extensive literature on acoustic and vibration engineering provide theknowledge needed for structural dynamics optimization [22, 7, 10].
We are not aware of any prior work on the systematic design ofvibrotactile floor panels for haptic interaction. Passive floor-based
vibrotactile actuation has been used to present low frequency information in audiovisual display applications, for special effects (e.g.,
vehicle rumble), in immersive cinema or VR settings [33]. The
fidelity requirements that must be met by an interactive haptic display are, all things being otherwise equal, higher, since its users areable to actively sample its response to actions of the feet.
Many designs for vibrotactile-augmented shoes or insoles havebeen proposed [19, 27, 25], but nearly all have been designed forsymbolic information display (e.g., directional indicators or encoded messages) or biofeedback stimuli, rather than for presenting virtual ecological stimuli. State of the art haptic force feedback
interfaces for walking [14] are capable of preserving kinesthetic degrees of freedom but are restricted to a small fraction of the bandwidth that our device achieves. As noted below, a wide bandwidthinterface is advantageous for reproducing the rich variety of highfrequency force information that is generated during walking in natural environments [28].
2 D ISPLAY CONCEPT AND MOTIVATION
The interface of the device (Fig. 5) consists of a rigid plate that
supplies vibrations in response to forces supplied by a user’s foot,via the shoe. The total normal force F(t) applied to the plate by auser is measured. It can be assumed to consist of two components:
isolated transients with high frequency content, generated by footimpacts with the plate, and low-frequency forces generated by active human motions, limited in bandwidth to no more than 10 Hz[3, 37]. Vibrotactile feedback is assumed to be constrained, due toactuator limitations, to frequencies greater than a minimum valueon the order of 20 Hz.

A.

B.

F(t)

v(t)

VE

Figure 1: (A.) The experience of stepping onto a deformable object
or surface is (B.) simulated via a rigid vibrotactile interface.

A haptic simulation (Fig. 1) provides feedback approximating
the vibration response felt during interaction with a virtual object.
Our rendering algorithms are of admittance type, computing velocities of displacement in response to forces applied to the virtual

A.

Fe
Object

ve

B.

vh

Tool
(Shoe)

Fd

Fe
VirtualObjectFhContact
State

Deviceve

vd

BiomechHumanControl

FhContact
State

vh

Tool
(Shoe)

BiomechHumanControl

Figure 2: The haptic display concept. (A.) A real system being simulated involves interaction with an object via a tool (the shoe) in auser’s grasp. The user exerts a force Fh (t) and experiences a vibration vh (t). (B.) The display mediates interaction with the virtualenvironment. The dashed lines demarcate system components associated with the object, or its haptic presentation, from those of theuser.

object. An example of such an algorithm is described in Sec. 2.2.
As with most vibrotactile displays, vibrations are presented in open
loop fashion. During the course of interaction, user coupling to
the device interface is expected to vary from no contact to full-footcontact with large forces. In the virtual environment, interaction
is mediated by an idealized proxy that is constrained to a constantregion on the virtual object surface, at which force is applied. In
these respects, the contact state is entirely modeled in the real world(Fig. 2). In other words, user-supplied forces (zero or otherwise),as measured by the device, are continuously mapped to the simulation, and there is no modeling of contact variation within the virtualenvironment.
2.1

Transparency

In order to ensure perceptual transparency of the display, the admittance of the virtual object it presents should resemble as closely as
possible that of its real counterpart. As illustrated in Figure 2, thisrequires that the (velocity) feedback generated from forces applied
to the virtual object closely match those produced by interaction
with the real one, and that the device transfer function Hd (s) be as
close to unity as possible. Here, we refer to the free (unloaded) response of the display, corresponding to components to the left ofthe dashed lines in Fig. 2. When coupled to a user, the acceleration
response of the interface will be modified due to the state of contact between the user and plate, and the biomechanical dynamics of
the user (measurements are presented in Sec. 5). These variations
are beneficial in allowing our device to mimic natural variations in
the response of a real object that is being simulated. The dependence of the virtual object response on the force exerted by the user
is incorporated explicitly, because our haptic rendering models areforce driven. This contrasts with the case of impedance based displays, where only position (or velocity) is measured. In order toensure transparent open-loop playback of haptic events in settings
like the latter, the device’s response requires grip-dependent corrections that account for changes in the display admittance due to grip
or arm dynamics [9]. Further discussion is provided in Sec. 4.5.

forces and high frequency, texture-like vibrations that are characteristic of human walking on different surfaces [28]. Figure 3 presents
an example of force and vibration data acquired from one footstep
on a gravel surface. Because the vibration signature is continuously coupled to the force input over time in such examples, there
is no straightforward way to convincingly use recorded footstep vibrations for vibrotactile rendering, although more flexible granularsound-synthesis methods could be used [1, 5]. For the modelingof simpler interactions, involving impulsive contact with solid materials, recorded transient playback techniques could be used [18].
10 kHz –0 Hz –
750 N –

Application to normal force texture simulation

An example application motivating the design reported here is thedisplay of normal force textures, in the form of high frequency vibrations simulating the feel of stepping onto natural ground materials [36]. When a shoe steps onto porous materials like soil or snow,
it is subjected to interactions that can include: viscoelastic components, describing the recoverable deformation of the volume of theground surrounding the contact interface; transient shock components, from the impact of toe and heel against the ground; and plastic components from the collapse of air pockets, brittle structuresor granular force chains, resulting in unrecoverable deformation[6, 29]. Combinations of such effects give rise to low-frequency

F(t )

0N–

t = 1.2 s|

Figure 3: Vibration spectrogram a(t, f ) and normal force F(t) measured from one footstep onto rock gravel (Authors’ recording). Notethe discrete, broadband impact events evidenced by vertical lines inthe spectrogram.

We briefly summarize one approach we have taken to the haptic
synthesis of interaction with such surfaces. It is based on fracture
mechanics, which has also proved useful for modeling other typesof haptic interaction involving damage [12, 20]. Figure 4 illustrates
the continuum model and a simple mechanical analog used for synthesis. In the stuck state, the surface has stiffness K = k1 + k2 andis governed by:F(t) = mẍ + bẋ + K(x − x0 ), x0 = k2 ξ (t)/K(1)

where ξ (t) represents the net plastic displacement up to time t. A
Mohr-Coulomb yield criterion is applied to determine slip onset:
When the force on the plastic unit exceeds a threshold value (which
may be constant or noise-dependent), a slip event generates an incremental displacement ∆ξ (t), along with an energy loss of ∆W
representing the inelastic work of fracture growth. Slip displacements are rendered as discrete transients, using an event-based approach [18]. High frequency components of such transient events
are known to depend in detail on the materials and forces of interaction, and we model some of these dependencies when synthesizing
the transients [38].
A high fidelity vibrotactile display such as that presented here isuseful for reproducing such phenomena without artifacts.
Fe

Fe

R2

2.2

a(t,f )

Force,

Fe(t)

m

ξ
R1

k2

k1

b

Slip energy,
E(ξ )

Slip
transientTime, t

A.

B.

C.

Figure 4: Normal force texture synthesis. A. A fracture mechanics
approach is adopted. A visco-elasto-plastic body undergoes shear
sliding fracture due to applied force Fe . B. A simple mechanical analog for the generation of slip events ξ (t) in response to Fe . C. For
vibrotactile display, each slip event is rendered as an impulsive transient using an event-based approach.

3.2 Sensing
In order to render an interactive response from a virtual ground surface using the kinds of models we have developed (Sec. 2.2), it
is necessary to capture the normal force applied to the tile by theuser’s foot. Positioning the force sensors beneath the plate is feasible, since the bandwidth of the force applied to the plate by theuser is limited. In the design presented here, the sensors are furthermore positioned beneath the elastic suspension of the device, so as
to better isolate them from the actuators.
Force sensing is performed via four load cell force transducers(Measurement Systems model FX19) located below the vibration
mount located under each corner of the plate. Although the cost foroutfitting a single-plate device with these sensors is not prohibitive,
many of the applications we have in mind consist of two dimensional m × n arrays of tiles, requiring a number N = 4mn of sensors. As a result, in a second configuration, four low-cost resistive
force sensors (Interlink model 402 FSR) are used in place of loadcells. After conditioning, the response of these sensors to an applied
force is nonlinear, and varies up to 25% from part to part (according
to manufacturer ratings). Consequently, a measurement and subsequent linearization and force calibration of each is performed, using
a calibrated load cell force sensor (details are provided in a separate publication [39]). After such a calibration, a linear response
accurate to within 5% can be obtained using low cost parts.
3.3 Actuation
The tile is actuated by a single Lorentz force type inertial motor(Clark Synthesis model TST429) with a nominal impedance of 6
Ohms. The actuator is coupled to the tile by a 1.25 cm diameter
threaded rod interfacing with an aluminum bracket, as shown in
Fig. 5. The actuator has a usable bandwidth of about 25 Hz to 20
kHz, and is capable of driving the plate above strongly enough toquickly produce numbness in the region of the foot that is in contact
with the tile.
3.4 Electronics
Analog data from the force sensors is conditioned, amplified, anddigitized via a custom acquisition board, based on an Altera FPGA,
with 16-bit analog-to-digital converters. Data from each sensor issampled at a rate of 1 kHz and transported to a host computer over80
60

Gain, dB

3 C OMPONENTS
3.1 Mechanical Structure
The mechanical design is broadly similar to that of the original device, but accounts better for both the static and dynamic performance requirements for the display. The top plate provides an interface to the body, which in the case of our device is assumed toconsist of a foot wearing a shoe. Statically, the device must resist bending when loaded vertically by a force of several hundred
Newtons. The rigid deflection of the plate under this load must be
minimized subject to the constraint that the plate be able to vibrate
freely. This trade-off is analyzed in Section 4.3.
The top plate consists of a commercially manufactured aluminum honeycomb sandwich panel component (Museum Services
Corp model 0513 SSP) with dimensions 30.4×30.4×2.54 cm anda weight of 400 g. The panel has aluminum facings with a thicknessof 0.08 cm. This material was selected for its high bending stiffness
to weight ratio. The panel sides are closed with a basswood frame toeliminate acoustic emissions or deformations that otherwise result
from small deflections of the honeycomb at the edges of the panel.
The plate is supported by cylindrical SBR rubber elastic elements
positioned as shown in Fig. 5. In dynamic or multi-tile configurations, a retaining socket surrounding the elastic support (not present
in the figure) is used to keep the plate from changing position. The
actuator is mounted via an aluminum bracket bonded to the center
underside of the plate.

40
20
0
-20
0

100

200

300

400

500

Frequency, Hz

Figure 6: Typical acceleration frequency response of the Clark Synthesis TST family of actuators (manufacturer supplied data, reproduced with permission).

UDP via the board’s 10 Mbps Ethernet interface. Digital to analog
conversion of the signal driving the actuator is performed using a
low noise 24-bit, 96 kHz audio interface (Edirol model FA-101),
and amplification is performed using a compact, class-D audio amplifier based on the Tripath TK2050. The amplifier is rated as capable of providing 100 W to a nominal 4 Ohm actuator impedance.
4

DYNAMIC R ESPONSE

The main factors affecting the dynamic response of the device are
the actuator characteristics, the dynamics of the rigid plate, andthat of the elastic suspension. In a suitable regime, one may regard these as lumped linear systems, with respective Laplace transform domain transfer functions Ha (s), H p (s) and Hs (s). The corresponding model device transfer function can be given by Hd (s) =Ha (s)H p (s)Hs (s). However, the spatial configuration of these elements relative to each other also contributes to the structural dynamics of the display.
4.1

Actuator Response

Fig. 6 shows a typical amplitude frequency response for this familyof actuators. The data was acquired from an accelerometer attachedto the mounting bold, with the actuator attached to a rigid wooden
surface. The shape of this nominal response affects that of our device (Sec. 5).
4.2

Plate Response

The contribution of the interface plate to the dynamic response of
the device can be predicted in terms of the vibrational characteristics of the plate, and the coupling between plate and actuator.
4.2.1

Free response

In the case of a homogeneous, isotropic plate, the free vibrations ofinterest are governed by a partial differential equation for bending
wave displacements. In the thin plate approximation, it is [10]:ρh∂ 2z+ D ∇4 z = 0,
∂t 2

D=

Eh3
12(1 − ν 2 )(2)Here, z = z(r,t) is displacement, r = (x, y) is a position on the tile
surface, t is time, E and ν are the Young’s modulus and Poisson’s
ratio of the plate material, ρ is its mass density, and h is the plate
thickness, D is known as the flexural stiffness, and we neglect effects of damping.
Below the first resonant frequency of the plate, f1 , the vibrational response is well approximated by that of an ideal, rigid mass
coupled to an elastic suspension (Sec. 4.3 below). Since we seek ausable display bandwidth with an upper limit of 1 kHz, we want toensure that f1 > 1 kHz. For a rectangular, homogeneous, isotropic
plate, the frequencies of the normal modes of bending oscillation

Suspension
Element

Composite
Plate

Voice-coilActuator

Force
Sensor30 cm

Figure 5: Vibrotactile floor interface hardware for a single tile unit. Left: Photo with large mens’ shoe, showing representative size. The model
shown is based on the low-cost force sensing resistor option. The cable in the foreground interfaces the sensors with the data acquisition unit.
Middle: View showing main components. Right: Side view with top dimension.

L
h

Core
(Honeycomb Matrix)

FacingFigure 7: A composite sandwich plate, shown in profile (side view).
It consists of a stiff, solid facing material bonded (typically laminated)
to a lightweight core, such as a metal or kevlar honeycomb matrix.

are of the form [10]:hk2
f (k) =
2π

s

D
,
ρh

k ∝ L−1(3)Here, k is the magnitude of the wavenumber vector k = (kx , ky ) of
the oscillation, and L−1 is the inverse length of the plate, and x andy are the directions tangent to the plate surface parallel to its edges.
For pure simply supported boundary conditions (which are neverachieved in practice), kx = mπ/L and ky = nπ/L, where m and n
are positive (non-zero) integers [10]. The lowest frequency mode is
f1 = f (|k1 |), with k1 = (π/L, π/L). The amplitudes of the normal
modes areηmn (r) = sin(kx x) sin(ky y)(4)After inserting the form of D from Eq. 2 into Eq. 3, Poisson’s
ratio ν contributes a factor (1 − ν 2 )−1/2 to f (k). This factor lies
in a range from 1.0 to 1.16 for solid materials such as are considered here, so in a first approximation we may ignore it. In order tomaximize the frequency f (k) for any given value of the wavenumber magnitude k, and given plate geometric properties L and h, theplate material should be selected to possess a large Young’s modulus E and low mass density ρ. Solid, isotropic materials such as
metals can achieve a high stiffness, but their mass density is typically commensurately higher, which is a limitation. In addition,
their mass grows linearly with thickness, making them less efficientto actuate. In practice, for a solid plywood plate (light enough tobe efficiently actuated) with dimensions 30.4 cm × 30.4 cm × 3.75
cm, one finds f1 ≈ 400 Hz, which falls short of the design target.
4.2.2

Composite plate

A class of structures that achieves higher stiffness-to-mass ratios
than is possible with uniform solids is that of composite sandwiches. Such a panel is formed via the use of thin layers of stiff

solid material bonded to a lightweight core. Fig. 7 illustrates a composite sandwich of the type used in our device. The core consists ofan aluminum honeycomb matrix, while the facing materials consistof aluminum sheet. The bending
stiffness of such a material is ap√
proximately given by E ≈ 3E f t f /h [15], where E f is the Young’s
modulus of the facing material, t f is the thickness of the facing material, and h is the core thickness (Fig. 7). To a first approximation,
the frequencies of the normal modes of bending oscillation of sucha composite sandwich plate can be obtained1 substituting this expression for E into Eq. 3. The resulting frequencies are:s
k2 E f t f h, k ∝ L−1
(5)f (k) =
2π
12ρ
Again, the admissible values of k depend on the boundary conditions. This equation (which is valid only for thin facings t f  h)depends on the stiffness E f of the facing material and the average
mass density of the entire panel. For our device, assuming√ idealized boundary conditions, the minimum value of k is π 2/L (seeSec. 4.4). The other factors are given by: h = 2.5 cm, t f = 0.083
cm, E f ≈ 60 GPa, and ρ ≈ 170 kg / m3 . For these values, Eq. (5)yields f1 ≈ 845 Hz. This overestimates the measured value of f1
for our device by approximately 10% (Sec. 5).
4.2.3 Actuator coupling
The actuated plate is driven by a surface force (pressure) distribution F(r,t), and the resulting governing equation possesses a driving term:∂ 2z(6)ρh 2 + D ∇4 z = F(r,t)∂t
For our device, the latter can be modeled as a F(r,t) = F(t)φ (r),where F(t) is the actuator force amplitude, and φ (r) approximatesa spatial Dirac delta function δ (r−r0 ) centered at the tile midpoint.
Generalizing slightly, one can consider the case of N independent
point actuators at locations ri , in which case F(r) = ∑Ni=1 Fi (t)δ (r−ri ), where Fi is the force signal from the ith actuator.
An arbitrary displacement z(r,t) can be expanded in the normal
modes ηmn (r) of vibration, yielding modal coordinates Zmn (t) defined by:z(r,t)=∑ Zmn (t)ηmn (r) , where(7)z(r,t)ηmn (r)d 2 r

(8)

m,n≥0

Z

Zmn (t)=1 The authors did not find this expression for f (k) in the research litera-ture, but approximations like it are presumably well-known.

In these coordinates, the physical equation is [22]:

55.

(9)

where ωmn is the angular frequency of mode (m, n). Modes having nodes at the actuator location, ηmn (ri ) = 0, satisfy the homogeneous form of Eq. (9), so are not excited by the corresponding
actuator signal, and instead contribute antiresonances to the device
response. As shown in Sec. 5, the bandwidth of our device is essentially limited by the antiresonance near 775 Hz for (m, n) = (1, 1).
4.3

Elastic Suspension

The actuator is designed to supply a force only along the directionin which it is attached, so we are primarily interested in normal
modes of oscillation in the z-direction. To a first approximation, theelastic (SBR rubber) suspension may be treated as a linear, lumped
element with stiffness K in the z-direction, coupled to a rigid platewith total mass M (Fig. 8). For small displacements, this stiffness isgiven by K = EA/h, where E is the Young’s modulus of the suspension element, A is its vertical surface area, and h is its height. Whenthe plate is not subjected to load from a foot, the mass M = M0
is due to the plate and actuator. For the device described here,
M0 = 2.7 kg.
Fa

A
h

E

K

M

Figure 8: Left: Geometry of one elastic suspension element withheight h, cross-sectional area A, and elastic modulus E. Right:
Lumped model of the tile-suspension system. Fa is the actuator supplied force, K = EA/h is the stiffness of a suspension element, andM is the combined mass of the actuator and tile.

Due to the symmetric placement of the actuator, there is a single dominant normal mode of oscillation, in which all suspension
elements are driven in-phase in the vertical direction. The resonant frequency
p of this mode in thepunloaded condition is given by
f0 = (2π)−1 4K/M0 = (2π)−1 4EA/(hM0 ). Above this frequency, the gain of the transfer function factor due to the suspension, Hsusp ( f ), is expected to be approximately constant.
A softer suspension leads to a larger response bandwidth (i.e.,
one with a lower frequency extent) but also to a higher static deflection δ z under a load F from a foot. The latter two are relatedby δ z = F/K = Fh/(EA). As nominal design specifications, weaimed to select E, A and h so that f0 ≤ 50 Hz, so that the passband
would overlap most of the frequency range of sensitivity of the FA
II (Pacinian) tactile mechanoreceptors in the foot. The latter closely
resembles the range for those in the hand [16, 34]. In addition, we
aimed to achieve a worst-case static deflection δ z ≤ 5 mm under aload of F = 1000 N, corresponding to a large human balanced at
one corner. Both f0 and δ z depend only on the ratio A/h. For convenience, we choose the cross sectional area A of the suspension
element to match that of the force sensor. To choose the remaining parameters, we perform a simultaneous grid search on h and E
to minimize f0 and δ z. Figure 9 illustrates the dependence of f0
and δ z on E for a representative set of selected parameter values,i.e., A = 8 cm2 and h = 2.5 cm. We selected SBR rubber vibration
mounts with geometry and Young’s modulus E = 2.0 MPa consistent with this optimization. As shown in the figure, the resulting
system is expected to achieve f0 ≈ 49 Hz and δ z ≈ 4.5 mm.

1.0
50.
0.8

45.
40.

0.6

Frequency f0, Hz


∂2
2
+
ω
mn Zmn (t) = ∑ ηmn (ri )Fi (t)∂t 2
iDisplacement δz, cm



60.

1.2

35.
0.4
30.
1.0 ! 10 6

1.5 ! 10 6

2.0 ! 10 6

2.5 ! 10 6

3.0 ! 10 6Young's Modulus, E

Figure 9: Resonant supension frequency f0 and static deflection δ z
vs. Young’s modulus for the system model with A = 8 cm2 and h = 2.5
cm. The value E = 2 MPa (grey vertical line) satisfies f0 < 50 Hz andδ z < 5 mm.

4.4 Simulation
The vibrational characteristics of the tile-actuator system were
simulated using finite element method (FEM) analysis. A threedimensional geometric model of the device was designed, incorporating the sandwich panel, actuator (modeled as a homogeneous
cylindrical mass), actuator bracket and connecting rod, elastic elements, and supporting structure. Material properties were assigned
approximating those of the device itself, with the core honeycomb
matrix replaced by a homogeneous solid with an equivalent density. Although this model entails a number of approximations, thequalitative results were expected to be correct.
4.4.1 Eigenfrequency analysis
At high frequencies, the resonant modes of the plate itself are observed. The first two are shown in Fig. 10. The lowest frequency
mode has wavenumber k = (1, 1), while the next highest resonanceshown appears to correspond to a plate-induced mixture of the (0, 2)
and (2, 0) modes. Their frequencies, 896 Hz and 1032 Hz, lie at aratio of about 1.15:1.

(1,1)(2,0) + (0,2)

f = f1

f = 1.15 f1

Figure 10: Visualization of the first two resonant modes of the device
due to the bending mode vibrations of the plate as identified in the
FEM analysis. The ring mode (right side) arises from the mixing of
the plate modes indexed by the integers shown [10]. The frequencies
are 896 Hz and 1032 Hz.

At low frequencies, a series of six resonances at frequencies of28, 45, 51, and 77 Hz is observed, corresponding to deformations of
the elastic support elements, in agreement with the lumped modelof Sec. 4.3. The number of resonances exactly matches the six degrees of freedom of perturbation of the rigid tile. The deformation
shapes recovered from the FEM analysis show that the 45 Hz resonance corresponds to oscillation in the direction normal to the platesurface; it is expected to dominate when the display is driven by theactuator.
4.4.2 Frequency response simulation
The FEM simulation of the frequency response was performed witha sinusoidal driving signal originating at the actuator. The z-axis

0

-20

-40

-60

55

100

200

400

600 800

1200

Freq., Hz

Figure 11: Result of a FEM analysis of the acceleration response of
the device as measured at four different points on the plate surface.
At frequencies below the first resonant mode, the device response isapproximately constant over the surface of the plate.

4.5

Modeling user-supplied loads

We have so far discussed the response of the device without accounting for effect of to its user. According to the haptic interaction
model adopted here (Sec. 2) it is correct to ignore the influence of
this load, as transparency requires that the free (unloaded) displaytransfer function approach unity. However, in other circumstances
it may be desirable to compensate for variations in the display response due to user contact. Examples where this might be the caseinclude passive vibrotactile stimulation for tactile communication
or psychophysical experiments, or for use with impedance-based
rendering algorithms or simulations that explicitly model user contact conditions in the virtual environment. At the frequencies of
A.

B.

M2

2

k2

b2
M1

k1
ks

5

E VALUATIONAs noted in Sec. 2.1, our assessment of the transparency of this device is based on the extent to which the unloaded transfer functionof the display approximates unity over the range of perceptuallysalient frequencies. We focus here on the flatness of the magnitude
frequency response. The vibrotactile sense is sensitive to phasedifferences [2], and it is possible that a vibrotactile display may
contribute enough phase distortion to affect perception, particularly
where transient signal components are concerned. However knowledge about vibrotactile sensitivity to temporal phase distortion isincomplete, and, as far as we are aware, phase linearity has neverbeen used to evaluate vibrotactile displays. It is nonetheless an important consideration in the related field of loudspeaker design.
5.1

Frequency response measurement

The magnitude frequency response of the device was measured bydriving the plate with the actuator using the chirp method, with aslow sinusoidal frequency sweep (rate of 100 Hz / s). Measurement
was performed using a piezoelectric accelerometer (AKG model
CP-411) bonded to the top surface of the plate, as described in
the caption of Fig. 13. Frequency response measurements weretaken for several different foot-plate contact conditions, while thefoot was wearing a rubber soled shoe. As noted above, these contact conditions modify the impedance of the display, altering its
response. The results are shown in Fig. 13.

0
ï5
ï10
ï15
ï20
ï25
ï30
ï35

b1
Mp

1

frequency response measurements we report below (Sec. 5.1). Similar grip-dependent effects are observed to affect manually operated
haptic [17, 9] and vibrotactile [41] devices.

Amp, dBz-Acceleration, dB

acceleration was measured at several points on the surface of theplate, with the results shown in Fig. 11. As determined above, thecross-shaped mode gives rise to an antiresonance, due to the actuator location. The magnitude effect of these resonances, and toa secondary degree their frequency, depends substantially on themeasuring point.

ï40
50

Fa(t)

Figure 12: (A.) A simplified model of a user-supplied load can beprovided in the form of a link-segment model or (B.) its equivalentmechanical network, coupled to the display device. Fa (t) is force
applied by the actuator.

interest, a user may be modeled as a passive viscoelastic mechanical system. Figure 12 shows a simple link-segment biomechanical model and equivalent mechanical network coupled to the display. Physiologically, biomechanical properties such as leg joint
stiffness cannot be regarded as static or linear during movement,
as muscular activation regularly modulates the dynamic propertiesof the lower limbs during activities on foot [26, 21, 8]. However,as a typical leg stiffness value one may take k = 10 kN/m [26].
Upon adopting a simple, single mass-spring-damper model withthis value, and assuming an effective mass of 50 kg, one finds thata user-supplied load should suppress frequencies in the vicinity of
200-250 Hz. This prediction is consistent with the load-dependent

100

200
400
Freq, Hz800 1200

Figure 13: The measured log magnitude frequency response of thedisplay. Measurements were taken at a point equidistant from theplate center and edge, on a line through the center, 15 degrees fromthe diagonal. The free response is shown with a black line, and otherfoot-floor contact conditions with varying load applied via the foot are
shown in gray.

The variation in the magnitude frequency response below 80 Hz
is, following the analysis above, likely to be attributed to a combination of the resonant modes of the vibration suspension and theactuator response (Fig. 6). The antiresonance around 775 Hz andthe resonance near 1100 Hz are due to the two lowest frequency
normal modes of the plate (Fig. 10) identified above. Variation in
the range from 70 Hz to 700 Hz can be attributed in part to the actuator response. The latter (Fig. 6) includes a resonance near 70 Hz
and additional coloration above 380 Hz, likely accounting for thesmaller notch seen in the measurements. Through additional measurements with a calibrated accelerometer (Analog devices modelADXL 320), it was determined that a force of 40 N could be transmitted at all frequencies between 50 and 750 Hz. Another pertinent
quantity, nonlinear distortion, was estimated from measurements at
300 Hz to be slightly more than 5% (mean absolute percent error)
up to a force of 30 N.
5.2

Digital correction

It is possible to improve the nominal frequency response Hd ( f ) of
the display by filtering the actuator signal F(t) via a suitably designed linear, time-invariant corrective filter, Hc . Here, we concentrate on the magnitude only: Hc is designed so that the corrected
device frequency response Hd 0 ( f ) = Hd ( f )Hc ( f ) ≈ g in the bandof interest, where g is a constant gain factor.
Since such a filter lacks any spatial dependency, correction ismost effective below the first resonant frequency of the device, f1 ,because above it the device transfer function varies across the surface of the plate (Fig. 11). As a result, correction is primarily usefulfor compensating factors, such as actuator characteristics, that canbe treated as lumped parameter system elements.
We designed the inverse filter Hc to equalize the device responsein the frequency range from f = 50 Hz to 750 Hz. It was implemented digitally as an IIR filter of order N, which was estimated using the least p-th norm optimization method [32]. Figure 14 shows
a comparison of the original (free) frequency response of the device
with responses corrected by filters of order N = 10 and 14. In thelatter case, the response is flat in a passband with -10 dB roll off
near 50 Hz and 750 Hz.

0ï5Amp, dB• Plate material selection: As presented in the analysis above,
a composite panel similar to that used here, but constructedfrom a honeycomb core with larger core thickness h, andfacing thickness t f would achieve a usable bandwidth that
extends to higher frequencies.
The first resonant frequency
pof the plate scales as t f h in the thin plate approximation(which will require corrections if the plate or facings are too
thick).
• Actuator design: The large voice coil actuator used in thepresent device introduces significant coloration in the frequency response of the device, much of which can be equalized. A better response may be achieved through the use ofsmaller, more efficient voice coil motors coupled to the structure in a spatial configuration chosen to optimize the device
transfer function.
• Vibration control: Active structural vibration control strategies exist that could improve the fidelity of such a display
using arrays of surface mounted sensors and actuators, together with closed-loop controllers [4, 30, 31]. Such techniques might be used to achieve accurately controlled vibrational responses under a wider array of contact loads.
In ongoing research in our lab, the device is being utilized to study
the rendering and display of virtual ground surface properties, related aspects of haptic perception, and the integration of such display components in multimodal virtual and augmented reality environments [39].

ï30

ACKNOWLEDGEMENTS
We thank Vincent Hayward and Guillaume Millet for useful discussions, and the anonymous reviewers for their helpful comments.
The authors gratefully acknowledge support from the MDEIE ofQuebec for the EU FP7 project NIW (no. 222107). The first author acknowledges support from the ESF COST Action on Sonic
Interaction Design (no. IC0601).

ï35

R EFERENCES

ï10
ï15
ï20
ï25

ï40
50

100

200
400
Freq, Hz800 1200

Figure 14: Measured device response without foot contact, uncorrected (lightest gray) and with correction by digital IIR filters of order
N = 10 (medium gray) and N = 14 (black).

6

Despite these results, a number of areas can be identified inwhich the device might be improved. They include:

C ONCLUSION

We have presented a vibrotactile display device integrated in a rigid
surface, consisting of an actuated and instrumented floor tile. The
analysis considered factors affecting the bandwidth of the device,including the response of the elastic suspension and rigid plate, theactuator coupling, and the static deflection of the suspension underload by a human foot. The plate was implemented as a lightweightcomposite sandwich panel constructed from aluminum honeycomb.
A digital filter was designed to compensate for artifacts in the measured frequency response. The device allows for accurate reproduction of frequencies between about 50 and 750 Hz.
The device is simple, and designed to be easily reproducible oradaptable to the demands of various applications or research tasks[37, 38]. Formulae such as Eq. (5) indicate how the response characteristics of the display can be expected to scale with system dimensions.

[1] S. Barrass and M. Adcock. Interactive granular synthesis of haptic
contact sounds. In AES 22nd International Conference on Virtual,
Synthetic and Entertainment Audio, 2002.
[2] S. Bensmaia and M. Hollins. Complex tactile waveform discrimination. The Journal of the Acoustical Society of America, 108:1236,
2000.
[3] G. Burdea and M. Akay. Force and touch feedback for virtual reality.
Wiley New York, 1996.
[4] K. Chandrashekhara and A. Agarwal. Active vibration control of laminated composite plates using piezoelectric devices: a finite element
approach. Journal of Intelligent Material Systems and Structures,
4(4):496, 1993.
[5] A. Crossan, J. Williamson, and R. Murray-Smith. Haptic granular synthesis: Targeting, visualisation and texturing. In Proc. Intl Symposiumon Non-visual & Multimodal Visualization, pages 527–532, 2004.
[6] S. Dixon and A. Cooke. Shoe-Surface Interaction in Tennis. Biomedical engineering principles in sports, page 125, 2004.
[7] F. Fahy. Foundations of engineering acoustics. Academic Press, 2001.
[8] C. Farley and O. Gonzalez. Leg stiffness and stride frequency in human running. Journal of Biomechanics, 29(2):181–186, 1996.
[9] J. Fiene, K. Kuchenbecker, and G. Niemeyer. Event-based haptics
with grip force compensation. In Proc IEEE Haptic Symposium, 2006.
[10] N. Fletcher and T. Rossing. The physics of musical instruments.
Springer Verlag, 1998.
[11] M. Fukumoto and T. Sugimura. Active click: tactile feedback for
touch panels. In CHI’01 extended abstracts, pages 121–122. ACM,
2001.

[12] V. Hayward. Physically-based haptic synthesis. In M. Lin and
M. Otaduy, editors, Haptic Rendering: Foundations, Algorithms andApplications. AK Peters, Ltd, 2007.
[13] V. Hayward and K. Maclean. Do It Yourself Haptics: Part I. IEEE
Robotics & Automation Magazine, page 89, 2007.
[14] J. Hollerbach. Locomotion interfaces and rendering. Haptic Rendering: Foundations, Algorithms and Applications. AK Peters, Ltd, 2008.
[15] J. Kee Paik, A. Thayamballi, and G. Sung Kim. The strength characteristics of aluminum honeycomb sandwich panels. Thin-walled structures, 35(3):205–231, 1999.
[16] P. M. Kennedy and J. T. Inglis. Distribution and behaviour of glabrouscutaneous receptors in the human foot sole. The Journal of Physiology, 583(3), 2002.
[17] T. A. Kern. Modeling the User. Engineering Haptic Devices (T. A.
Kern, Ed.), Springer-Verlag, 2009.
[18] K. Kuchenbecker, J. Fiene, and G. Niemeyer. Improving contact realism through event-based haptic feedback. IEEE Transactions on
Visualization and Computer Graphics, 12(2):219–230, 2006.
[19] M. Magana and R. Velazquez. On-shoe tactile display. In IEEE Intl
Workshop on Haptic Audiovisual Environments and Games, 2008.
[20] M. Mahvash and V. Hayward. Haptic rendering of cutting: A fracture
mechanics approach. Haptics-e, 2(3):1–12, 2001.
[21] D. Marigold and A. Patla. Adapting locomotion to different surface
compliances: neuromuscular responses and changes in movement dynamics. Journal of neurophysiology, 94(3):1733, 2005.
[22] L. Meirovitch. Dynamics and control of structures. John Wiley &Sons, 1990.
[23] A. Nashel and S. Razzaque. Tactile virtual buttons for mobile devices.
In Proceedings of CHI, pages 854–855. ACM, 2003.
[24] I. Poupyrev, S. Maruyama, and J. Rekimoto. Ambient touch: designing tactile interfaces for handheld devices. In Proceedings of UIST.
ACM, 2002.
[25] A. Priplata, J. Niemi, J. Harry, L. Lipsitz, and J. Collins. Vibrating insoles and balance control in elderly people. The Lancet,
362(9390):1123–1124, 2003.
[26] S. Rapoport, J. Mizrahi, E. Kimmel, O. Verbitsky, and E. Isakov. Constant and Variable Stiffness and Damping of the Leg Joints in Human
Hopping. Journal of Biomechanical Engineering, 125, 2001.
[27] A. Rovers and H. Van Essen. Guidelines for haptic interpersonal communication applications: an exploration of foot interaction styles. Virtual Reality, 9(2):177–191, 2006.
[28] J. Sabatier and A. Ekimov. A Review of Human Signatures in Urban
Environments Using Seismic and Acoustic Methods. In 2008 IEEE
Conference on Technologies for Homeland Security, pages 215–220,
2008.
[29] V. Stiles, I. James, S. Dixon, and I. Guisasola. Natural Turf Surfaces:
The Case for Continued Research. Sports Medicine, 39(1):65, 2009.
[30] U. Stobener and L. Gaul. Modal vibration control for PVDF coatedplates. Journal of Intelligent Material Systems and Structures,11(4):283, 2000.
[31] N. Tanaka and T. Sanada. Modal control of a rectangular plate using
smart sensors and smart actuators. Smart Materials and Structures,
16(1):36–46, 2007.
[32] J. Taylor and Q. Huang. CRC handbook of electrical filters. CRC,
1997.
[33] H. Tramberend, F. Hasenbrink, G. Eckel, U. Lechner, and M. Goebel.
CyberStage – An Advanced Virtual Environment. ERCIM News, 31,
October 1997.
[34] M. Trulsson. Microreceptive afferents in the human sural nerve. Exp
Brain Res, 137:111–116, 2001.
[35] Y. Visell. Tactile sensory substitution: Models for enaction in HCI.
Interacting with Computers, In press, 2008.
[36] Y. Visell, J. Cooperstock, B. Giordano, K. Franinovic, A. Law,
S. McAdams, K. Jathal, and F. Fontana. A Vibrotactile Device for
Display of Virtual Ground Materials in Walking. In Proceedings ofEurohaptics, 2008.
[37] Y. Visell, F. Fontana, B. Giordano, R. Nordahl, S. Serafin, and
R. Bresin. Sound design and perception in walking interactions. International Journal of Human-Computer Studies, 2009.
[38] Y. Visell, A. Law, and J. Cooperstock. Touch Is Everywhere: Floor

Surfaces as Ambient Haptic Interfaces. IEEE Transactions on Haptics, 2009.
[39] Y. Visell, A. Law, J. Ip, S. Smith, and J. R. Cooperstock. Interaction
Capture in Immersive Virtual Environments via an Intelligent Floor
Surface. In Proc. of IEEE Virtual Reality, 2010 (To appear).
[40] Y. Visell, S. Smith, A. Law, R. Rajalingham, and J. R. Cooperstock.
Contact Sensing and Interaction Techniques for a Distributed, Multimodal Floor Display. In Proc. of IEEE 3D User Interfaces, 2010 (Toappear).
[41] H. Yao, V. Hayward, and R. Ellis. A tactile enhancement instrument
for minimally invasive surgery. Computer Aided Surgery, 10(4):233–
239, 2005.