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The cloak of invisibility: Challenges and applications


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Is it possible to create a cloak of invisibility - a flexible artifact that can make anything inside it invisible and preserve invisibility despite mobility and deformation? Exploring the algorithmic and technological challenges involved reveals tantalizing information.
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1536-1268/02/$17.00 © 2002 IEEE
The Cloak of Invisibility:
Challenges and
nyone who’s read the Harry Potter
books by J.K. Rowling understands
the concept of an invisibility cloak.
Furthermore, humans have dreamt of
what invisibility might mean since the
beginning of civilization, and this dream persists in
today’s literature and culture. However, although
more improbable methods of invisibility will remain
unrealized, an invisibility cloak could be feasible in
the future through technology. In this article, we
attempt to show this via technical “pencil and paper”
arguments and a conceptual implementation.
Generally speaking, we pro-
pose a fabric of small computing
devices that can receive and
retransmit light emissions in a
directional way as well as inter-
act with each other in a wireless
amorphous network.
someone or something is inside the cloak, the cloak’s
devices would cause external observers to perceive
the light configurations they would see if the wearer
wasn’t there. Sensors on the side of the cloak not fac-
ing the observers could receive such configurations
and, via distributed coordination, communicate them
to emitters on the observer’s side for retransmission.
Building a solid wall exhibiting such properties
for a nonmoving observer might be difficult. Even
more challenging problems arise when preserving
such properties
For any observer in any position
For any shape of the cloak
Despite movement of the cloak’s fabric
Although we haven’t identified fully fledged
technical solutions for all these complex prob-
lems, you could collectively exploit numerous
recent findings in different research areas (such
as mobile computing,
distributed and peer-
to-peer coordination,
MEMS (microelectromechanical)
and sensor net-
) to sketch promising solutions. Follow-
ing that, you might then achieve the cloak’s actual
implementation and numerous related, innova-
tive artifacts.
For the sake of readability, we present our argu-
ments incrementally. For each step, we discuss the
Is it possible to create a cloak of invisibility—a flexible artifact that can
make anything inside it invisible and preserve invisibility despite mobility
and deformation? Exploring the algorithmic and technological
challenges involved reveals tantalizing information.
Franco Zambonelli and
Marco Mamei
Università di Modena e Reggio
This is an unusual article. It does not fall neatly
into any of the typical genres of papers published
in this magazine, such as a research report, retro-
spective, survey, or tutorial. Rather, it is a carefully
reasoned technical speculation on an intriguing
idea—the use of sensor-impregnated garments
to achieve invisibility through real-time scene
manipulation. Although the paper is pure specu-
lation, the Associate Editors in Chief and I felt
that IEEE Pervasive Computings readership would
be well served by including this thought-provok-
ing article in this issue. To provide balance, we
include brief comments by vision experts Martial
Hebert of Carnegie Mellon University and Steve
Shafer of Microsoft Research.
M. Satyanarayanan, Editor in Chief
associated hardware and software chal-
lenges and the artifacts you might create
after resolving the challenges.
Step 1. The invisible wall
Let’s consider the basic scenario of mak-
ing a rigid, flat wall invisible to an unmov-
ing observer at a known position (for
example, centered in front of the wall at a
known distance from it). You could do this
simply by having a camera capture every-
thing behind the wall (from the observer’s
known fixed perspective) and project it on
the front side.
Alternatively, we propose building the
invisible wall by using a network of small
computer-based devices. (This serves as a
basic building block toward defining the
invisibility cloak, for which we will remove
the constraint of a flat, rigid shape and of a
single, fixed observer.) For this, we will need
In devices, sensors that can perceive
light emissions and transform them into
digital signals, such as a digital camera’s
CCD sensors
Out devices that can appropriately emit
light on the basis of specific signals
received, such as LCD displays, LEDs,
and microlasers
Of course, you might also have devices act-
ing as both In sensors and Out emitters.
To create the wall, we would deploy
densely packed In and Out devices on the
wall, one type on each side. We do not con-
sider devices placed in regular, possibly
wired, grids as in cameras and monitors.
Instead, we consider the wall randomly
filled with unwired devices to avoid place-
ment and wiring efforts and to enable, say,
“painting” or spraying the wall with trans-
parent glue containing sensors and emit-
ters. Such a choice, while increasing flexi-
bility and fault tolerance, requires devices
to have short-range wireless communica-
tion capabilities (optical- or radio-based)
and to be either internally self-powered (for
example, via solar energy or a light bat-
or laid on a conductive substrate and
fed with external power.
Once applied, each In device must
record its local light information on the
wall and transmit it to the corresponding
Out device on the opposite side, to glob-
ally reconstruct the image. Such transmis-
sions, owing to short-range communica-
tion capabilities—and to avoid limiting the
wall’s size and thickness—must occur in
multiple steps, by properly routing mes-
sages across the network to their destina-
tion (see Figure 1a). Of course, this requires
both sides of the wall to be seamlessly part
of the same network, so that a message can
pass from one side to the other by contin-
uously traveling over the network. For
example, in Figure 1a, we assume that
devices also fill the wall’s gray lateral parts.
Software issues
Deploying sensors and emitters without
a predetermined layout can dramatically
cut the costs of building our wall. How-
ever, it complicates software design. In par-
ticular, when dealing with the software to
control such an artifact, we must ask,
To properly establish the In and Out
pairs, how can devices determine their
How do you route data across the net-
work from In to Out devices?
For the first question, because we have
spread the devices randomly on the wall,
they do not have any a priori knowledge
about their position. However, fundamen-
tally, each device will find its mate by look-
ing for the device on the opposite side of the
wall having the same coordinates. We can’t
use Global Positioning System technology
because it lacks the required accuracy and is
Alternatively, thanks to recent
research in localization technologies and
we can let each device deter-
mine its own position in the wall, accord-
ing to a relative set of coordinates, by rely-
ing on a few devices with known positions.
Such localization algorithms can rely on
the geometrically intuitive fact that you can
uniquely determine a point’s position on a
surface by measuring its distance from
three nonaligned reference points, beacons,
through triangulation.
So, for the invis-
ible wall, we can establish the global coor-
dinate system in four main steps.
First, we choose at least three beacons—
either via an external stimulus or by a leader
election algorithm—defining a coordinate’s
frame (in our case, we might choose devices
along the wall’s edges, as in Figure 1a).
Second, each beacon must produce some
= 2,
= 3,
= 3
= 2
(a) (b)
Figure 1. The invisible wall: (a) a global
view and (b) local routing of a tuple
toward a specific point.
sort of signal to let other devices estimate
their distance from the three beacons and
eventually, via triangulation, their posi-
Devices can estimate distance by
exploiting either a physical property of the
signal the beacons emit (for example, its
attenuation, although this method’s accu-
racy at such small scales might be inade-
quate) or a geometrical property (for exam-
ple, the devices’ average density coupled
with expanding ring hop count messages
Third, the triangulation process spreads
to further devices—as soon as they know
their position with respect to the coordi-
nate system—and diffuses across the whole
The last step is to execute a distributed,
iterative algorithm
on the surface to
improve the accuracy of the estimation,
which could have produced notable errors
during the diffusion process, until reach-
ing the required accuracy. Although this
might take some time, the process’s execu-
tion time is not relevant because it only
takes place at bootstrap.
Given a set of coordinates’ availability,
the same for both sides of the wall, you can
restate the second question as: “How can
you route the data sensed by an In device at
coordinates (x
, y
) to the Out device posi-
tioned at the (x
, y
) coordinates on the
wall’s opposite side?” Or, better, because an
Out device might not necessarily exist at the
same coordinates (or because such a device
could be dead or temporarily unreachable),
you might say “How can you route such
data to the Out device closest to (x
, y
In this case, the answer is rather simple (see
Figure 1b). Each In device must propagate
a message (that is, a tuple) in the form (x
, color), representing the image informa-
tion it captured at its own coordinates. You
can then route such a tuple from device to
device toward the wall’s closest edge.
Because a device knows its own coordinates
and can store its neighbors’ coordinates (as
obtained during localization), it also knows
whether it must propagate a message and
where, on the basis of simple Euclidean con-
siderations. Once the tuple has reached the
wall’s opposite side, routing proceeds from
device to device toward the (x
, y
) coor-
dinates. Propagation stops when the tuple
reaches the Out device at (x
, y
) or when
no emitter closer to the goal can be found
in the neighborhood.
Optical and hardware issues
At what size do the In and Out devices
provide a reasonable visual rendering? Fol-
lowing the Listings-Donders model of the
human eye
(see Figure 2), we can define
min as the minimum angle for which an
observer would perceive points A and B
separately. This angle is approximately
1/60 degree, the minimum at which two
light rays hit two distinct cone cells sepa-
rated by an unhit cone cell.
Thus, considering Figure 2, you would
perceive A and B separately only if
For a good image, the distance between
two devices must be less than d/3400 (for
example, you would perceive two objects
separated by 1 mm as a single object from
a distance of 3,400 mm, or 3.4 m).
For instance, to rend invisible a 1 m
from a distance of 10 m, you’d need 115,600
devices on each side. In fact, the allowed
maximum distance between two devices to
provide the impression of smoothness is
10/3400 = 2.9 mm. So, each device must
>⋅ tan( / ) .160
eveloping large arrays of microsensors on flexible surfaces is
an interesting area of research that could lead to many appli-
cations. In that respect, the article investigates interesting concepts
for implementing such devices. However, although the goal of in-
visibility is quite catchy and sure to motivate much discussion, the
claims are at odds with standard results in computer vision and
computer graphics, and it would be wise to motivate work on sen-
sor and processor networks without resorting to Harry Potter.
Although it’s possible, in principle, to project the image received
by an array of input sensors through another array of output sen-
sors, the extrapolation from an invisible wall with a fixed observer
to a general cloak overlooks several known facts in the geometry
and photometry of image formation. More precisely, serious issues
arise when you consider the case of an observer in an arbitrary
position in a 3D world.
From a geometric standpoint, assuming that the observed
world has a general 3D structure—as opposed to a flat world—
it is well known that, because of parallax effects, you cannot recon-
struct exactly the view that an observer in an arbitrary position
would see. Even if you reconstructed the 3D structure from the
input sensor—something the authors do not propose—you still
could not reconstruct the view because parts of the scene that are
occluded from the input sensors’ view, but visible to the observer,
cannot be reconstructed. A vast literature on scene reconstruction
and image-based rendering addresses these issues. Shuffling the
set of input rays into a set of output rays will not generally gener-
ate a correct image.
Ignoring the geometric issues, faithful reconstruction from an
arbitrary observer viewpoint assumes implicitly a simple reflection
model for the objects observed in the environment. Specifically, as
soon as the light reflected from an object depends on the surface
orientation and viewing direction, you can no longer recover in a
simple manner the intensity that you would see from a different
direction. —Martial Hebert
Martial Hebert
is a professor at Carnegie Mellon University’s Robotics
Institute. His interests include computer vision (particularly object recogni-
tion and 3D model reconstruction) and mobile robotics (particularly per-
ception for mobility and autonomous driving).
Simply Difficult
be approximately (2.9 mm)
8.4 mm
wide; a linear meter must have at least 340
devices and a square meter 115,600 devices
The above requirements appear feasible
with regard to the state of the art in optical
MEMS technologies. For instance, three
years ago, the Smart Dust project at Berke-
ley developed optical (laser-based) inter-
nally powered computer-based sensors and
emitters of 1 mm
, which could well serve
our purpose.
Even the amount of data that each
device and its wireless communication
channels must deal with is not a challenge.
If we assume each device should record and
transmit a 24-bit value for the color infor-
mation (16 million colors) with two 16-bit
values representing device coordinates, this
results in a 56-bit tuple (24 + 16 + 16). You
must update these values 30 times per sec-
ond, the normal television frequency. For
a 1 m
wall, with devices approximately
2.9 mm apart, and assuming that the com-
munication range lets a device connect only
to its closest neighbors (a very strict hy-
pothesis), a tuple’s routing process takes
170 steps on average and, in the worst case
of centrally located pairs, 340 steps. Thus,
devices located at the wall’s edges (the ones
dealing with the highest traffic) will take
charge of routing information for the 170
other devices on the line between them and
the wall’s center. All this considered, a sin-
gle device’s wireless link bandwidth should
be (170 56 bits) 30 Hz 286 kbits/sec
to sustain such peaks, which is low enough
for modern micro devices to sustain.
We emphasize that we are considering
here the human eye’s physiological limits.
For several applications, less strict constraints
(and coarser renderings) might suffice.
Because the described wall can render
the image only from a fixed perspective, it
cannot render invisibility: the image pro-
duced by the Out devices would not
change as an observer moves, making the
illusion vanish. Still, a transparent wall can
have several potential applications in cases
where you’d like to observe without being
observed—for example, in therapy and
investigation settings as well as for enter-
tainment. This installation has an advan-
tage over more traditional technologies,
such as using cameras or mirrors, in its self-
containment. It also doesn’t require spe-
cific infrastructures or skills.
This technology would also allow build-
ing further interesting artifacts. Specifically,
you could use an analogous amorphous
network to produce a paintable television
or monitor—that is, a television sold as a
s this paper a joke or a serious contribution to the literature? This
much I know for sure: These authors have an overactive imagina-
tion! And that is probably what we all need because the field of per-
vasive computing is on the whiz-bang edge of computer science to
begin with.
On purely technical grounds, do I believe this proposal can
work? Not really. The optical sensors and emitters required would
be impossibly dense, especially considering the issues involved in
each unit’s directionality, determination of the viewer’s position,
intermingling sensors and emitters on the surface, determination
of sensor and emitter positions, and so on. Do I believe we’re
going to invent cloaks of invisibility soon? No.
But it would be kind of cool, wouldn’t it? There’s something to
be said for papers that go way outside the bounds and inspire
people to wild feats of imagination. In that regard, I actually wish
this article were more about cool concepts and less about how
(not) to achieve them. Maybe we can’t make an invisibility cloak,
but we could make a “mirror” that does something particularly
cool. The “maybes” here are endless.
So, is this paper to be taken seriously? Not by me. But who
cares? If I were teaching, I might give it to my class anyway and
ask them to think about it. This might not be possible in my
lifetime, but could be in theirs. Steve Shafer
Steve Shafer
is a senior researcher in ubiquitous computing at Microsoft
Research. His current work is in location awareness for mobile devices and
intelligent environments; his previous work was in computer vision, model-
ing optical properties of materials, and cameras.
Kind of Cool
Figure 2. The Listings-Donders model of
the human eye.
5 mm 15 mm
paint that, once painted, works as a nor-
mal flat-screen television. In this case, you
would need a TV-signal receiver at one of
the painted wall’s edges to also act as a bea-
con for the network coordinate system.
Once all emitters are localized, the receiver
can transmit tuples in the form (x, y, color),
to be propagated in the network of emitters
to render the TV image.
Step 2. The invisible object
You can only enable the real power of
invisibility, and a larger class of related appli-
cations, by making it possible to paint invis-
ible objects of any shape and by enhancing
image rendering to relax the constraint of
the fixed and single point of observation.
You want the object be completely covered
by a sensor network so that, for any point
of its surface, a ray of light incident from
any direction gets properly captured and
retransmitted on the opposite side.
By assuming that one or more observers
can move around the object and see all its
sides, you must integrate the In and Out
devices in a single device or, they must be
both densely painted on the whole surface
so that you no longer separate the object
into In and Out sides. Moreover, if we want
the object to show what’s behind it inde-
pendent of the observers’ position, each
portion of the surface should be able to
retransmit different light configurations in
different directions, to virtually extend a
reasonable number of light rays on the
object (see Figure 3). For this purpose, we
can consider a device as a compound object
capable of acquiring different light infor-
mation (In function) and of firing different
light rays (Out function) in different direc-
tions. Alternatively, we can consider a
device as a monodirectional sensor or emit-
ter. By distributing these monodirectional
devices densely on the object surface with
a random orientation, any portion of the
surface will have, with high probability, sen-
sor and emitters pointing in all directions
Software issues
In this case, implementing invisibility
closely resembles the case of the previously
described invisible wall: each In device
must provide light information to the Out
device on the object’s “opposite” side—
that is, to the emitter on the surface that is
the closest (in surface position and orien-
tation) to the virtual extension of the light
ray that the sensor captures. However, in
this case, answering how devices determine
their position and the In-Out pairs and
how you can route data from In to Out
devices is more challenging.
For our explanation, it’s important to
distinguish between extrinsic and intrinsic
coordinates. Extrinsic coordinates identify
a device’s position and orientation with
respect to a 3D frame attached to the object
(see Figure 4a). You could represent a
device’s extrinsic coordinates, for instance,
by its (x, y, z) coordinates and by the two
angles (
) determining its orientation.
Intrinsic coordinates specify devices’ posi-
tions in the object surface. In other words,
they are 2D coordinates mapped on the
surface, establishing a frame on the object’s
surface (see Figure 4b).
Figure 3. The invisible object.
Multiple sensors pointing in different directions
(or a compound multidirectional sensor)
Figure 4. Coordinates: (a) extrinsic and
(b) intrinsic.
( , )
A device’s extrinsic coordinates are fun-
damentally important in that they unam-
biguously determine the coefficients of the
specific light ray associated with the
device—that is, the light ray an In device
receives and blocks or the light ray an Out
device reproduces. So, you must establish
an In-Out pair between two devices whose
extrinsic coordinates identify the same
straight line—that is, the light ray to be
reproduced. Therefore, each device must
know its extrinsic coordinates to establish
such a pair.
Determining a device’s extrinsic coordi-
nates in a distributed way from local infor-
mation can take place by extending the
beacon-based localization mechanism to
consider the object’s local curvature and
the devices’ orientation (see Figure 4a).
You can determine local curvature from
within the surface in a completely distrib-
uted manner by taking into account the fol-
lowing geometrical property: While on a
plain surface, the ratio of the circumfer-
ence to a circle’s radius is always 2π. On a
curved surface, the ratio of the circumfer-
ence to a circle’s “radius,” as measured on
the surface, decreases as the curvature
increases. This is because the measured
radius is actually an arc on the surface.
Starting from this property, each device can
measure the local curvature of the object
on which it is located by measuring the cir-
cumference and the radius of a small cir-
cle centered on itself. This can operatively
take place by having each device probe the
neighborhood, determine the number of
devices at a given distance (the circumfer-
ence) and the number of devices on the
shortest path from the central device to a
neighboring device (the radius), and then
examine how far the ratio of these num-
bers is from 2π.
Once you do this, you can get the
device’s orientation on the surface by the
curvature information and by comparing
the beacon’s orientation with other devices’
orientations epidemically. To this end, you
must equip each device with a system capa-
ble of determining relative orientations,
such as the Cricket Compass.
you’ve gathered the curvature and devices’
orientations, you can easily obtain the
extrinsic coordinates by a simple variant
of the triangulation procedure.
Unfortunately, even once each device
knows its extrinsic coordinates, this knowl-
edge doesn’t help establish the correct In-
Out pairs that would enable a light ray to
be reproduced. In fact, if an In device starts
propagating a tuple reporting its extrinsic
coordinates and the color to be reproduced
(x, y, z,
, color), you cannot exploit this
information to properly route the message
toward the corresponding Out device. In
fact, extrinsic coordinates do not indicate
where a light ray entering the object will
exit, this being dependent on the object’s
shape. Without local information about the
object’s shape (which is impossible to store
locally unless the object is very regular), you
cannot know a priori where the tuple
should eventually arrive or what the right
direction is to approach the destination.
To solve this problem without flooding
tuples across the whole network, we need
a strategy to route information without
explicit knowledge of mates’ extrinsic
coordinates. This is where intrinsic coor-
dinates come in. Evaluating intrinsic coor-
dinates is perfectly analogous to the flat
wall case. Also, you can effectively exploit
intrinsic coordinates to route tuples toward
a specific point in the surface, by making a
tuple progressively approach the needed
We propose that each device, once it has
determined its extrinsic coordinates, can
determine the coefficients coeffs of the
straight line that coincides with the light
ray incident on it. Of course, two In and
Out devices are mates if and only if they
compute the same (or very close) coeffs.
Now suppose that all devices agree on a
continuous hash function H that maps an
equation’s coefficients in intrinsic coordi-
nates (
). An In device A can then send
the tuple containing the color information
to the device at intrinsic coordinates
). An Out emitter B, on its side of
the wall, can try to collect color informa-
tion from the device at intrinsic coordinates
). So, if A and B are mates, the cal-
culated intrinsic coordinates are H(coeff
= H(coeff
), identifying a unique device
closest to those coordinates. This device
will act as a rendezvous point (see Figure 5)
to establish the pair and exchange the
needed information. Of course, the mes-
sage must carry the extrinsic coordinates
to deal with hash collisions—that is, to
check the correctness of a forming pair in
the case of multiple pairs using the same
rendezvous node.
You can optimize this process: only the
first communication between an In and Out
pair occurs via the rendezvous, after which
the two devices become known to each
other and can interact via direct tuple rout-
ing. However, such a solution is less reli-
able: it does not consider that a device can
die or run out of power, a problem that the
rendezvous solution, establishing In-Out
couples dynamically, does not experience.
Internet-scale peer-to-peer computing
and content-based routing have already
addressed similar problems. There, peers
forming an unstructured and dynamic com-
munity must exchange data and messages
based not on an IP addressing scheme but
rather on the messages’ content (for exam-
ple, “I need the mp3 of ‘Hey Jude,’ no mat-
ter who can provide it to me”). Data struc-
turing in a peer-to-peer community defines
a sort of extrinsic coordinate scheme: it is
one on which messages must be delivered
but provides no help in routing them. So,
to avoid Gnutella’s flooding approach, var-
ious proposals
exploit the common idea
of relying on a virtual overlay network,
Light ray
(x , y , z )
, η
) = H(coeff
) = H(coeff
(x , y , z
Figure 5. Rendezvous communication.
defining an intrinsic coordinate scheme
facilitating routing between peers. If you
need to send or receive a message on the
basis of its content, you can hash the mes-
sage’s content into the intrinsic coordinates
and then route it toward the rendezvous
point in the overlay network.
Optical and hardware issues
If you consider each sensor and emitter
a separate device, the number of directional
devices involved in rendering an object
invisible might be very high. In fact, the
object surface must be densely filled with
sensors or emitters oriented toward all pos-
sible directions of the object’s outer space.
To provide some quantitative data, we
can reapply considerations made previously
to a 1-m-diameter sphere. Consider again
for a moment a fixed point of observation;
in this case, to render invisibility at a 10 m
distance, approximately 372,000 devices,
each 8.44 mm
wide, must cover the
sphere’s surface. We derive this number
from the Listing-Donders model: from a 10
m distance, a device of 8.44 mm
is seen as
a single point, and we can easily calculate
that a 1-m-diameter sphere has room for
372,000 such devices. When you have to
preserve such a property for any direction
of observations, however, the 8.44 mm
previously occupied by a single device must
now include numerous sensors and emit-
ters pointing in different directions. As a
first approximation, we can say that in cre-
ating a smooth 3D view of an object, the
number of directional sensors and emitters
in the 8.44 mm
area must be at least one-
half the total number of such areas—that
is, 186,000 (372,000/2). This is because, to
acquire and display a coherent image from
all possible points of view in each of the
8.44 mm
areas, you need at least one sen-
sor or emitter to support any of the other
sensors and emitters directly visible from a
common viewpoint (approximately the
number of sensors and emitters in half a
surface—for example, a hemisphere).
To fill a 8.44 mm
area with 186,000
sensors and with a similar number of emit-
ters, each device should occupy an area
smaller than 5 µm 5 µm. It’s hard to imag-
ine a single standalone computer-based
device of that size. Still, you can think of
packing in multiple optical microdevices
pointing in different directions and con-
trolling them via a single compound device.
Efforts such as those at Texas Instruments,
where they’ve produced microdisplays
made up of electrostatically actuated mir-
rors of a few µm, and at Philips Research
showing the possibility of
growing µm-scale LCD cells on any type of
surface, demonstrate such an approach’s
potential feasibility.
For bandwidth requirements, we can
apply calculations similar to the ones in the
previous section. Coding the (color, x, y, z,
) information requires 104 bits (24 + 5
16 bits). Each tuple must carry its extrin-
sic coordinates to avoid hash collisions; you
can dynamically recompute at each hop the
intrinsic coordinates required for routing.
Considering that, in the worst case, you
must route each message for 1.57 m (one-
half of a maximum circle in the sphere), an
In-Out communication occurring through
a rendezvous device would require, in the
worst case, 3.14 m—that is, 1,082 hops.
(We assume that the wireless-communica-
tion range is long enough to transmit over
the 8.44 mm
area.) So, for a single direc-
tional facet, or monodirectional device, the
required bandwidth to route 30 messages
per second for a maximum worst case of
1,082 other devices is 1,082 104 bits
30 Hz 3.4 Mbits/sec (although the aver-
age required bandwidth for sensors might
be lower). If you pack all the devices con-
tained in the 8.44 mm
area (372,000
devices) in a single compound device, the
devices’ bandwidth requirements increases
tremendously (to approximately 1.2
Tbits/sec). As challenging as this might be,
it’s not technically impossible, especially
when you consider recent advances in ter-
ahertz-band technologies.
you could also exploit AI and image-recog-
nition technologies to have sensors track
observers’ positions and reduce the sen-
sors’ efforts by rendering invisibility from
a limited set of viewpoints.
Perhaps the most natural applications
for invisible objects fall in the military mar-
ket (for example, invisible cars and tanks)
and in the nonintrusive study of natural
You could also paint the interior of an
object, such as a room, instead of its exte-
rior. For example, you could produce real-
istic, immersive virtual reality environ-
ments, freeing users from wearing intrusive
and from staying immobile at
a specific position in a specific room where
specific displays are placed.
A related
application with a great potential market
in southern Europe would be to produce
paintable windows. Tall buildings, very
dark inside due to both narrow windows
and narrow streets, characterize southern
European cities. Because local laws forbid
changing these buildings’ structures, paint-
ing virtual windows could greatly improve
the quality of living there. From the inside,
they would look like large, real windows;
from the outside, you wouldn’t perceive
changes to the building.
More generally, you could effectively
exploit the outlined technology to produce
visibility despite occluding objects. For
instance, appropriately painting trucks
would improve their rear visibility. Also,
you could improve limited visibility in
mountain streets by painting portions of
the occluding slopes.
Step 3. The invisibility cloak
The last constraint we have to remove
to build the cloak of invisibility (or more
generally, a comfortable cloth) is rigidity.
We need to deploy our network of devices
on a flexible fabric, which you can reform
accordingly for unpredictable dynamics
and shapes, due to factors both external
(for example, wind) and internal (for exam-
ple, the wearer’s movements).
Software issues
Unlike the previous cases, a flexible
cloak’s In-Out pairs must be continuously
reestablished to reflect the cloak’s move-
ments. In particular, although the device’s
intrinsic coordinates remain fixed, extrin-
sic coordinates can change continuously.
So, the routing problem becomes particu-
larly challenging, and you must account
for the overhead in maintaining an over-
lay coherent structure over the cloak’s
amorphous network. We have two strate-
gies for solving this problem.
First, devices could reevaluate their
extrinsic coordinates continuously (for
example, 30 times per second) to account
for cloak reshaping. The communication
would then proceed with the rendezvous
approach. Unfortunately, this strategy
imposes a notable computational and com-
munication overhead on devices, leaving
little room for the activities related to image
rendering. Also, because the localization
process might require several iterations to
reach satisfying accuracy, we can’t predict
whether this process would be fast enough
for execution at 30 times per second.
Alternatively, you could rely on a small,
rigid portion of the cloak (for example, a
belt or a necklace) as a central point for
geometrical references. Both In and Out
devices, without being forced to know a
priori their extrinsic coordinates, could
send a partially undefined tuple (contain-
ing only the color information) toward the
rigid reference point. While being routed
from the source toward the cloak’s rigid
section, each of the intermediate devices
could dynamically compute the geometric
information related to the path that the
tuple followed and include this informa-
tion in the tuple before propagating it.
Once the tuple arrives at the cloak’s rigid
section, it can exploit the information col-
lected during its travel to discover the
source’s extrinsic coordinates. At this
point, it can apply the hash-based ren-
dezvous mechanism to meet its mate. A
drawback is load imbalances, produced by
concentrating computational and com-
munication activity in (and in the proxim-
ity of) the cloak’s rigid area.
We do not exclude that better strategies
and algorithmic solutions might exist. You
might find inspiration from mobile ad hoc
networks, which focus on enabling mobile
peers to communicate with each other,
despite the networks’ continuously chang-
ing topology.
Optical and hardware issues
Cloak flexibility does not change the
devices’ optical and size characteristics.
What might change instead is their band-
width requirement, as induced by the addi-
tional communication overhead to support
cloak deformations and dynamic reform-
ing of the In-Out pairs.
If we consider the first solution proposed
(dynamic recomputing of positions and
orientations), optimistically assuming that
this solution is computationally feasible,
the bandwidth requirements will likely
increase dramatically, owing to the relo-
calization process’s iterations. If we con-
sider the second proposed solutions, the
bandwidth requirements do not seem to
even double. In fact, before a device could
route a message to the appropriate ren-
dezvous place, the message must travel
toward the rigid reference point (for exam-
ple, the belt). So, each message on a flexi-
ble cloak travels for a total distance that
would be less than twice the distance it
would have traveled for a rigid object.
However, you must carefully check such
considerations against the load imbalances
Additionally, energy recharging can give
a mutable, wearable cloak a distinct advan-
tage over a wall or rigid object. Even when
lacking an external power supply,
You can use inertial forces induced by
cloak movements to mechanically re-
charge the devices
The human body’s thermal energy can
provide an alternate energy source for
wearable computing systems (for exam-
ple, Infineon Technology offers thermal-
body-powered clothes)
A final note relates to the artifact’s cost.
The Institute for Defense Analysis has pre-
dicted that large-scale production of
MEMS computer-based systems will reduce
their cost, in the near future, to well below
1 Euro each.
A cloak of invisibility of 3 m
would require approximately 372,000
compound (multidirectional) devices to be
invisible at a 10m distance, implying an
overall cost well below a half-million Euros.
Of course, you could move from cloaks
to any type of clothing, applying the same
technology. They could significantly im-
pact military operations and investigations,
although raising questions of ethics. We’d
rather see invisible clothes appear in fash-
ion and entertainment markets. For fash-
ion, you could enrich small (and cheap)
portions of clothes and accessories (for
example, T-shirts, bracelets, or necklaces)
with invisibility frames. Moreover, an
invisibility cloak could effectively augment
virtual reality games in theme parks such as
Another application we have considered,
but aren’t sure if it’s feasible, is internal body
monitoring. You could have a patient drink
(or be injected with) a set of sensors and let
them disperse in a zone of the body (for
example, the stomach). Then, via an emit-
ter-based cream that you’d paint on the
patient (for example, the belly), you could
see the body’s interior, despite the internal
movements of the body and of the sensors
within it. If impossible in a human body,
you could be probably do it in other types
of “interiors” characterized by dynamic
internal activity, such as an underground
river or a complex pipeline.
ecent advances in MEMS and
wireless communication tech-
nologies, together with con-
ceptual advances in distributed
coordination, let us envision the possibility
of building an invisibility cloak in our life-
times, possibly accordingly to our concep-
tual implementation.
Our research group currently faces
issues related to distributed coordination
in pervasive and mobile computing sce-
narios, which brings us closer to realiza-
tion of the invisibility cloak and related
First, we are studying the impact of envi-
ronmental dynamics on the local states of
sets of locally connected sensors and on
their global behaviors.
We’ve found that
you can effectively exploit environmental
dynamics (for example, the type and
dynamics of the stimuli received) to achieve
a globally organized behavior in a large set
of distributed sensors. For an invisibility
cloak, you could use this to let In sensors
in a region of the cloak perform some sort
of dynamic and distributed data compres-
sion, to drastically reduce the data travel-
ing over the cloak.
Second, we are studying a novel approach
to content-based routing, aimed at letting
data flow toward its destination in a com-
plex network by relying on distributed com-
putational fields, providing dynamic, appli-
cation-specific views of a region of physical
You can then achieve content-based
routing by letting data follow the shape of
such fields, which will lead them to their des-
tinations despite dynamic environmental
changes. For the cloak, you could effectively
use such computational fields to dynami-
cally route information from In to Out
devices despite the cloak’s changes in shape.
These approaches, together with ap-
proaches from other areas (for example,
amorphous computing, multiagent sys-
and sensor networks) will likely
improve the cloak’s conceptual design and
shorten its time to market and related
We thank Tim Kindberg, Roy Want, and the anony-
mous referees for helpful comments and corrections
on this article’s earlier drafts.
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For more information on this or any other comput-
ing topic, please visit our Digital Library at http://
Franco Zambonelli
is a professor of computer science at the University of Modena
and Reggio Emilia. His research interests include distributed and pervasive comput-
ing, multiagent systems, and agent-oriented software engineering. He obtained his
Laurea in electronic engineering and his PhD in computer science from the Univer-
sity of Bologna. He is a member of the management committee of the European
Network of Excellence “Agentlink II” and, within the same network, is the coordina-
tor of the Special Interest Group on Methodologies and Software Engineering for
Agent Systems. He is a member of the IEEE, ACM, AIIA (Italian Association for Artifi-
cial Intelligence), and TABOO (Italian Association on Object-Oriented Technologies). Contact him at
Dipt. di Scienze e Metodi dell’Ingegneria, Univ. di Modena e Reggio Emilia, Via Allegri 13, Reggio
Emilia, Italy;
Marco Mamei
is PhD student in computer science at the University of Modena and
Reggio Emilia. His research interests include distributed and pervasive computing,
complex and adaptive systems, and multiagent systems. He has a Laurea in computer
science from the University of Modena and Reggio Emilia. He is a member of the
AIIA (Italian Association for Artificial Intelligence) and TABOO (Italian Association on
Object-Oriented Technologies). Contact him at Dipt. di Scienze e Metodi dell’Ingeg-
neria, Univ. di Modena e Reggio Emilia, Via Allegri 13, Reggio Emilia, Italy; mamei.
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