Clay Tronic s Final

CLAYTRONICS

CHAPTER 1

INTRODUCTION

In the past 50 years, computers have shrunk from room-size mainframes to lightweight

handhelds. This fantastic miniaturization is primarily the result of high-volume nanoscale

manufacturing. While this technology has predominantly been applied to logic and

memory, it’s now being used to create advanced microelectromechanical systems using

both top-down and bottom-up processes. One possible outcome of continued progress in

high-volume nanoscale assembly is the ability to inexpensively produce millimeter-scale

units that integrate computing, sensing, actuation, and locomotion mechanisms. A

collection of such units can be viewed as a form of programmable matter.

The Claytronics project (www.cs.cmu.edu/~claytronics) is a joint effort of

researchers at Carnegie Mellon University and Intel Research Pittsburgh to explore how

programmable matter might change the computing experience. Similar to how audio and

video technologies capture and reproduce sound and moving images, respectively, we are

investigating ways to reproduce moving physical 3D objects. The idea behind claytronics

is neither to transport an object’s original instance nor to recreate its chemical

composition, but rather to create a physical artifact using programmable matter that will

eventually be able to mimic the original object’s shape, movement, visual appearance,

sound and tactile qualities.

Large-scale systems composed from thousands of tiny devices are becoming widely

used in a variety of applications. Sensor networks are a prominent example of such an

application that uses many small simple nodes to create a useful complex system. One of

the most important aspects of such systems is establishing location information

throughout the network of nodes. This localization task presents several difficulties –

correctness, accuracy, and speed. Accuracy is usually chosen as the primary metric, since

most of the systems are directly used to compute the positions of objects, such as cell

phones in a network of cell phone towers. However, as the size of the system becomes

significantly large, the scalability of the approach becomes the crucial factor.

MIT, Pune 1 Department of Information Technology

CLAYTRONICS

A variety of hardware and software approaches have been explored in the past to

solve the problem of establishing positions for myriads of nodes. The main difficulties in

designing such highly-scalable algorithms are that they must operate quickly, be robust,

and present an efficient way to propagate information between nodes. Determining the

orientation of individual nodes in addition to their position presents yet another challenge.

However, this is rarely explored since position information is usually more important than

orientation information.

For example, when tracking down a stolen vehicle, it is much more valuable to

determine where the vehicle is currently located than which way it is facing. In this thesis,

we design several localization algorithms that are capable of simultaneously establishing

the position and orientation for each node in a large system. The algorithms are designed

in a fully distributed fashion to avoid scalability problems. We address several potential

issues such as multi-cluster localization and misaligned boundaries. The performance and

correctness of these approaches are verified on a simulator. Although we explore these

approaches in the context of the Synthetic Reality framework, it is worth noting that they

are applicable to a variety of fields.

1.1 CLAYTRONICS

Just like displays and speakers enabled video and audio replication, Claytronics will be

the technology behind constructing an instance of synthetic reality. Claytronics itself is a

form of programmable matter – a collection of nodes that can be reconfigured into any

shape. The nodes themselves are called catoms, standing for ‘Claytronic atoms’. While

some of the ideas and key concepts behind Claytronics might seem futuristic, the overall

design and the current prototype implementation are very much real.

In order to experiment, as well as to create the first functioning model of the system, we

assembled a Macro-scale two-dimensional version of synthetic reality. As shown in

Figure 1-1, each catom is about 5cm in diameter, 5cm tall cylindrical stack of circuit

boards. The onboard processor is a low-cost and low-power PIC 16F877 CPU. The

processor features 300 bytes of RAM and 8K bytes of ROM. Linx 900MHz RF

transmitter and receiver chips are used to enable communication between the catoms in

the system. In addition to that, each catom has a 6-line LCD display. Each component is

built on a separate circuit board and is connected to other components via a common

serial interface as shown in Figure 1.1. This modular design allows us to easily exchange


CLAYTRONICS

components as well as to perform hardware upgrades. To create a certain shape, the

system needs to have some means to reconfigure itself.

In the current implementation, we use electro-magnets to rearrange this macro-

scale Claytronics prototype. Electro-magnets provide a significant force needed to move

the catoms and they also only need to be powered when we need to invert the polarity of

the magnet, which is important in terms of power consumption constraints. Thus in order

to rearrange the system into some given shape, we can use the magnets to rotate catoms

around other catoms by using proper combinations of polarities as shown in Figure 1-2.

One of the interesting aspects of the Claytronics is that each catom is completely self-

contained– all onboard electronics, magnets, and everything else is managed entirely by

the catom itself. However, what is also interesting is that each catom by itself is also

completely useless. Since catoms can only be moved using other catoms, the only way to

rearrange catoms into a shape is by using a collection of catom nodes. This interesting

requirement is the primary motivation for the first two steps of bringing this prototype to

life – communication and localization. We need to be able to establish a reliable,

efficient, and robust communication between all nodes, so that they can coordinate their

movement. We also need an ability to localize nodes with respect to their local

coordinate frame, primarily so that the system can have feedback on its current status

Figure 1.1 a)Planner Catom Prototype. Components of the Catom : b)PIC processor and

power converter, c)magnets board, d)RF Transmitter and receiver and e)LCD screen


CLAYTRONICS

Figure 1.2 Catom Rotation

1.2. Catoms

Programmable matter consists of a collection of individual components, which we call

claytronic atoms or catoms. Catoms can

1. Move in three dimensions in relation to other

catoms,

2. Adhere to other catoms to maintain a 3D shape,

3. Communicate with other catoms

in an ensemble, and

4. Compute state information with possible assistance

from other catoms in the ensemble.

In the preliminary design, each catom is a unit with a CPU, a network device, a

single-pixel display, one or more sensors, a means of locomotion, and a mechanism for

adhering to other catoms. Although this sounds like a microrobot, we believe that

implementing a completely autonomous microrobot is unnecessarily complex. Instead,

we take a cue from cellular reconfigurable robotics research to simplify the individual

robot modules so that they are easier to manufacture using high-volume methods.

1.3 Synthetic Reality

Your sensory-rich 3-D replica would be capable of two-way communication. Moreover,

your distant participation would be much more realistic than attending through televised

video-conferencing. People with whom you want to meet could also send claytronic

versions of themselves to you to close the loop in your conference room and to make

transactions among catom-based and atom-based individuals seem completely real. As

colleagues interact with your claytronic presence in their space, you would conduct the


CLAYTRONICS

business of the meeting with their claytronic representatives in your space.

Reproductions from catoms would have a look, feel and movement that will evolve with

the technology toward greater and greater realism.

However, the surface characteristics of these reproductions will have no underlying

anatomical or physical structure.The catoms will assemble a surface upon which features

will be painted electronically, similar to the way that video displays today use individual

pixels to contribute tiny dots of color and shadow to paint a much larger moving image.

Electrostatic forces will hold the catoms together in the form on which the image will be

“painted” and, if you were to penetrate the object with a knife, you would find the object

to be hollow inside. If you turn off the juice that powers the pile of catoms, the catoms

return to a formless pile—ready for another charge and the software instructions they

need to form another object.

How did this concept come about? Goldstein is particularly interested in the

study and creation of nanotechnology, which involves very small-scale devices. He saw

the potential for nanotechnology to build some of the world’s tiniest robots into a new

electronic medium that could create 3-D representations of almost any object. “We

wanted to come up with a project that would be equivalent to the challenges faced in the

days when people came up with the idea of sending a person to the moon,” Mowry says.

Mowry envisions a world in which claytronic conferencing would reduce much of the

need for business travel. Claytronics also would support an entirely new realm of

interactivity in games and entertainment and even overcome the physical distances

separating families and friends. “We already play tricks with sight and sound,” Mowry

says. “Claytronics will let us play tricks with space and make it feasible to work and play

in locations that we don’t actually occupy.” Does this human fax machine sound like

science fiction? The horseless carriage probably did, too.

Computers already have the capacity to handle the heavy lifting of information

processing that will be required to form reproductions of real people. You can see this

processing capacity in the realism of computer- created characters in movies such as

Shrek, Happy Feet and Polar Express. Needed now is the hardware—a manufacturable

version of the tiny catom that can carry and respond to microelectronic data—and the

software engineering to develop programs that will enable such a vast number of tiny

computing devices to work together.


CLAYTRONICS

“I consider claytronics to be the most prominent instance of our strategic focus on

’big intellectual bets,’” says Randall Bryant, dean of CMU’s School of Computer

Science. “Looking back over the 50 years of computer science at CMU, we can see that

the reason we’re the top computer-science school today is that a number of visionary

people were able to see the potential for computer technology far past the horizon most

people were viewing. It’s important to have far-reaching projects like claytronics, which

force us to think about what we could do with computer technology once it reaches the

point that a computer can be the size of a grain of sand.” Bryant goes on to say that CMU

has been at the forefront of key conceptual insights that have shaped the world of

computing, including machines that exhibit intelligent behavior and recognize spoken and

written natural languages. The claytronics project, he adds, also reflects the kind of

thinking in the university that conceived the assembly of large numbers of commodity

microprocessors into supercomputers.Most of all, he believes that claytronics presents the

type of scientific and engineering challenge that will keep CMU’s classrooms filled with

the world’s brightest students for decades.

1.4 An Example

Imagine this potential use of claytronics:

Cameras capture the image and motion of a doctor in a clinic and transmit his or her

sensory-rich reproduction to a private home, where there is a claytronic device to

reproduce the actions of the doctor. The 3-D reproduction of the doctor making this

claytronic “house call” can then help a person in the house who is having chest pain—or

other unusual symptom. As the real doctor in the clinic monitors the replica’s every

move and guides it from a distance, the claytronic reproduction can take vital signs and

provide assistance to the ailing person, even before a live crew of emergency medical

technicians arrives in an ambulance. The patient is taken to a hospital, where the

physician determines he needs a heart transplant. Today, a surgeon prepares to operate by

studying flat-screen images of a patient's anatomy. However, claytronics could provide a

3-D replica of a person’s internal organs assembled from body scans. Long before making

the first incision, the doctor could review a replica of the tissue and determine the best

approach for a surgery.


CLAYTRONICS

1.5 Pario

Figure 1.3. Audio, Video and the next media ‘Pario’

Pario is a next generation form of replication and synthesis of an environment. Coming

from the Latin root ‘par’ meaning ‘to create’, and in contrast to video and audio, pario is a

media type that will allow users to create a dynamic physical artifact which will be a copy

of the matter that is being captured. The replica itself will be modeled via complex

programmable matter called Claytronics. Just as a photo-copier can produce a copy of a

paper, Claytronics will be able to produce a replica of the physical phenomenon being

copied. Such Claytronic objects can be used to create an entirely new replicated

environment called Synthetic Reality. Unlike virtual reality, Synthetic Reality will be a

physically-constructed dynamic environment that will be a replica of the actual physical

environment elsewhere. In the long term, this will allow for the creation of high-fidelity

three dimensional copies of objects that are being replicated. As an extreme example, this


CLAYTRONICS

technology will allow one to create a detailed replica of a person thousands of miles

away, similar to how phones and teleconferencing allow us to replicate voice and images

today. This idea is illustrated in Figure 1.1 – cell phone is an example of an audio

communication capable of retransmitting the ghosts voice and video is capable of

showing us the ghost on TV; Claytronics on the other hand, will be capable of

constructing a moving replica. The earlier versions, denoted by Claytronics 2D, will be

most likely two dimensional and will construct a crude approximation of the shape – for

example using cylinders or spheres as building blocks. However, the later and more

advanced systems, denoted by Claytronics 3D in the picture, will be able to construct an

artifact that will be nearly identical in appearance to the original shape.

1.6 Vision and Goal Behind Claytronics

The applications and possibilities for pario are enormous. Just imagine a world where a

doctor can be synthesized directly right where the emergency occurred or a tiny football

game being played on your desk with tiny players running around the field. One can also

imagine objects that are being dynamically created around you as you need them. If you

need to eat dinner these tiny computers can form a table; and if you would like to watch

TV afterwards – they can form a couch for you to sit on. While the ultimate intention is to

have a working 3D version of Claytronics capable of all of the above features, our short

range goal is to bring to life a crude macro-scale prototype. This prototype

implementation will obviously lack many features, but it will be a good test bed and will

allow us to experiment with the functional hardware system.

“Claytronics will let us play tricks with space and make it feasible to work and play

in locations that we don’t actually occupy.” —Todd Mowry

“Claytronics will reproduce images of individuals that will have the look and feel of

a real person—with a hand that feels like real skin extended in greeting.” —Seth

Goldstein

If prof. Goldstein makes it to the realization of this technology, it will be a

remarkably big revolution in the field of communication and computing. This technology

may take time to release and reach to common individuals but its certainly an entry point

to new dimension. It’s Claytronics.


CLAYTRONICS

CHAPTER 2

HOW CLAYTRONICS WORKS?Amazing as the concept sounds, makes a room for science fiction authors to write on the

concept. This , however, can’t make this to reality. Here we enter into the picture.

Hoping that some of us will be working on it soon, let’s get into the technical details of

this concept.

1. Ensemble Principle

Realizing this vision requires new ways of thinking about massive numbers of

cooperating millimeter-scale units. Most importantly, it demands simplifying and

redesigning the software and hardware used in each catom to reduce complexity and

manufacturing cost and increase robustness and reliability. For example, each catom must

work cooperatively with others in the ensemble to move, communicate, and obtain power.

Consequently, our designs strictly adhere to the ensemble principle: A robot module

should include only enough functionality to contribute to the ensemble’s desired

functionality. Three early results of our research each highlight a key aspect of the

ensemble principle:

1. easy manufacturability

2. powering million-robot ensembles

3. surface contour control without global motion planning.

1.1 Easy Manufacturability

Some catom designs will be easier to produce in mass quantity than others. Our present

exploration into the design space investigates modules without moving parts, which we

see as an intermediate stage to designing catoms suitable for high-volume manufacturing.

In our present macroscale (44-mm diameter), cylindrical prototypes, shown in Figure

2.1, each catom is equipped with 24 electromagnets arranged in a pair of stacked rings.

To move, a pair of catoms must first be in contact with another pair. Then, they must

appropriately energize the next set of magnets along each of their circumferences. These

prototypes demonstrate highspeed reconfiguration—approximately 100 ms for a step-

reconfiguration involving uncoupling of two units, movement from one pair of contact

points to another, and recoupling at the next pair of contact points.


CLAYTRONICS

At present, they don’t yet incorporate any significant sensing or autonomy. The

current prototypes can only overcome the frictional forces opposing their own horizontal

movement, but downscaling will improve the force budget substantially. The resulting

force from two similarly energized magnet coils varies roughly with the inverse cube of

distance, whereas the flux due to a given coil varies with the square of the scale factor.

Hence, the potential force generated between two catoms varies linearly with scale.

Meanwhile, mass varies with the cube of scale. These relationships suggest that a 10-fold

reduction in size should translate to a 100-fold increase in force relative to mass. Energy

consumption and supply will still be an issue, but given sufficient energy, smaller catoms

will have an easier time lifting their own weight and that of their peers, as well as

resisting other forces involved in holding the ensemble together. Our finite-element

electromagneticphysical simulations on catoms of different sizes appear to confirm this

approximation and closely match our empirical measurements of magnetic force in the

44-mm prototypes. We’re also studying programmable nanofiber adhesive techniques that

are necessary to eliminate the static power drain when robots are motionless, while still

maintaining a strong bond.

Figure 2.1 Claytronic atom prototypes. Each 44-mm-diameter catom is equipped with 24electromagnets arranged in a pair of stacked rings.


CLAYTRONICS

1.2 POWERING MICROROBOT ENSEMBLES

Some energy requirements, such as effort to move versus gravity, scale with size.

Others, such as communication and computation, don’t. As microrobots (catoms) are

scaled down, the onboard battery’s weight and volume exceed those of the robots

themselves.

To provide sufficient energy to each catom without incurring such a weight and

volume penalty, we’re developing methods for routing energy from an external source to

all catoms in an ensemble. For example, an ensemble could tap an environmental power

source, such as a special table with positive and negative electrodes, and route that power

internally using catom-tocatom connections. To simplify manufacturing and accelerate

movement, we believe it’s necessary to avoid using intercatom connectors that can carry

both supply and ground via separate conductors within the connector assembly. Such

complex connectors can significantly increase reconfiguration time. For example, in

previously constructed modular robotic systems such as the PARC’s PolyBot

(www2.parc.com/spl/projects/modrobots/chain/polybot/index.html) and the Dartmouth

Robotics Lab’s Molecule it can take tens of seconds or even minutes for a robot module

to uncouple from its neighbor, move to another module, and couple with that newly

proximal module.

In contrast, our present unary-connector- based prototypes can “dock” in less than

100 ms because no special connector alignment procedure is required. This speed

advantage isn’t free, however: A genderless unary connector imposes additional

operational complexity in that each catom must obtain a connection to supply from one

neighbor and to ground from a different neighbor. Several members of the Claytronic

team have recently developed power distribution algorithms that satisfy these criteria.

These algorithms require no knowledge of the ensemble configuration— lattice spacing,

ensemble size, or shape—or power-supply location. Further, they require no on-catom

power storage.

1.3 SHAPE CONTROL WITHOUT GLOBAL MOTION PLANNING

Classical approaches to creating an arbitrary shape from a group of modular robots

involve motion planning through high-dimensional search or gradient descent methods.

However, in the case of a million-robot ensemble, global search is unlikely to be

tractable. Even if a method could globally plan for the entire ensemble, the

communications overhead required to transmit individualized directions to each module


CLAYTRONICS

would be very high. In addition, a global plan would break down in the face of individual

unit failure. To address these concerns, we’re developing algorithms that can control

shape without requiring extensive planning or communication. While this work is just

beginning, Claytronics researchers have had early success using an approach inspired by

semiconductor device physics. This approach focuses on the motion of holes rather than

that of robots per se. Given a uniform hexagonal- packed plane of catoms, a hole is a

circular void due to the absence of seven catoms. Such a seven-catom hole can migrate

through the ensemble by appropriate local motion of the adjacent catoms. Holes migrate

through the ensemble as if moving on a frictionless plane, and bounce back at the

ensemble’s edges. Just as bouncing gas molecules exert pressure at the edges of a balloon,

bouncing holes interact frequently with each edge of the ensemble without the need for

global control. As Figure 2.2 illustrates, edges can contract by consuming a hole or

expand by creating a hole, purely under local control.

Figure2.2 Edges can (a) contract by consuming a hole or (b) expand bycreating a hole, purely under local control

We initiate shape formation by “filling” the ensemble with holes. Each hole receives

an independent, random velocity and begins to move around. A shape goal specifies the

amount each edge region must either contract or expand to match a desired target shape.

A hole that hits a contracting edge is consumed. In effect, the empty space that constitutes

the hole moves to the outside of the ensemble, pulling in the surface at that location.

Similarly, expanding edges create holes and inject them into the ensemble, pushing its


CLAYTRONICS

contour out in the corresponding local region. Importantly, all edge contouring and hole

motion can be accomplished using local rules, and the overall shape of an ensemble can

be programmed purely by communicating with the catoms at the edges. Hence, we use

probabilistic methods to achieve a deterministic result. Our initial analyses of the

corresponding 3D case suggest surface contour control will be possible via a similar

algorithm.

2. Problems and Challenges in Implementation

Our initial research results suggest it may be possible to construct, power, and control

large microrobot ensembles to model 3D scenes. While many difficult problems remain,

successful implementation of a dynamic physical rendering system could open the door to

a new era of humancomputer interface design and new applications. Economic feasibility

also poses a high bar to the manufacture and deployment of multimillion-robot

ensembles. However, the innovative application of high- volume manufacturing

techniques bridged a similarly large gulf in cost and physical scaling in computer

hardware. Achieving the Claytronics vision won’t be straightforward or quick, but by

taking on some of the problems associated with operating and building these ensembles,

we hope to advance the state of the art in modular reconfigurable microrobotics and

encourage others to undertake related research.

3. Current Research

Current research is exploring the potential of modular reconfigurable robotics and the

complex software necessary to control the “shape changing” robots. “Locally Distributed

Predicates or LDP is a distributed, high-level language for programming modular

reconfigurable robot systems (MRRs)”. There are many challenges associated with

programming and controlling a large number of discrete modular systems due to the

degrees of freedom that correspond with each module. For example, reconfiguring from

one formation to one similar may require a complex path of movements controlled by an

intricate string of commands even though the two shapes differ slightly.

In 2005, research efforts to develop a hardware concept were successful on the scale

of millimeters, creating cylindrical prototypes 44 millimeters in diameter which interact

with each other via electromagnetic attraction. Their experiments helped researchers


CLAYTRONICS

verify the relationship between mass and potential force between objects as “a 10-fold

reduction in size [which] should translate to a 100-fold increase in force relative to mass”.

Recent advancements in this prototype concept are in the form of one millimeter diameter

cylindrical robots fabricated on a thin film by photolithography that would cooperate with

each other using complex software that would control electromagnetic attraction and

repulsion between modules.

Today, extensive research and experiments with claytronics are being conducted at

Carnegie Mellon University in Pittsburgh, Pennsylvania by a team of researchers which

consists of Professors Todd C. Mowry, Seth Goldstein, Ph. D. candidates, graduate and

undergraduate students, and researchers from Intel Labs Pittsburgh.

The effort to produce reliable and robust modular robotic systems has led researchers

to explore a large design space of mechanisms for locomotion, adhesion, communication,

and power. Ostergaard, et al. survey different locomotion and adhesion mechanisms for

self-actuating robots in. Of the many research efforts the most relevant to our work is

Fracta. Fracta is a two dimensional modular robot which uses a combination of permanent

magnets and electromagnets for locomotion and adhesion. It is the only other internally

actuated system which has no moving parts. As in our planar catoms, to move a module

requires communication between the moving module and its neighbors. The two main

differences between Fracta and planar catoms are due to changes in underlying techology

and the use of permanent magnets. Fracta modules are constrained to be in a hex-lattice

whereas the planar catoms have additional actuators and can be arranged in a cubic or hex

lattice, as well as more arbitrary formations.

Significant advances in VLSI enable us to create smaller lighter units which do not

use permanent magnets. We also harness the magnets for more than locomotion and

adhesion, i.e., the magnets also serve as the main mechanism for power transfer, sensing,

and communications. Planar catoms are our first step along the path towards realizing

three dimensional claytronics. Part of their raison d’etre is to understand the ensemble

axiom and how the tradeoff between individual unit hardware complexity and

computation affects design. As such, work in externally actuated modular robots is also

relevant. For example, neither programmable parts nor 3D stochastic robots have any

moving parts. Both of these systems simplify each robot by using external forces for

actuation. The robots rely on the external forces and move stochastically, adhering to

each other under control of the program running on the robot. The ensemble principle is


CLAYTRONICS

carried even further in the latter project; robots are unpowered until they adhere to a

powered robot. Earlier prototypes of the planar catoms described in this paper have been

demonstrated at AAAI and have been briefly described in the general media. This paper

is the first complete description and introduces the ideas behind using a single device

(electromagnets) to implement locomotion, adhesion, power transfer, communication, and

sensing.

4. Hardware

The driving force behind programmable matter is the actual hardware that is manipulating

itself into whatever form is desired. Claytronics consists of a collection of individual

components called claytronic atoms, or catoms. In order to be viable, catoms need to fit a

set of criteria. First, catoms need to be able to move in three dimensions relative to each

other and be able to adhere to each other to form a three dimensional shape. Second, the

catoms need to be able to communicate with each other in an ensemble and be able to

compute state information, possibly with assistance from each other. Fundamentally,

catoms consist of a CPU, a network device for communication, a single pixel display,

several sensors, an onboard battery, and a means to adhere to one another.

Figure 2.3 Catom Structure

4.1 CURRENT CATOMS

The researchers at Carnegie Mellon University have developed various prototypes of

catoms. These vary from small cubes to giant helium balloons. The prototype that is most

like what developers hope catoms will become is the planar catom. These take the form of


CLAYTRONICS

44 mm diameter cylinders. These cylinders are equipped with 24 electromagnets arranged

in a series of stacked rings along the cylinder’s circumference. Movement is achieved by

the catoms cooperatively enabling and disabling the magnets in order to roll along each

other’s surfaces. Only one magnet on each catom is energized at a time. These prototypes

are able to reconfigure themselves quite quickly, with the uncoupling of two units,

movement to another contact point, and recoupling taking only about 100 ms. Power is

supplied to the catoms using pickup feet on the bottom of the cylinder. Conductive strips

on the table supply the necessary power.

Figure 2.4 A progression of catom magnet designs. The rightmost magnet is

our current revision.

4.2 FUTURE DESIGN

In the current design, the catoms are only able to move in two dimensions relative to each

other. Future catoms will be required to move in three dimensions relative to each other.

The goal of the researchers is to develop a millimeter scale catom with no moving parts,

to allow for mass manufacturability. Millions of these microrobots will be able to emit

variable color and intensity of light, allowing for dynamic physical rendering. The design

goal has shifted to creating catoms that are simple enough to only function as part of an

ensemble, with the ensemble as a whole being capable of higher function.

As the catoms are scaled down, an onboard battery sufficient to power it will exceed

the size of the catom itself, so an alternate energy solution is desired. Research is being

done into powering all of the catoms in an ensemble, utilizing the catom-to-catom contact

as a means of energy transport. One possibility being explored is using a special table

with positive and negative electrodes and routing the power internally through the

catoms, via “virtual wires.”


CLAYTRONICS

Another major design challenge will be developing a genderless unary connector for

the catoms in order to keep reconfiguration time at a minimum. Nanofibers provide a

possible solution to this challenge. Nanofibers allow for great adhesion on a small scale

and allow for minimum power consumption when the catoms are at rest.

Figure 2.5 A Possible Future Catom

5. Software

The essence of claytronics—a massively distributed system composed of numerous

resource-limited catoms—raises significant software issues: specifying functionality,

managing concurrency, handling failure robustly, dealing with uncertain information, and

controlling resource usage. The software used to control claytronics must also scale to

millions of catoms. Thus, current software engineering practices, even as applied to

distributed systems, may not be suitable. We are just beginning to explore the software

design principles needed. We have broken down the software issues into three main

categories: specification, compilation, and runtime support. Our goal is to specify the

global behavior of the system in a direct and descriptive manner. The simplest model we

are investigating with respect to specification is what we call the Wood Sculpting model.

In this model, a static goal shape is specified. We are investigating two alternative

compilation methodologies, both of which fit into the general category of single-program-

multiple data (SPMD) programming models. In the first, we are compiling the

specification into a planning problem. In this approach we are inspired by work done in

communicating soccer robots and in the context of reconfigurable robots, by the

constraint-based control framework in which a high-level description such as a particular

gait which is translated to a distributed, constraint-based controller. Our second approach


CLAYTRONICS

is based on emergent behavior. Prior work seems particularly appropriate in this latter

approach with respect to claytronics.

At the highest level of abstraction a shape is specified in terms of Origami folding

directives. Through a process of planning, these folding directives are translated into low-

level programs for autonomous agents; achieving the shape by local communication and

deformation only. Underlying the user-level software is a distributed runtime system.

This system needs to shield the user from the details of using and managing the massive

number of catoms. Our initial steps in this direction use emergent behavior to determine a

catoms location and orientation with respect to all catoms as well as to build a

hierarchical network for communication between catoms. Efficient localization is

achieved by having the catoms determine their relative location and orientation in a

distributed fashion. Then as regions of localized catoms join up they unify their

coordinate systems. Our algorithm takes O(1) time if the network is capable of broadcast.

With a network limited to point-to-point connections the algorithm takes O(√3 n) time in

3D. Once catoms are localized we form a hierarchical communication network, again

using simple local programs on each catom. A tree is formed in parallel by having nodes

join with their neighbors until all the nodes are in a single tree. This simple algorithm

produces a surprisingly efficient tree from which can then be further optimized.

7. Scaling and Design Principles

A fundamental requirement of Claytronics is that the system must scale to very large

numbers of interacting catoms. In addition to previously stated principles for the design of

modular robots we have the following four design principles:

1. Each catom should be self-contained, in the sense of possessing everything necessary

for performing its own computation,communication, sensing, actuation, locomotion, and

adhesion.

2. To support efficient routing of power and avoid excessive heat dissipation, no static

power should be required for adhesion after attachment.

3. The coordination of the catoms should be performed via local control. In particular, no

computation external to the ensemble should be necessary for individual catom execution.

4. For economic viability, manufacturability, and reliability, catoms should contain no

moving parts.


CLAYTRONICS

CHAPTER 3

LOCOMOTION

Using the ensemble axiom as a guiding design principle requires that we design very

small robotic modules capable of actuating relative to one another. As discussed earlier,

to make reliable modules that can be readily scaled down in size, we have taken the

extreme position of eliminating all moving parts within our robotic modules. Motion

without moving parts is achieved instead by the use of force-at-adistance actuation

between modules. The mechanisms that work well for this purpose are highly dependent

on the absolute scale of the module design. We chose the centimeter range for our

prototypes, as it was the smallest size we could implement self-contained modules using

commercially available electronic components and circuit board design techniques. At

this scale we are well beyond the practical application of surface tension, Van der Waals

force, or electrostatic attraction, and therefore employ electromagnetism for our actuation.

A. Relative Motion using Pairs of Electromagnets

In keeping with the ensemble axiom, planar catom motion requires two modules to

perform the simplest locomotion. Our actuation can be likened to a rotary linear motor,

e.g. a stepper motor in which the stator and rotor are mechanically decoupled into two

separate, identical modules set side by side. Rather than permanent magnets, both catoms

generate their fields with the appropriate polarities via electromagnets. Catoms in contact

may orbit each other in a clockwork fashion by simultaneously activating electromagnets

adjacent to the pair currently in contact. The magnetic force will create a torque that

pivots the two catoms about the edge and onto the next face. Once in position, the catoms

can again activate the next adjacent pair and continue their orbit. In ideal conditions, this

motion takes as little as 50ms to complete one step, or 1.2s for a complete revolution.

However, unlike a stepper motor, which is carefully designed with tight mechanical

tolerances and excellent axial alignment, our catoms must regularly deal with mechanical

misalignment both in and out of the plane of motion. As magnetic force falls off

proportional to the cube of the distance, these small misalignments seriously compromise


CLAYTRONICS

the efficiency of our motion. When using simple open-loop control, it is necessary to

power the coil for much longer than needed for the ideal case, to give the catoms time to

exert themselves over farther distances. In some generations of prototypes, this

conservative on-time has been 10-20x longer than the ideal. This variability in

performance thus has a large effect on power efficiency, and suggests why closedloop

control is highly desirable in our system yet generally not implemented in standard

stepper motors.

Figure 3.1 A typical movement scenario. (a) is the start configuration. (b) is a blow up of the

mover-pivot pair. (c) is the final configuration. The yellow magnets exert a small holding

force. The green magnets exert a large force to move the mover around the pivot.

B. Ensemble Motion

While the basic motion primitive requires the participation of only two catoms, any

motion which performs actual work, i.e., motion which changes the configuration of the

ensemble, requires the involvement of more than two catoms. We distinguish three types

of catoms in ensemble motion. The mover catom moves around a pivot catom with

respect to the rest of the ensemble. The others surrounding the pivot catom, holders, keep

the pivot catom in formation as the mover moves around it. In a basic movement

scenario, the pivot catom and all its neighbors except the mover catom actuate their

magnets with a low holding force (the yellow magnets in Fig. 3.1a). The mover and pivot

then energize the magnets used to move the mover catom (the green magnets in Fig. 3.1a


CLAYTRONICS

and b). This causes the mover catom to pivot around the edge it shares with the pivot

catom, resulting in Figure 3.1c.

C. Magnet Design and Constraints

Our initial investigations focused on permanent magnet solutions, as these have provide a

holding force without a static power dissipation. We experimented with programmable or

“soft” magnetics, using AlNiCo magnets that can be made to change polarity when

subjected to brief pulses from an encompassing electromagnet. Unfortunately these were

too weak to generate useful forces for us, and are known to degrade over time when

subjected to large numbers of polarity shifts. We also considered using the surrounding

electromagnet as our primary actuator, using the soft magnetic material only as a passive

holding actuator, but the AlNiCo had poor permeability and low saturation, preventing us

from generating enough force in the electromagnets. By using a more traditional

electromagnet core material, we were able to design magnets with effective force.

Additionally, as we Fig. 3.2.

The main body of the catom is comprised of two rings of magnets offset by 15

degrees. will see in later sections, the electromagnets can be used for other purposes.

Thus, the planar catoms use the same electromagnets for locomotion, adhesion, power

delivery, communication, and sensing. The design constraints involved in determining the

size, shape and number of magnets are numerous. First and foremost, the magnets must

provide sufficient torque to rotate a catom around a shared edge (e.g., the highlighted

edge in Figure 3.1b). The torque required is influenced by catom mass and diameter, as

well as the friction between a catom and the floor. The electromagnets themselves are

quite heavy as they have a large copper winding and the core and flux shunt are

composed of steel.

The minimum amount of core material is dictated by magnetic flux saturation—

reducing the crosssectional area of the core would dramatically reduce magnet strength.

The copper coil is limited by the power density— reducing the cross-sectional area of the

coil would force proportionaly higher current through less material, increasing heat

dissipation and dramatically lowering the effective duty cycle of the actuator. Friction

cannot be lowered arbitrarily as low friction constants make the movement between

catoms unstable (e.g., the catoms tend to fly away from each other).


CLAYTRONICS

Figure 3.2 The main body of the catom is comprised of two rings of magnetsoffset by 15 degrees.

In addition to being strong and compact, the magnets must also be carefully shaped so

that they can be placed around the circumference of the catom without interfering with

each other. Furthermore we want to restrict the lattice packing as little as possible,

supporting at least hex and cubic lattices. We used these three factors and the fact that

magnetic force falls off with the cube of the distance to determine that 24 magnets would

be the best balance of constraints. To prevent the magnet core material from being close

enough to cause interference, we stagger the magnets in two rings of twelve spaced 4mm

apart as in Figure 3.2.

This has the added benefit of giving us larger effective area for our coil

windings. Using more than two rings is prohibitive, because it begins to introduce

significant out of plane torques as the magnet layers become farther and farther from the

friction plane. With each individual magnet designed to maximuze flux density, reduce

saturation, minimize overheating, we finally consider resistance and wire gauge so that

our voltage and current requirements can be met with high density surface mount

components such as MOSFETs. Commercially available, off-the-shelf electromagnets

proved insufficient for our actuators. They did not fit well in our cylindrical geometry,

and had far too conservative power usage and duty cycles to satisfy our torque needs.

Thus, we had to design our own magnets. After several iterations, our current design

places the coil vertically and uses two thick trapezoidal endplates that combine to form a

horseshoe electromagnet. The ends of the horseshow are flat to improve catom-to-catom

alignment.


CLAYTRONICS

Fig. 3.3. At the start of a motion (top), the flux saturates the bottom tip ofeach magnet, generating the initial torque of 12mN-m. At the end (bottom), the flux is evenly

distributed and provides far greater holding torque (200mNm)for the same power

The sharp edges of the endplates also provide a natural pivot point. (Initially we tried

rounded ends, but this results in an unstable system.) The current design also helps

ameliorate the inverse cubic falloff of magnetic force, as at the start of a move operation

the actuating magnets already have a narrow but complete flux path, greatly increasing

our initial strength. The flux paths may be seen in Figure 3.3 at both the initial and final

stage of a motion step. The resulting system has 24 magnets arranged in two rings of 12

magnets forming a faceted, self-aligning structure, with a large potential excitation

capability and acceptable duty cycles. The coil height is 3mm and has 452 turns of 39

guage wire around a 4.4mm AISI1010 steel core, and presents its flux at the catom’s

perimeter, 4.2mm from the center of the solenoid, via two 3mm thick flux shunts. When

energized at full power for relative motion, these coils are capable of co-generating a

torque of 12mN-m. The worstcase torque needed, that of moving one catom about a

second fixed catom, is given by the formula _ = mgrμ, and is around 3mN-m given

a .105kg module under low friction circumstances of around .12. When energized for

holding torque, they can generate over 200mN-m at full power. By using a small fraction

of full power we can generate adequate holding torque without danger of overheating the

coils.

D. Control Circuits

When moving a catom the magnets require high excitation currents for short periods

of time. Conversely, when holding two catoms together, the magnets are next to each

other and thus require very little excitation, but should remain on continuously. The

magnet control circuits is designed to support both situations. This greatly simplifies


CLAYTRONICS

ensemble control, as without a holding force, accurate synchronization between many

catoms would be required if they were to hold one catom in place while another rotated

about it. We also need control of the polarity, to coordinate an attractive force between

two separate catoms. Consequently, our drivers must be capable of independent,

bidirectional delivery of over 30 Watts in sub-second bursts, as well as delivering a few

watts over multi-minute periods. Fortunately, modern MOSFETs support the required

power densities in packages small enough for us to fit the drivers for the entire magnet

array onto the catom itself. Our initial controller design implemented 24 full bridges for

completely independent control of each magnet. Fitting everything necessary into a

44mm2 area was a laborious process and greatly increased manufacturing costs. As we

continued to investigate the motion and lattice constraints, we realized that no movement

circumstances would ever require us to activate more than one of any four consecutive

electromagnets around the 24-gon. By separating the full bridges into half-bridges, and

using one shared half bridge between these four, we were able to reduce the number of

half bridges from 48 to 30, as well as multiplex the magnet control signals. This

dramatically reduced the circuit density, as shown in Figure 3.4, and made pulse width

modulation (PWM) signal generation practical for our control signals.

Fig. 3.4. Density comparison of implementing independent full bridges (top)vs. multiplexed half-bridges (bottom).


CLAYTRONICS

PWM allows for simple open-loop current control. Thus, in addition to a full-duty, high

excitation pulse, we can also generate our low power holding currents that can remain on

continuously without harming the electromagnets. Our current electronics are capable of

continuously delivering up to 1.5A at up to 50V. Higher voltages exceed the rating of our

high density interconnect and approach the breakdown voltage of our existing

semiconductors. Given that this power level is sufficient to cause thermal breakdown in

our coils in a matter of seconds, our duty cycles are limited solely by the electromagnets

and not our drive electronics.

E. Discussion

We found that the two most important factors in achieving a robust system are the

effective magnet torque and the manufacturing precision. Despite several iterations

focused solely on maximizing the torque generated, we have only been able to generate

four times the torque needed under ideal conditions. This is barely adequate to provide for

robust locomotion, as even small misalignments of the magnets can disrupt the system

dramatically due to the non-linear falloff of magnetic force. Angular misalignments of the

magnets orthogonal to the plane of motion are especially severe as it imparts torques that

actually impede motion. Thus, repeatable and precise manufacturing was critical to

creating robust designs and required several iterations.


CLAYTRONICS

CHAPTER 3

CONCLUSION

Claytronics is one instance of programmable matter, a system which can be used to

realize 3D dynamic objects in the physical world. While our original motivation was to

create the technology necessary to realize pario and synthetic reality, it should also serve

as the basis for a large scale modular robotic system. At this point we have constructed a

planer version of claytronics that obeys our design principles. We are using the planer

prototype in combination with our simulator to begin the design of 3D claytronics which

will allow us to experiment with hardware and software solutions that realize full-scale

programmable matter, e.g., a system of millions of catoms which appear to act as a single

entity, in spite of being composed of millions of individually acting units.

As expected, simplifying the mechanism increases the algorithmic complexity of

completing a motion. Each movement of a single catom requires the participation of the

entire ensemble. This makes local communication and sensing critical to the operation of

a claytronic ensemble. Also essential are scalable distributed algorithms capable of

synthesizing ensemble functionality from the abilities of each individual catom. Our

simulator environment allows us to explore these fully while also providing a direct

interface to our current hardware. Multi-purpose magnetic force effectors are a first step

towards scalable claytronic hardware. Distilling the complexity of a robotic module into

an array of identical features greatly reduces the domain of design constraints that must

be addressed during miniaturization. Furthermore, creating hardware that seamlessly

integrates into our physics-based simulation environment allows real world scenarios to

inform the development of distributed coordination algorithms.


CLAYTRONICS

References

[1] K. Autumn, M. Sitti, Y.A. Liang, A.M. Peattie, W.R. Hansen, S. Sponberg, T.W.

Kenny, R.S. Fearing, J.N. Israelachvili,

and R.J. Full. Evidence for van der waals adhesion in gecko setae. Proceedings of

National Academy of

Sciences, 99(19):12252–6, 2002.

[2] H. Benjamin Brown, Michael VandeWeghe, Curt Bererton, and Pradeep Khosla.

Millibot trains for enhanced mobility.

IEEE/ASME Transactions on Mechatronics, 7(4):452 – 461, December 2002.

[3] M. Butts, A. DeHon, and S. Goldstein. Molecular electronics: Devices, systems and

tools for gigagate, gigabit chips.

In ICCAD-2002, Nov. 2002.

[4] James Cameron andWilliam Wisher Jr. Terminator 2: Judgment Day. Columbia

TriStar, 1991.

[5] A. Castano, W.M. Shen, and P. Will. Conro: Towards deployable robots with inter-

robot metamorphic capabilities.

In Journal of Autonomous Robots, vol. 8, no. 3, pages 309–324, July 2000.

[6] Y. Cui and C. Lieber. Functional Nanoscale Electronic Devices Assembled Using

Silicon Nanowire Building Blocks.

Science, 291:851, 2001.

[7] Committee for the Review of the NNI. Small wonders, endless frontiers: Review of

the national nanotechnology initiative. National Academy Press, Washington, D.C., 2002.

http://www.nsf.gov/home/crssprgm/nano/smallwonders pdffiles.htm.

[8]A Modular Robotic System Using Magnetic Force Effectors, B. Kirby, B. Aksak, J.

Hoburg, T. Mowry, P. Pillai.


Documents

Clay Tronic s Final