IEEE Robotics & Automation Magazine - September 2010 - 45

stimuli, such as light, may be used to create a phase gradient
across the oscillators in the system. As the result of such a
gradient, the system as a whole will move toward the light
source. The Slimebot system is unique, because it does not
rely on traditional algorithms or careful planning to achieve
coordinated movement. Instead, it relies on analog processes
that mimic nature.
Around 2005, Goldstein et al. [64] and Goldstein and
Mowry [65] published several articles describing what they
termed claytronic atoms or catoms. These vertically oriented
cylindrical robots, which were incapable of independent motion,
used 24 electromagnets around their perimeters to achieve rolling
locomotion about their neighbors. While the Catom system
could be considered a lattice-type system, we have categorized
it as a free-form system because its modules do not need to
form a regular lattice structure to function.
Goldstein et al. [64] envisioned a system in which millions
of smaller catoms could form arbitrary shapes using a randomized algorithm that avoided conveying a complete description
of the shape to each module in the system. Instead, the algorithm only distributed shape information to the modules at the
boundary of the collection. By creating or absorbing void
pockets (areas without any modules), the edge catoms could
expand or contract the edge in their own proximity. Although
not explicitly demonstrated in their article, the authors claimed
that their shape-formation algorithm could be distributed across
all modules in the system and that each module only required
local information to execute it successfully.
One of the newest catoms systems is one envisioned by
Karagozler et al. in [66]. The system that still appears to be
under heavy development employs hollow cylinders rolled
from SiO2 rectangles patterned with aluminum electrodes.
The authors hope that two of these cylinders, termed Catoms,
when placed in close proximity with their axes aligned, will be
able to rotate with respect to one another using electrostatic
forces. Specifically, the electrodes (which reside on the inside
of each cylinder and are electrically isolated by the SiO2) will
be charged, so that they attract and repel mirror charges on the
neighboring cylinder in a way that causes rotation. For the purposes of our classification, it appears that single Catoms are able
to move independently of their neighbors if they are placed on
an insulating, unbroken conducting substrate. In its current
instantiation, the Karagozler's system appears to be constrained
to form 2-D structures. The authors claim the completed system will have a yield strength similar to that of plastic and that
the modules will be able to transfer power and communication
signals capacitively from neighbor to neighbor.

Self-Assembling Systems
In an attempt to simplify the process of creating intricate
modular robotic systems, researchers have attempted to mimic
and improve upon natural self-assembling systems. Self-assembling systems are common in nature: Geologic forces crystallize polygonal columnar basalts with remarkable regularity,
and DNA in all living organisms uses a soup of free nucleotides
to self-replicate during cell division. Scientists and engineers
have long been interested in these types of self-assembling
SEPTEMBER 2010

systems because they display the ability to spontaneously create
complex structures from simple components.
Whitesides et al. have investigated a wide variety of engineered self-assembling systems [67], [68]. In one system, they
employed truncated octahedra covered in electrical contacts
to form 3-D electrical networks [69]. They found that if
these 5-mm octahedra were placed in a liquid at a temperature above the melting point of the solder covering the
electrical pads and gently agitated, the modules would selfalign to form structures as large as 12 units. The main drawback of this system is that one cannot control the final shape
of the assembled structure: the modules may form a chain, a
cube, or a more irregular shape.
Miyashita et al. performed a more theoretical analysis of
self-assembly using pie-shaped pieces to form complete circles
[70]. The authors performed analysis, simulations, and experiments to better quantify how angular size of the pie-shaped
pieces affected the yield rate of completely assembled circles.
In the process, they followed Hosokawa et al.'s lead [71] and
modeled the system as chemical reaction. For their experiments, the authors used floating modules with permanent
magnets to bond with their neighbors and vibrating pager
motors to induce stochastic motion. By varying the voltage
applied to all motors, the authors could affect what types of
structures were formed even though the modules lacked any
intelligence or communication capabilities. Other researchers
have proposed equally simple system in which the modules do
not have any innate actuation ability. Shimizu and Suzuki have
developed a system of passive modules capable of self-repair
when placed on a vibrating table [72]. The vibrations of the
table cause rotational motion in the modules that wind in a
string attaching each to the other modules in the system.
When all the strings are wound in and taut, the system assumes
an ordered configuration.
Some computer scientists have also investigated theoretical
aspects of self-assembly in the context of 2-D tiles that selectively bond with their neighbors to form simple well-defined
shapes, such as squares [73]-[75]. Typically, these tiles are
allowed to translate but not rotate when moving randomly in
the plane. Each side of every tile in the system has an associated
bonding strength (different edges may have different strengths).
When two tiles collide, they remain attached only if their
cumulate bond strength exceeds a globally defined system
entropy. The shape formed by this type of tile system is dictated by both the system entropy (which can be adjusted
dynamically) and the types of tiles involved. To form a specific
shape, one needs to undertake the relatively complicated task
of designing a set of tiles with appropriate bonding strengths.
Once this design step is complete, the tiles themselves do not
need to display more than the minimal amount of intelligence
necessary to determine when to bond.
Klavins et al. have worked to develop a more intelligent
self-assembling system that employs triangular modules driven
by oscillating fans on an air table to self-assemble different
shapes [76]. The modules in the system can communicate and
selectively bond using mechanically driven magnets. In addition to developing this hardware platform, the authors employ
IEEE Robotics & Automation Magazine

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2010