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Stochastic Catoms

High School Techologists Discover Claytronics

A concept being tested in the Carnegie Mellon-Intel Claytronics Research Project is the use of stochastic reconfiguration in ensembles of modular robots.   In this mode of reconfiguration, the module relies on random motion and follows unmapped paths to gain in the ensemble a position where it can determine its exact location and contribute its form to the overall structure.

Stochastic Balloons
Depending upon the scale of the device, actuation of the module 's motion can be created with various sources of energy, including currents of air, electrostatics or, in the case of a study of the phenomenon during Andrew 's Leap, Carnegie Mellon 's summer enrichment program, the propelling motion of high school students throwing helium-filled balloons.  

From such forces, a module derives an initially incoherent motion that causes random contacts with other modules. In these contacts, the module evaluates the appropriateness of forming a connection with the other module.   The module makes its decision by evaluating the relation of its form in the instance of the contact location to the ensemble 's overall goal for a predetermined shape.   Based on this evaluation, the module either forms a bond or continues in motion.  


Above, Krissie Lauwers, an instructor for the Andrew 's Leap program, anchors an ensemble of four Stochastic Helium Catoms that have linked to each other.


To demonstrate the applicability of stochastic reconfiguration to modular robots, the Andrew 's Leap students constructed an ensemble of Mylar balloons in the shape of cubes, each approximately 1/2 meter on a side.   They also created a lightweight electronic module to support each catom 's functionality as well as simple latches for the faces of each cube to provide a means of data exchange and attachment among catoms.   To create bouyancy, each catom was filled with helium.  

Computations within the electronic module follow a simple program, known as a graph grammar, which enables each stochastic catom independently to determine its location in relation to other catoms in the ensemble - and in relation to a predetermined shape into which the catoms locate their positions from random motion.

Localizing its position while in contact with other catoms, a catom either engages its electrostatic latch in order to bind to an adjacent robot or signals for separation and further stochastic motion until it identifies a location where it will contribute to the desired global shape.  

As a type of swarm behavior conceived for nano-scale robots, stochastic motion among catoms would draw upon mathematical probability whose effective potential to shape forms would increase with greater numbers of smaller-scale modules.

While the student technologists worked with a few large-scale, low-mass modules, they were able to test algorithms that implemented valid steps for the sorting of random associations among catoms.   They were also successful in the design of latches that enabled catoms to exchange data, localize positions within an ensemble and determine the appropriateness of connections with randomly-encountered catoms to the goal-shape desired for the ensemble.

Brian Kirby Explains Latch Alignment


At right, Brian Kirby, a member of the claytronics research team, explains the alignment of electrostatic latches to Jim Male, left, and Nathan Rubright, students in the Andrew 's Leap program who built Stochastic Catoms.   Kirby explains how the design and functionality of stochastic catoms provide claytronics researchers with a platform to test stochastic - or random - motion as a means of actuation in ensembles of modular robots.


With the students ' specific contribution to the Carnegie Mellon-Intel Claytronics Research Project of a first generation of stochastic catoms, the Andrew 's Leap project also introduced a group of aspiring technologists to cutting-edge ideas in modular robotics.   This achievement is in keeping with the overall goal of the research collaboration, which seeks not only to create the basic research for engineering claytronics but also to excite the imaginations of a new generation of technologists and researchers in the frontiers of computer science, electrical engineering, nanotechnology and robotics.      

As participants in Andrew 's Leap, the high school students working on the stochastic catom team learned step-by-step analysis of algorithm design and programmed solutions, rudiments of the integration of electro-mechanical systems and computation, the engineering of simple electrostatic devices and perhaps   the most basic lesson of all, that complex science and engineering problems can be explored with materials that are as simple to assemble as balsa wood, aluminum foil, plastic and Mylar.   Indeed, with such materials, they helped to inaugurate a new domain of claytronics research -- the investigation of random motion as a basis for the actuation of catoms in an ensemble.

To gain a close-up view of this hardware and further discussion of its functionality, read these design notes .


Video segments at right present the students ' demonstration of the Andrew 's Leap project and a segment of balloon velocity testing.   In addition, a brief animation presents a simulation of stochastic motion among thousands of sub-millimeter robotic modules deployed in a system of self-assembly for nanotechnology. An abbreviated demonstration of self-assembly employing graph grammar can also be seen.


Publications and Documents

NOT FOUND: "Hierarchical Motion Planning for Self-reconfigurable Modular Robots,
NOT FOUND: Graph Grammars for Self-Assembling Robotic Systems
NOT FOUND: Internal Localization of Modular Robot Ensembles