Carnegie Mellon University Website Home Page

Shape Sculpting in Claytronics

Lifting Catoms into the 3 RD Dimension

Creating dynamic motion in 3-D poses the ultimate goal of the Carnegie Mellon-Intel Claytronics Research Project.  

A claytronics designer might demonstrate the complexity of this challenge of forming 3-dimensional objects from millions of robotic catoms, each less than a millimeter in diameter, by presenting an ensemble of these tiny spherical devices laid side-by-side on a flat surface. This arrangement would present a 2-dimensional square, approximately a meter on each side.   This is the organized position that an ensemble could assume before the application of any external forces.   How then to give it a 3-D shape?

Planar Catom Magnets

With a flow of power into the ensemble, the sensors of adjacent catoms could induce an electrostatic alignment or latching effect to increase the hold of one catom to another across this million-member network of distributed computing devices.  

With the fine grain particularity of each individual catom, the charge in the ensemble might enhance colors and shadings across the pixilated surface of each catom to induce subtle lines and surface perspectives that would appear with the activation of the individual voxels -- in much the same way that pixels activate images on a video screen.  

In this state, moreover, each catom would possess sufficient microprocessing capacity to implement algorithms that instruct the device to localize its position in relation to other catoms.   This information would enable each catom to initiate motion and change its alignment with adjacent catoms until the tiny spheres reach other locations.   Thus, the ensemble would reshape as it creates a new contour in a boundary line or opens a void inside its boundary while still lying flat.  

The Ensemble Rises  

All of these changes in form depend for visual effect upon the number of catoms actuated across the length and width of the ensemble.   Yet the state of actuation described thus far, even as it demonstrates important advances in distributed computing, nanotechnology and modular robotics, would also highlight the greater challenge of attaining a 3-dimensional perspective -- in which catoms would rise from the flat surface to represent not only the outline but also the volume and motion of a fully-shaped object, animal or person.

To gather height and volume from the array of a million catoms lying alongside each other within a level plane, the ensemble must not only overcome the resistance of local inertia but also mass sufficient internal force to oppose gravity -- perhaps the most difficult challenge facing claytronic algorithm designers.

Thus far, in this demonstration of the capacity of self-actuating modular robots, the claytronic architect works with forces that can be manipulated with the mass of two catoms sharing equal amounts of work.     The catoms generate motion, for example, by employing their round shapes to form a simple lever between them, one that exchanges a small electrostatic force across matching sensors to create a rotational (or kinetic) force, which is sufficient to shift the mass of one catom around the pivot point of its spherical shape.   Balanced between individual catoms, this force is sufficient to move any catom on a flat surface to any position within an ensemble.

To rise above the level plane, however, the ensemble must multiply its catom forces (the mass of a single catom plus the electrostatic energy that each device can carry) to overcome gravitational force, which increases resistance by the mass of catoms needed to form a specific shape in the 3rd dimension.   Thus, to accomplish the lifting of more than one catom, the ensemble needs the algorithmic equivalent of ropes and pulleys in order to lift multiple catoms and build a taller structure.    

Cranes and Joints for Ensemble Construction

Such multipliers of catom forces can also be thought of as the analogs of cranes at construction sites or muscles and joints in the bodies of animals.   As groupings of catoms directed by algorithms, these concentrated patterns of catom motion become the mechanisms for building complex and stable 3-dimensional shapes and providing those shapes with a means to sustain stable motion against the active resistance of gravity.  

Creating leverage to move amassed components into a complex structure is a familiar issue in construction engineering.   However, software engineers have much less experience with this challenge than do other engineering disciplines.   So development of algorithms that create leverage to perform physical work at the scale of claytronic devices represents not only the creation of a tool that is valuable to this new technology.   It also creates an important intellectual product from this research that benefits a larger domain of applied engineering.

Many Dimensions of Claytronics Software

An understanding of the complexity of the software engineering needed to achieve Collective Actuation - a general term for algorithms to control the motion of micro-electro-mechanical levers inside ensembles - also helps to illustrate the structure of software research for the Carnegie Mellon-Intel Claytronics Research Program.


At its important initial stages of software development, claytronics research has designed algorithms that instruct individual catoms to achieve motion without moving parts by leveraging electrostatic forces between individual catoms and then to use that motion to assemble geometric groups of catoms to work in unison.

As a next stage of design for the control of claytronic ensembles, researchers have conceived algorithms to instruct catoms to form and transform complex and irregular patterns.   These algorithms will give ensembles a capacity to form an endless variety of shapes.

Claytronics research also develops algorithms that create hierarchies of efficient motion among more complex shapes.   These hierarchies enable an ensemble to replicate patterns at various scales.   Thus, complex forms within an ensemble of millions of catoms can be rendered quickly and uniformly by drawing upon a book of patterns.

Around the development of algorithms, meanwhile, researchers have also created a structure of programming language with which to instruct the ensemble in the steps of computation used to implement algorithms throughout the ensemble.   Developed to manage a distributed environment of parallel computing that operates without fixed wires or individually-identified nodes, programming languages provide the streetwise component of efficient communication in a venue of one million tiny computers that maintain a capacity to connect while often momentarily detached from their network.

These levels of software development thus build up the platform upon which the ensemble can begin to shape catoms into the volume and motion of a 3rd dimension - with algorithms that enact the leveraging of   catom forces known as collective actuation.  

Collective Actuation provides the tool that enables the actual construction of forms from groups of catoms in processes that combine the forces of individual catoms to engineer larger structures and fluid motion in shapes that withstand the opposition of gravity.    

Drawing upon this expanding tool box of algorithms and programming languages, a claytronic ensemble begins to achieve the leverage needed to achieve its primary goal - elevating millions of tiny modular robots under the force of gravity to form dynamic, 3-dimensional representations of real-life figures and forms.  

Publications and Documents

Collective Actuation,
    Jason D. Campbell and Padmanabhan Pillai. International Journal of Robotics Research, 27(3-4):299–314,2008.
Locomotion of Miniature Catom Chains: Scale Effects on Gait and Velocity,
    David Johan Christensen and Jason D. Campbell. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA '07), pages 2254–2260, April, 2007.
Hierarchical Motion Planning for Self-reconfigurable Modular Robots,
    Preethi Srinivas Bhat, James Kuffner, Seth Copen Goldstein, and Siddhartha S. Srinivasa. In 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), October, 2006.
Scalable Shape Sculpting via Hole Motion: Motion Planning in Lattice-Constrained Module Robots,
    Michael De Rosa, Seth Copen Goldstein, Peter Lee, Jason D. Campbell, and Padmanabhan Pillai. In Proceedings of the 2006 IEEE International Conference on Robotics and Automation (ICRA '06), May, 2006.