Take a piece of paper ... fold here ... crease there ... turn inside out ... fold flap, repeat ... and voila! You've got a pirate's hat. Or a swan. Or a drinking cup.

		Graphic: Origami butterfly

Origami, the Japanese art of folded-paper sculpture, can be just that simple. Or it can be intricate, involving numerous, exacting folds that yield objects as complex as a rose, an albatross or the double helix of a DNA molecule.

But from the standpoint of a robot, nothing about paper folding is easy. Flexible, unstretchable paper is hard to handle with existing robotic tools and the three-dimensional objects crafted from an almost two-dimensional material are hard to mathematically represent in a robot's digital mind.

"Origami is way out there ---- it's like a space shot," said Matthew Mason, a professor of computer science and robotics at Carnegie Mellon University whose research interests include the mechanics of manipulation.

So when one of his graduate students, Devin Balkcom, decided to build an origami-making robot for his doctoral thesis, Mason wasn't enthusiastic. Such a robot was virtually unprecedented and chances were good that the whole enterprise would crash and burn, leaving Balkcom without any publishable results and without his degree.

That was in January 2003. Today, Balkcom has a robot that can crank out paper airplanes and pointed hats, he's on schedule to earn his doctorate in August and his talk on robotic origami drew a standing-room-only crowd at a recent technical conference.

"The robot itself is not the biggest part of the project," Balkcom said, noting it consists primarily of a small industrial robot arm and a work table akin to a sheet metal press.

Rather, the bigger challenge was coordinating movement of the parts so that paper could be folded with some semblance of a crease and so that the paper's natural tendency to unfold did not foul up succeeding steps. And he needed to find a way to mathematically describe the origami structure itself.

"Even if we had a robot with 10 fingers, we still wouldn't know how to program it to do origami," Balkcom said.

Consider the difficulty in mathematically modeling a piece of paper, Mason said. Paper is so thin that it's easy to think of it as two-dimensional. But it's not. As thin as it is, it can't be folded indefinitely (seven times is the rule of thumb limit). Also, when something is folded over on itself, the computer has to find a way to describe the layers and the folds that connect the layers.

Likewise, paper hardly stretches at all. But it does stretch. In fact, it has to stretch. "There's a tiny bit of stretching that has to happen to fold something," Mason said. That's hard to describe mathematically.

Picking up and moving paper turned out to be easier than expected "once you found the right suction cup," Balkcom said. But humans have huge advantages over machines. People not only have wondrously dexterous hands, but they also have nerves in their finger tips and stereoscopic vision that provides sensory information far superior to anything possible for a robot.

The machine performs origami much differently than would a human.

When making a paper airplane, for instance, a person typically folds the airplane's wings as the last step. But people have fingernails to help separate the layers of paper. The robot is unable to do that, so it folds the wings as one of its first steps.

Also, in this early stage of development, flipping the paper is a challenge, so Balkcom designed the machine to flip the paper everytime it is folded.

To create a 180-degree fold, the robot arm uses its air-controlled suction cups to position the paper over a long gutter that runs through the work table. The arm uses an attached straight-edge ruler to push the paper into the gutter; the gutter then slams shut to fold and crease the paper.

To create a 90-degree fold, the paper can be held vertically in the gutter while the arm sweeps its straight edge along the work table, bending the paper down.

Videos of the origami robot making an airplane and a hat are available at www.cs.cmu.edu/~devin.

It can also make a cup and some other simple shapes. But the range of shapes is still limited.

"To make a swan would be 10 PhDs worth of work," Balkcom said.

But Balkcom said he intends to continue studying robotic origami, both to better understand "foldability" and other basic characteristics of origami and as a way of extending robots' ability to manipulate objects.

Mason also is enthusiastic about robotic origami. A visiting professor in Mason's lab, Yasumichi Aiyama of Tsukuba University in Japan, is working now with two small, finger-like robots to see if they can fold paper more like a human, without use of a gutter. Mason hopes Aiyama will continue the origami research when he returns to his Japan lab.

Industrial robots have proven adept at manipulating rigid objects, Mason said, but rigid objects are "a thin sliver of the real world." Surgical robots, for instance, must deal with tissues that are anything but rigid or dry. Robots will become more valuable and useful as they are able to handle a much wider variety of objects.

Balkcom and Mason said robotic origami potentially could become a benchmark for measuring progress in the field of robotic manipulation, much as chess is for artificial intelligence, robotic soccer is for robotic cooperation and the Grand Challenge desert race is for autonomous vehicle navigation.