The origami of space systems
System design optimization for lasers and other components requires minimizing energy consumption, semiconductor materials, and other costs. In origami, optimization means creating the most extensive form possible using a single sheet of paper.
In the mid-1990s, Robert Lang took his expertise gained at NASA’s Jet Propulsion Lab in California and created an open-source software called TreeMaker, the first program available to design complex origami figures. Lang’s design software uses an equation to map the points that will become features like a head and limbs. It helps decide exactly how far apart any two points have to be, depending on their location in the final shape.
Lang worked on building an optical computer that uses light rather than electricity to carry out calculations, based on nonlinear constrained optimization.
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“Over the years of solving mathematical problems to describe lasers and optoelectronics, I built up a toolkit to use as I worked on a hobby basis on this problem of computational origami design,” he said. “One of the theoretical fields I learned about at JPL turned out to be the key to being able to plug in a description of a shape you wanted and then find the best possible design in great detail — every single crease you needed to make that shape,” said Lang. “And that turned out to be nonlinear constrained optimization.”
In 2001, he left his last engineering job to become a full-time origamist, and he remains one of the world’s leading figures at the intersection of math and paper folding. Lang’s work ranges from small paper sculptures to huge public art made from metal and other materials, which he co-creates with other artists.
In his representational art, he said, he’s drawn to complicated, challenging subjects like insects, which only became possible with the introduction of math-based methodologies. “Because I‘m able to design fairly complex figures using these mathematical design techniques, I’ll take on subject matter that requires a very technical approach,” he said.
In designing his nonrepresentational pieces, he often reverses the process, beginning with the math and then working out a subject, he said. “If you look at some of the more geometric or abstract pieces I’ve done, those were driven by solving a mathematical problem related to folding and then saying, ‘OK, now that I have a solution, how can I create a beautiful piece of artwork that illustrates that solution?’”
As an example, he cites a tessellation he folded from a laser-scored rectangle of wood laminate after collaborating with Brigham Young University on the mathematical problem of foldable rigid quadrilateral meshes. The purpose of the collaboration was to create engineering mechanisms, but after the team won an award for its scientific paper, he set about applying the principles to his art.
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Since Lang left NASA, the agency has called him back in to consult on a few projects that capitalized on his dual background in engineering and origami. One of those was the Starshade concept, a design for a baseball diamond-sized disk that would fold up tightly to fit in a rocket fairing and then unfurl in space. There, it would block the light from a given star so a space telescope could photograph its planets.
The art of folding has even crept into space technology in recent years. Commercial companies now seek out Lang for his origami and engineering backgrounds to consult on folding hardware, including a collapsible radio antenna and Lawrence Livermore National Laboratory’s Eyeglass space telescope. He has also returned to NASA to help figure out how to fold large objects for launch inside rocket fairings.
“The irony is that, when I was employed full-time at NASA, I was not working on origami, but after I left, I’ve been invited back a couple of times to work on origami-related projects,” he said.
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