The Agility Equation: Discovering the Math of Human Movement for Robotic and Advanced Footwear Technologies

Researchers from four UMass Amherst schools and colleges have received $490,000 from the U.S. National Science Foundation to define the primary mathematical components of running.

Compared to walking, much less is understood about agile movement, and shedding light on this movement will support the development of innovative wearable technology, such as robotic exoskeletons and advanced running shoes.

Nathan Wycoff, assistant professor of math and statistics in the College of Natural Sciences, will serve as primary investigator, applying advanced mathematical concepts to the locomotion research inherent to the labs run by his fellow co-PIs on the project, Wouter Hoogkamer, associate professor of kinesiology in the School of Public Health & Health Sciences, Donghyun Kim, assistant professor in the Manning College of Information & Computer Sciences, and Meghan Huber, assistant professor of mechanical engineering in the Riccio College of Engineering.

Among their core research aims, Hoogkamer studies advanced running shoes, Kim develops humanoid robots and Huber develops robotic exoskeletons.

Mathematically describing the phenomenon of running feels impossibly complex, but fundamentally, it's a solvable problem.

"A human has maybe hundreds of muscles and tendons associated with locomotion, but the way they behave can actually be described by three to four parameters," says Kim. "The problem is that we cannot find those three or four parameters because they correlate with many different things. Nathan showed us that there's a way-even when you think it's infinitely long, large problems, you can find the primary component. And once we have developed one, then the problem now becomes solvable."

To achieve this, the team is building a digital twin-a robust, computational model-of a runner. Part of the strength of this system is that it will continuously measure the physical system and feed the information about it back into the model so that it is synchronized with the real world.

"The math is not an alternative to building and testing," says Wycoff. "The type of math we're developing on this project is all about trying to make sure that we squeeze the most possible information out of our builds and tests. We plug those results into this new math we're developing, and that will tell us what we ought to build and test next to learn the remaining facts we don't know, with as few iterations as possible."

For this work the researchers will be focused on advanced footwear and ankle exoskeleton development.

"We measure how people run in shoes, and then we can apply that to a new, digital shoe, and see how that shoe performs," says Hoogkamer. "That's what we're doing now." What remains to be seen is how the individual would respond to the new shoe. "This project will get us a lot closer in predicting what the person will do and how [the technology] affects them."

The other technology is the ankle exoskeleton. "These exoskeletons act on your joints-pushing your joint one way or the other way. As you're running, it needs to change the direction that it's pushing," Wycoff says. "There's infinitely many different ways you could try pushing forward or backwards at different points in time, and so that makes the problem of finding the best way to run the exoskeleton really difficult from a mathematical perspective."

The researchers also see applications beyond this initial scope of the research. Huber sees how this digital twin can help inform the double-edged sword that robots and humans can both adapt to each other, and not always in advantageous ways. And Kim notes that this can help answer questions such as: How many actuated "toes" does a humanoid need to be as agile as a human or other biological systems?

"Humans can do amazing things with their bodies, and we don't really understand how they do it," says Huber. "You can almost think of a humanoid robot as a model of our understanding of the human. It's a good representation of how much, or sometimes how little, we know about humans."