The Math of Human + Machine

Maegan Tucker moves people. As a first-year graduate student in mechanical engineering at Caltech, she developed an accessory for walking canes that vibrates to alert users when they may be in danger of falling. She researches ankle exoskeletons that could help people with ambulatory impairments walk farther with less effort, and full-body suits that could return mobility to those who have lost it.

But Tucker, who has been supported by Caltech’s Theodore Y. Wu Graduate Fellowship, seeks to understand these devices on a deeper level and, in so doing, find new and better ways for humans and machines to work together. In the Advanced Mechanical Bipedal Experimental Robotics Lab (AMBER) of Aaron Ames, Caltech’s Bren Professor of Mechanical and Civil Engineering and Control and Dynamical Systems, she bridges the practical and the theoretical by investigating the fundamental mathematics behind human-robot interactions.

“The goals are to make things that improve the lives of people who need them, and at the same time deepen our understanding of the underlying theory.”
- Maegan Tucker

A gift from the Caltech Department of Mechanical and Civil Engineering’s Big Ideas Fund supported her ankle exoskeleton research, and she has received funding from the National Science Foundation’s Graduate Research Fellowship Program for her project to build a better cane. In the AMBER laboratory, her work maintains Caltech’s signature focus on fundamental science, which unites robotic mobility research across the Institute and drives the new Robotic Assisted Mobility Science (RoAMS) initiative, which is supported in part by a gift from the Zeitlin Family Fund to Break Through: The Caltech Campaign.

Bringing the Human into the Loop

Tucker focuses on technologies that work in conjunction with human wearers to assist their mobility. This interest was a natural fit for Caltech’s Design for Freedom from Disability course, which inspired her to reimagine the cane. Now she has a provisional patent for her prototype invention, which attaches to a traditional cane. It includes a tilt sensor and vibration motor to warn users of possible danger, such as holding the cane at an angle that will not support them if they fall. The device is undergoing tests at a local rehabilitation center.

READ MORE FROM THE CALTECH EFFECT: “The Human Side of Engineering”

Tucker’s exoskeleton (“exo”) research, which encompasses both ankle and full lower-body exoskeletons, could enable people who have had strokes or suffer conditions such as foot drop to walk farther and fall less often. She tests the lower-body exo on student subjects wearing metabolic masks that measure oxygen and carbon dioxide exchange rates, which she and her colleagues use to calculate the amount of energy expended. As part of Caltech’s RoAMS initiative, Tucker collaborates with other Institute engineers on a full-body exoskeleton project that can help restore bipedal mobility.

The challenge with this kind of wearable medical technology is that each bespoke device must draw from a wide swath of scientific expertise and requires trial and error to perfect. For example, roboticists study how robots respond to the interactions between bodies and machines. Biomechanics researchers study the human response. And clinicians hand-tune prosthetics to accommodate individual patients’ unique bodies and needs.

Math is the place where all threads converge. When researchers understand the mathematics of human-machine interactions, Tucker says, they will be able to build robots that collaborate better with humans and require less fine-tuning. “You have to understand the math underlying the system,” she says. “And you have to understand the human connection.”

Unexpected Directions

Someday, Tucker aims to lead her own university laboratory, one that reflects the balance of theory and practice in Ames’s Caltech lab and could inspire new generations of engineers along the way.

“The simpler you make a device, the better the chance your product will become accessible for people,” she says. “But at the same time, understanding the theory and mathematics has a longer-term application for helping other research labs understand how to incorporate the full system.”

It’s a risk. Tucker and the other researchers on Ames’s team may find that their mathematically rigorous approach to robotics leads them in unexpected directions. In addition, the development of prosthetics and medical exoskeletons is a broad, interdisciplinary venture that connects the frontiers of neuroscience, robotics, mathematics, and biomechanics, which makes the field both exciting and uncertain.

“I think it’s daunting for a lot of funding agencies,” Tucker says. “But one thing I’ve noticed about Caltech is that it encourages you to do ambitious things even if success is not guaranteed.”

To learn how you can support the RoAMS Initiative and help Caltech scientists build new robotic mobility solutions, email or call Laura Grinnell at or (626) 395-2385.

Giving Priorities