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Natural Dynamics and Robotic Locomotion

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Roboticist and Assistant Professor David Remy uses the description of a simple experiment to help illustrate a key concept underlying his work. "Let's say I have you climb onto a treadmill and walk while I use electromyography (EMG) to measure your muscle activity. You would expect to see a lot going on since your entire body is in constant motion -- your legs are moving back and forth, your arms are swinging, your torso is twisting. You'd expect to see that your muscles are doing a lot of work."

But that is not the case.

"When looking at the EMG readings, we would see that your muscles aren't really doing much," explained Remy, who joined the U-M faculty in 2012 and directs the Robotics and Motion Laboratory. That's due to the natural dynamics of the human body. Legs swing as if they were mechanical pendulums, driven by inertia and gravity. The arms follow. Muscles and tendons create elastic oscillations. In short, mechanical dynamics create most of the motion, allowing us to walk almost effortlessly. 

"We're a system that's extremely well built for walking," said Remy, whose goal is to exploit these natural dynamics in legged robots and in rehabilitative devices for humans.

In a current project, Remy is conducting a simulation study to understand the role of different gaits in legged locomotion. In nature, using different gaits allows us to save energy. Think of a human walking faster and faster; at some point, it feels easier to break into a run.

"When you walk, your legs are like pendulums," Remy explained. "When you run, your knees are bent, and your legs act more like springs. Each creates a different set of natural dynamics and is better exploited at a different locomotion velocity."

A similar idea holds true in horses and other quadrupeds that have an even wider variety of gaits than bipeds. “Our hypothesis is that this is an effect of the natural dynamics," he said.

With the help of a numerical optimization algorithm, Remy and his students identified energy optimal gaits for computer models of bipedal and quadrupedal robots. That is, the computer automatically identified the best possible way in which the robots could move. 

The team found that, just as in humans, it makes sense for a bipedal robot to switch gaits. "The optimization algorithm discovered that the robot should transit from walking to running at a particular velocity to minimize energy, just as a car switches gears," Remy said. In quadrupedal robots, the team found that, similar to horses, robots transitioned from walking to trotting to save energy.

Remy also found intriguing differences. In a bipedal robot, he noted an intermediate gait with the footfall pattern of walking but the elastic energy storage of running. In quadrupedal robots, unlike horses, his robotic models were more efficient when trotting rather than galloping, even as velocity continued to increase.

“These differences are particularly interesting, since they tell us what we have to change when transferring nature’s principles to robotics,” Remy said. For example, to account for a robot's rigid main body as opposed to a horse's flexible spine.

In related work, Remy is now looking more closely at how gaits are generated. His research group simplified its models as much as possible while still producing realistic motions. The simplest model remaining consisted of four massless springs and a connecting rod.

"Even with this much-simplified model, we were still able to generate all the gaits you find in nature -- walking, trotting, tölting, bounding, pacing," Remy said. "This brings us another step closer to understanding what gaits are and how we can exploit them in robotics." 

The next step is to move from simulations to studies in a real bipedal robot, RAMone, which has high-compliance elastic actuators that enable a wide range of natural dynamic motions.

A member of a Rehab-Robotics Cluster at U-M, Remy is also interested in human locomotion. He’s currently exploring whether humans, too, can be "optimized." In a recent study, he asked research volunteers to walk on a treadmill to a metronome beat. While they walked, he and his team measured oxygen consumption and carbon dioxide production to determine how much energy subjects were using. The metronome beat varied from slow (long, less frequent steps) to fast (short, quick steps).

"When you look at energy consumption," said Remy, "you see a U-shaped curve -- high energy consumption at low frequencies and high energy consumption at high frequencies but low in the middle, another consequence of the natural dynamics. If we turn off the metronome and let you walk at your normal pace, your steps would be dead on the minimum of that curve because you’re trying to walk as efficiently as possible."

Remy's team then took real-time measures of human oxygen consumption and implemented an optimization algorithm in which a computer found the most efficient step frequency automatically. He compared that to subjects' own self-selected step frequency without the metronome. "We are very close," he said, "which demonstrates that we can optimize a parameter, in this case step frequency, to minimize energy consumption."

Remy's experiments mark the first time researchers have conducted such an optimization in real time.

Remy's work continues toward a longer-range vision. "Imagine someone wearing an exoskeleton, prosthesis or other assistive device. Imagine the device motor has a controller, and the controller has a set of parameters that the user has to tune. You could use the same method that we used to find optimal parameter values so the assistive devices could automatically adapt to a disabled user and provide optimal support."