Walking and slithering aren't as different as you think
At least, if you have enough legs
Peer-Reviewed PublicationAbrahamic texts treat slithering as a special indignity visited on the wicked serpent, but evolution may draw a more continuous line through the motion of swimming microbes, wriggling worms, skittering spiders and walking horses.
A new study found that all of these kinds of motion are well represented by a single mathematical model.
"This didn't come out of nowhere—this is from our real robot data," said Dan Zhao, first author of the study in the Proceedings of the National Academy of Sciences and a recent Ph.D. graduate in mechanical engineering at the University of Michigan.
"Even when the robot looks like it's sliding, like its feet are slipping, its velocity is still proportional to how quickly it's moving its body."
Unlike the dynamic motion of gliding birds and sharks and galloping horses—where speed is driven, at least in part, by momentum—every bit of speed for ants, centipedes, snakes and swimming microbes is driven by changing the shape of the body. This is known as kinematic motion.
The expanded understanding of kinematic motion could change the way roboticists think about programming many-limbed robots, opening new possibilities for walking planetary rovers, for instance.
Shai Revzen, professor of electrical and computer engineering at U-M and senior author of the study, explained that two- and four-legged robots are popular because more legs are extremely complex to model using current tools.
"This never sat well with me because my work was on cockroach locomotion," Revzen said. "I can tell you many things about cockroaches. One of them is that they're not brilliant mathematicians."
And if cockroaches can walk without solving extremely complex equations, there has to be an easier way to program walking robots. The new finding offers a place to start.
Slipping feet complicates typical motion models for robots, and the assumption was that it might add an element of momentum to the motion of many-legged robots. But in the model reported by the U-M team, it is not so different from lizards that "swim" in sand or microbes swimming in water.
Because microbes are small, the water seems a lot thicker and stickier—as if a human was trying to swim in honey. In all of these cases, the limbs move through the surrounding medium, or slide over a surface, rather than being connected at a stationary point.
The team discovered the connection by taking a known model that describes swimming microbes and then reconfiguring it to use with their multi-legged robots. The model reliably reflected their data, which came from multipods—modular robots that can operate with 6 to 12 legs—and a six-legged robot called BigAnt.
The team also collaborated with Glenna Clifton, assistant professor of biology at the University of Portland in Oregon, who provided data on ants walking on a flat surface. While the robot legs slip a lot—up to 100% of the time for the multipods—ant feet have much firmer connections with the ground, slipping only 4.7% of the time.
Even so, the ants and robots followed the same equations, with their speeds proportional to how quickly they moved their legs. It turned out that this kind of slipping didn't alter the kinematic nature of the motion.
As for what this suggests about how walking evolved, the team points to the worm believed to be the last common ancestor for all creatures that have two sides that are mirror images of each other. This worm, wriggling through water, already had the foundations of the motion that enabled the first animals to walk on land, they propose. Even humans begin learning to propel ourselves kinematically, crawling on hands and knees with the three points of contact on the ground at any time.
The skills of managing momentum—running with four legs or fewer, walking or running on two legs, flying or gliding—ladder on top of that older knowledge about how to move, the researchers suggest.
The research was supported by the Army Research Office (grants W911NF-17-1-0243 and W911NF-17-1-0306), the National Science Foundation (grants 1825918 and 2048235) and the D. Dan and Betty Kahn Michigan-Israel Partnership for Research and Education Autonomous Systems Mega-Project.
Zhao is now a senior controls engineer at XPENG Robotics.
Study: Walking is like slithering: a unifying, data-driven view of locomotion (DOI: 10.1073/pnas.202113222)
JOURNAL
Proceedings of the National Academy of Sciences
DOI
Sept. 6, 2022
Contact: Katherine McAlpine, kmca@umich.edu
Captions: Walking and slithering aren't as
different as you think
Produced video for social media MP4 | YouTube
Credit: Hans Anderson, Michigan News
Data collected using modular robots with six to
twelve legs helped to show that many-legged walking,
slithering and some kinds of swimming follow the same
mathematical model.
Credit: BIRDS Lab, University of Michigan
Data gathered from ants helped to show that many-legged walking,
slithering and some kinds of swimming follow the same mathematical model.
Credit: Clifton Group, University of Portland
A six-legged ant-inspired robot. Data collected with this robot
helped to show that many-legged walking, slithering and some
kinds of swimming follow the same mathematical model.
Credit: BIRDS Lab, University of Michigan
The physics of walking is simpler than we thought
Walking for multi-legged creatures is a lot like slithering, researchers find by comparing ants to robots
Peer-Reviewed PublicationVIDEO: B-ROLL OF ANTS WALKING, A MULTIPOD ROBOT WALKING AND THE BIGANT ROBOT WALKING. view more
CREDIT: UNIVERSITY OF CALIFORNIA SAN DIEGO/UNIVERSITY OF MICHIGAN
The physics of walking for multi-legged animals and robots is simpler than previously thought. That is the finding described by a team of roboticists, physicists and biologists in the Sept. 5 issue of the Proceedings of the National Academy of Sciences, in a paper titled “Walking is like slithering: a unifying, data-driven view of locomotion.”
“This is important because it will allow roboticists to build much simpler models to describe the way robots walk and move through the world,” said paper coauthor Nick Gravish, a faculty member in the Department of Mechanical and Aerospace Engineering at the University of California San Diego.
The researchers had previously studied ant walking and wanted to see how their findings could be applied to robots. In the process, they discovered a new mathematical relationship between walking, skipping, slithering and swimming in viscous fluids for multi-legged animals and bots.
The team studied several colonies of Argentine ants at UC San Diego, and two different types of multi-legged robots at the University of Michigan.
“Argentine ants are very easy to study in the lab,” said paper coauthor Glenna Clifton, a faculty member at the University of Portland, who conducted most of the ant research while she was a postdoctoral scholar in Gravish’s lab at UC San Diego.
Argentine ants are good walkers that can go long distances over various terrains. These ants also easily acclimate to lab settings, rebuilding their colonies quickly. Researchers then can motivate them to walk by placing food in specific locations. “These ants will set up foraging trails and follow them,” Clifton said. “They bounce back quickly and they don’t hold a grudge.”
To study these different animals and robots, researchers used an algorithm developed by the research group of Shai Revzen at the University of Michigan, which turns complex body motions into shapes. “This algorithm allows us to create a simple relationship between what posture you’re in and where you are going to move next,” Gravish said.
The researchers found that the same algorithms could be applied both to ants and the two different types of robots in the study, even though the amount of slipping motions when they walk differs widely. Argentine ants also don’t slip much when they walk – just 4.7% of total motion. By contrast, that slipping percentage is 12% to 22% for the six-legged BigANT robot and 40% to 100% for the multipod robots with six to 12 legs in the study, which sometimes crawl.
By using this model, researchers can predict where the insect or robot is going to move next simply based on what posture–or shape–they’re making. “This provides a universal model for location that applies whenever the movement is dominated by friction with the environment,” the researchers write.
The mathematics the researchers used aren’t new. But the math was understood to only apply to slithering and swimming in viscous liquids. The team showed that the same equations apply to multi-legged walking, whether the walkers are slipping or not. In addition, the same rules apply from millimeter-scale insects, such as ants, to meter-scale robots. An early version of the paper title was “walking like a worm.”
“The universality of this approach may have applications in robot design and motion planning, and provides insight into the evolution and control of legged locomotion,” the researchers write.
Researchers hypothesize that these universal principles may have implications for understanding major evolutionary transitions, for example from swimming to walking. Given that walking, even with slipping, follows the same general control principles as viscous swimming, early land animals might already have had the neural circuitry needed for locomotion on land.
Researchers didn’t study two-legged creatures, but the model would apply to them as long as they move slowly; have both feet on the ground at the same time; and do not fall. (Picture Michael Jackson doing the moonwalk.)
The team still has more fine tuning to do, to understand, for example, the role friction forces play in the model.
“Either way, walking can be much simpler than we usually think,” Gravish said.
Walking is like slithering: a unifying, data-driven view of locomotion
University of Michigan: Dan Zhao, Brian Bittner, Shai Revzen
University of Portland: Glenna Clifton
University of California San Diego: Nick Gravish
JOURNAL
Proceedings of the National Academy of Sciences
METHOD OF RESEARCH
Experimental study
SUBJECT OF RESEARCH
Animals
ARTICLE TITLE
Walking is like slithering: A unifying, data-driven view of locomotion
ARTICLE PUBLICATION DATE
9-Sep-2022
CAPTION
Experimental equipment to study ants walking similar to the one used in the study
CREDIT
David Baillot/University of California San Diego
CAPTION
Researchers Glenna Clifton, from the University of Portland, and Nick Gravish, from the University of California San Diego, harvest ants on the UC San Diego campus.
CREDIT
David Baillot/University of California San Diego
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