Video of Jerboa hopping/Simulation videos
While exploring how best to design robots that use tails to reorient their bodies in midair, a team of researchers at the University of Michigan and University of California San Diego found that mammals had already figured out how to do more with less.
They say that the simulation approach will inform the design of robots with lighter but more effective tails—and illuminate how animals use physics principles to maneuver.
"Nature essentially developed two types of vertebrate tails. The heavy, muscled tails of lizards are able to reorient the body in one plane of rotation, and have inspired many rigid-tailed robots," said Talia Moore, U-M assistant professor of robotics and corresponding author of the study in the Journal of the Royal Society Interface.
"At first glance, the light, tendon-driven tails of mammals like cats seemed like they might be less effective at rotating the body. But we noticed that mammal tails could form more complex, 3D curves, and many mammals appear to be capable of tail-induced body rotations all the same."
More than a decade ago, Moore had tried to study whether jerboas, long-tailed desert rodents that hop on two legs, used their tails for this purpose. But the equation used to describe tail motion ignored the ways that mammalian tails curve and whip around—and it also said no way could a jerboa move its tail fast enough to rotate its body. She set the question aside.
Then Xun Fu, a doctoral student in Moore's group at the time, wanted to design a robot with a tail. They revisited the problem with detailed computer simulations designed to explore how the joints of the tail affect the ability to rotate a body in space. The team says that their study is the first to compare the effectiveness of different complex appendages for twisting and turning in 3D space through simulations.
In particular, they wanted to know whether increasing the number of bone segments and varying their lengths would enhance a tail's ability to rotate the body. The team set up challenges: through tail motion alone, a box-like body must reorient itself, flipping and rotating in a zero-g space.
Each tail was judged by how close its body came to each goal. To keep the tails on a level playing field, the team limited how much total effort they could use to change their position—in tails with multiple segments, the maximum effort summed across all joints was equal to the maximum effort generated at the single joint from which the one-segment tail was controlled.
"We did not know what the results would look like when exploring the impact of different tail joint configurations, particularly when allowing the length of individual bones to vary as part of the optimization process," said Fu, first author of the study and now a robotics Ph.D. graduate.
With help from Ram Vasudevan, U-M professor of robotics, and robotics doctoral student Bohao Zhang, the team used the model to discover the tail structure optimized for inducing body rotations: It had the maximum number of segments, starting with a short bone, quickly elongating to the longest bone, and then gradually shortening toward the tip of the tail.
Moore and Fu then reached out to collaborators based at UCSD, who were exploring museum specimens of mammal tail bones. In the UCSD data, nearly all of the mammals that rely on mid-air reorientation showed a similar pattern of bone lengths.
"Mammal tail skeletons are so different from one another, and now we can say that this specific type of tail evolves to facilitate inertial maneuvering. We're looking forward to seeing how other types of tails move," said Ceri Weber, a postdoctoral researcher who works with Kimberly Cooper, UCSD professor of cell and developmental biology.
Moore suggests that simulations like theirs could be extended to compare the effectiveness of moving arms, legs or wings in complex, 3D shapes in order to twist and turn in midair, maintain balance and more. The results could shed light on the biomechanics of humans and animals as well as guiding the design of robots.
"The pattern of a crescendo-decrescendo length distribution in the optimized tails, like what biologists have observed in certain mammal tails, was both surprising and intriguing," Fu said. "In some ways, I think this highlights how much more we still need to uncover about these animals to truly bridge the gap between biophysics and robotic performance."
The team undertook the study with funding from individual discretionary awards: the Oak Ridge Associated Universities Ralph E. Powe Junior Faculty Enhancement Award (Moore), the Ruth L. Kirschstein National Research Service Award Individual Postdoctoral Fellowship (Weber), the Wu Tsai Human Performance Alliance and the Joe and Clara Tsai Foundation (Cooper).
Study: Jointed tails enhance control of three-dimensional body rotation (DOI: 10.1098/rsif.2024.0355)
Journal
Journal of The Royal Society Interface