The internet is full of wisdom on cheetah tails, and most of it describes “heavy” tails that “act as a counterbalance” to the rest of the cheetah’s body. This makes intuitive sense, but it’s also quite wrong, as Amir Patel figured out:
The aerodynamics of cheetah tails are super important, and actually something I discovered by accident! Towards the end of my PhD I was invited to a cheetah autopsy at the National Zoological Gardens here in South Africa. The idea was to weigh and measure the inertia of the cheetah tail because no such data existed. Based on what I’d seen in wildlife documentaries (and speaking to any game ranger in South Africa), the cheetah tail is often considered to be heavy, and used as a counterweight.
However, once we removed the fur and skin from the tail during the autopsy, it was surprisingly skinny! We measured it (and the tails of another 6 cheetahs) as being only about 2 percent of the body mass—much lower than my own robotic tails. But the fur made up a significant volume of the tail. So, I figured that there must be something to it: maybe the fur was making the tail appear like a larger object aerodynamically, without the weight penalty of an inertial tail.
A few years ago, Patel started to characterize tail aerodynamics in partnership with Aaron Johnson’s lab at CMU, and that work has lead to a recent paper published in IEEE Transactions on Robotics, exploring how aerodynamic drag on a lightweight tail can help robots perform dynamic behaviors more successfully.
The specific tail design that Minitaur is sporting in the video above doesn’t look particularly cheetah-like, being made out of carbon fiber and polyethylene film rather than floof, and only sporting an aerodynamic component at the end of the tail rather than tip to butt. This is explained by cheetahs in the wild not having easy access to either carbon fiber or polyethylene, and by a design that the researchers optimized to maximize drag while minimizing mass rather than for biomimicry. “We experimented with a whole array of furry tails to mimic cheetah fur, but found that the half cylinder shape had by far the most drag,” first author Joseph Norby told us in an email. “And the reduction of the drag component to just the end of the tail was a balance of effectiveness and rigidity—we could have made the drag component cover the entire length, but really the section near the tip produces most of the drag, and reducing the length of the drag component helps maintain the shape of the tail.”
Aerodynamic tails are potentially appealing because unlike inertial tails, the amount of torque that they can produce doesn’t depend on how much they weigh, but rather with the velocity at which the robot is moving: the faster the robot goes, the more torque an aerodynamic tail can produce. We see this in animals, too, with fluffy tails commonly found on fast movers and jumpers like jerboas and flying squirrels. This offers some suggestion about what kind of robots could benefit most from tails like these, although as Norby points out, the greatest limitation of these tails is the large workspace required for the tail to move around safely.
Image: Norby et al
A variety of animals (and one robot) with aerodynamic drag tails, including a jerboa and giant Indian squirrel.
While this paper is focused on quantifying the effects of aerodynamic drag on robotic tails, it seems like there’s a lot of potential for some really creative designs—we were wondering about tails with adjustable floofitude, for example, and we asked Norby about some ways in which this research might be extended.
I think a foldable or retractable tail would greatly improve practicality by reducing the workspace when the tail is not needed. Essentially all of the animals we studied had some sort of flexibility to their tails, which I believe is a crucial property for improving both practicality and durability. In a similar vein, we’ve also thought about employing active or passive designs that could quickly modify the drag coefficient, whether by furling and unfurling, or simply rotating an asymmetric tail like our half cylinder. This could perhaps allow new forms of control similar to paddling and feathering a canoe: increasing drag when moving in one direction and reducing drag in the other could allow for more net control authority. This would be completely impossible with an inertial tail, which cannot do work on the environment.
Photo: Evan Ackerman/IEEE Spectrum
Gratuitous cheetah picture.
Even though animals had the idea for lightweight aerodynamic drag tails first, there’s no reason why we need to restrict ourselves to animal-like form factors when leveraging the advantages that tails like these offer, or indeed with the designs of the tails themselves. Without a mass penalty to worry about, why not put tails on any robot that has trouble keeping its balance, like pretty much every bipedal robot, right? Of course there are plenty of reasons not to do this, but still, it’s exciting to see this whole design space of aerodynamic drag tails potentially open up for any robot platform that needs a little bit of help with dynamic motion.
Enabling Dynamic Behaviors With Aerodynamic Drag in Lightweight Tails, by Joseph Norby, Jun Yang Li, Cameron Selby, Amir Patel, and Aaron M. Johnson from CMU and the University of Cape Town is published in IEEE Transactions on Robotics.