# One-Wheel Cubli Balances Like Magic

## A single reaction wheel enables two-axis balancing, which shouldn’t work—but does

Eight years and 14 million views ago, ETH Zurich introduced the Cubli, a robotic cube that can dynamically balance on a single point. It’s magical to watch, but at the same time fairly straightforward to understand: There are three reaction wheels within the Cubli, one for each axis. And in a vivid demonstration of Newton’s third law, spinning up a reaction wheel exerts a force on the cube in the opposite direction, resulting in precision control over roll, pitch, and yaw that allows the Cubli to balance itself, move around, and even jump.

This is very cool, but obviously, controlling the Cubli in three axes requires three reaction wheels. If you took out a reaction wheel, one of the Cubli’s axes would just do whatever it wanted, and if you took out two reaction wheels, then surely it would topple over, right?

Right…?

Figuring that an appropriate number of actuated degrees of freedom for a self-balancing cube was somehow too easy, researchers from ETH Zurich (Matthias Hofer, Michael Muehlebach, and Raffaello D’Andrea) decided to build a One-Wheel Cubli, which manages to balance on a point just like the original Cubli, except with only a single reaction wheel. Whoa.

The One-Wheel Cubli (OWC) uses its single reaction wheel to control itself in both pitch and roll. The yaw degree is uncontrolled, meaning that the OWC can spin around on its pivot point—although, thanks to friction, it doesn’t. Having more degrees of freedom than actuators (in this case, reaction wheels) means that the OWC is underactuated. But obviously, full control over two very separate axes is required to pull off this balancing act. So how does it work?

Designer Matthias Hofer explains that you can think of the One-Wheel Cubli’s balancing as if you were trying to balance both a pen and a broomstick vertically on your palm. That is, if you also imagine that you only have to worry about balancing them on one axis—they’ll only tip toward you or away from you, and you can move your palm underneath them to compensate. The pen, which is shorter, will be harder to balance and require small, rapid movements of your palm. Meanwhile, the broomstick is much easier to balance, and you can do so with slower movements. This is essentially the working principle of the OWC: You may only have one control input to work with, but the small, fast movements and the large, slow movements are decoupled enough that one actuator can manage them both independently, by making the small, fast movements within the large, slow movements. And this, incidentally, is the reason for that long beam with the weights on the end that differentiates the One-Wheel Cubli from the original Cubli: it’s there to maximize that difference in inertia between the two axes you’re trying to independently control.

“Seeing the OWC balance for the first time was counterintuitive, as the working principle is not obvious,” Hofer told IEEE Spectrum. “It was very satisfying for us, as it meant that every puzzle piece of the project that Michael Muehlebach, Raffaello D’Andrea, and I, along with our technical staff (Michael Egli and Matthias Müller), contributed to finally worked—including the theoretical analysis, the prototype development, the modeling, the state estimation, and the control design.”

All those puzzle pieces took a long time to fit together, and required years of work to get from something that would theoretically work on paper to an actual working system. After the failure of a couple of early hardware iterations, the researchers put some extra effort into a much more detailed modeling approach, which they then leveraged into the control system that was ultimately successful. One of the most important tricks, it turned out, was to carefully model exactly how the beam with the weights on its ends deflects. The deflection isn’t much, but it’s enough to screw everything up if you’re not careful. And as you can see in the video, the control system is successful enough that despite the underactuated nature of the OWC, it’s even able to compensate for some gentle nudging.

The One-Wheel Cubli is more than just an abstract hardware and software project. There are potential useful applications here, one of which is attitude control of satellites. Many satellites already use reaction wheels to keep them pointing in the right direction, and these reaction wheels are so critical to a satellite’s functionality that spares are typically included, which add mass and complexity. For satellites that have long structures (like instrument booms) that provide different mass moments of inertia along different axes, the OWC’s control technique could provide an additional means of redundancy in case of multiple failures of reaction wheels.

We asked Hofer about what he might like to work on next, and it sounds like taming that uncontrolled yaw axis is a potential way to go. “An interesting extension would be to also control the yaw degree of freedom,” Hofer says. “If the reaction wheel is not mounted orthogonally to the yaw direction, it would affect both tilt angles plus the yaw direction. If all three degrees of freedom have different mass moments of inertia, the current working principle of the OWC could possibly be extended to all three degrees of freedom.”

The Conversation (1)
Simeon Bamford20 Dec, 2022
M

Great stuff! Here's an earlier, but much less impressive, 2-from-1-DOF controller: https://www.youtube.com/watch?v=Wk8Pp7XDtj8

## The Bionic-Hand Arms Race

### The prosthetics industry is too focused on high-tech limbs that are complicated, costly, and often impractical

Horizontal

The author, Britt Young, holding her Ottobock bebionic bionic arm.

Gabriela Hasbun. Makeup: Maria Nguyen for MAC cosmetics; Hair: Joan Laqui for Living Proof
DarkGray

In Jules Verne’s 1865 novel From the Earth to the Moon, members of the fictitious Baltimore Gun Club, all disabled Civil War veterans, restlessly search for a new enemy to conquer. They had spent the war innovating new, deadlier weaponry. By the war’s end, with “not quite one arm between four persons, and exactly two legs between six,” these self-taught amputee-weaponsmiths decide to repurpose their skills toward a new projectile: a rocket ship.

The story of the Baltimore Gun Club propelling themselves to the moon is about the extraordinary masculine power of the veteran, who doesn’t simply “overcome” his disability; he derives power and ambition from it. Their “crutches, wooden legs, artificial arms, steel hooks, caoutchouc [rubber] jaws, silver craniums [and] platinum noses” don’t play leading roles in their personalities—they are merely tools on their bodies. These piecemeal men are unlikely crusaders of invention with an even more unlikely mission. And yet who better to design the next great leap in technology than men remade by technology themselves?

As Verne understood, the U.S. Civil War (during which 60,000 amputations were performed) inaugurated the modern prosthetics era in the United States, thanks to federal funding and a wave of design patents filed by entrepreneurial prosthetists. The two World Wars solidified the for-profit prosthetics industry in both the United States and Western Europe, and the ongoing War on Terror helped catapult it into a US \$6 billion dollar industry across the globe. This recent investment is not, however, a result of a disproportionately large number of amputations in military conflict: Around 1,500 U.S. soldiers and 300 British soldiers lost limbs in Iraq and Afghanistan. Limb loss in the general population dwarfs those figures. In the United States alone, more than 2 million people live with limb loss, with 185,000 people receiving amputations every year. A much smaller subset—between 1,500 to 4,500 children each year—are born with limb differences or absences, myself included.

Today, the people who design prostheses tend to be well-intentioned engineers rather than amputees themselves. The fleshy stumps of the world act as repositories for these designers’ dreams of a high-tech, superhuman future. I know this because throughout my life I have been fitted with some of the most cutting-edge prosthetic devices on the market. After being born missing my left forearm, I was one of the first cohorts of infants in the United States to be fitted with a myoelectric prosthetic hand, an electronic device controlled by the wearer’s muscles tensing against sensors inside the prosthetic socket. Since then, I have donned a variety of prosthetic hands, each of them striving toward perfect fidelity of the human hand—sometimes at a cost of aesthetics, sometimes a cost of functionality, but always designed to mimic and replace what was missing.

In my lifetime, myoelectric hands have evolved from clawlike constructs to multigrip, programmable, anatomically accurate facsimiles of the human hand, most costing tens of thousands of dollars. Reporters can’t get enough of these sophisticated, multigrasping “bionic” hands with lifelike silicone skins and organic movements, the unspoken promise being that disability will soon vanish and any lost limb or organ will be replaced with an equally capable replica. Prosthetic-hand innovation is treated like a high-stakes competition to see what is technologically possible. Tyler Hayes, CEO of the prosthetics startup Atom Limbs, put it this way in a WeFunder video that helped raise \$7.2 million from investors: “Every moonshot in history has started with a fair amount of crazy in it, from electricity to space travel, and Atom Limbs is no different.”

We are caught in a bionic-hand arms race. But are we making real progress? It’s time to ask who prostheses are really for, and what we hope they will actually accomplish. Each new multigrasping bionic hand tends to be more sophisticated but also more expensive than the last and less likely to be covered (even in part) by insurance. And as recent research concludes, much simpler and far less expensive prosthetic devices can perform many tasks equally well, and the fancy bionic hands, despite all of their electronic options, are rarely used for grasping.

Activity arms, such as this one manufactured by prosthetics firm Arm Dynamics, are less expensive and more durable than bionic prostheses. The attachment from prosthetic-device company Texas Assistive Devices rated for very heavy weights, allowing the author to perform exercises that would be risky or impossible with her much more expensive bebionic arm.Gabriela Hasbun; Makeup: Maria Nguyen for MAC cosmetics; Hair: Joan Laqui for Living Proof

## Function or Form

In recent decades, the overwhelming focus of research into and development of new artificial hands has been on perfecting different types of grasps. Many of the most expensive hands on the market differentiate themselves by the number and variety of selectable prehensile grips. My own media darling of a hand, the bebionic from Ottobock, which I received in 2018, has a fist-shaped power grip, pinching grips, and one very specific mode with thumb on top of index finger for politely handing over a credit card. My 21st-century myoelectric hand seemed remarkable—until I tried using it for some routine tasks, where it proved to be more cumbersome and time consuming than if I had simply left it on the couch. I couldn’t use it to pull a door shut, for example, a task I can do with my stump. And without the extremely expensive addition of a powered wrist, I couldn’t pour oatmeal from a pot into a bowl. Performing tasks the cool bionic way, even though it mimicked having two hands, wasn’t obviously better than doing things my way, sometimes with the help of my legs and feet.

When I first spoke with Ad Spiers, lecturer in robotics and machine learning at Imperial College London, it was late at night in his office, but he was still animated about robotic hands—the current focus of his research. Spiers says the anthropomorphic robotic hand is inescapable, from the reality of today’s prosthetics to the fantasy of sci-fi and anime. “In one of my first lectures here, I showed clips of movies and cartoons and how cool filmmakers make robot hands look,” Spiers says. “In the anime Gundam, there are so many close-ups of gigantic robot hands grabbing things like massive guns. But why does it need to be a human hand? Why doesn’t the robot just have a gun for a hand?”

It’s time to ask who prostheses are really for, and what we hope they will actually accomplish.

Spiers believes that prosthetic developers are too caught up in form over function. But he has talked to enough of them to know they don’t share his point of view: “I get the feeling that people love the idea of humans being great, and that hands are what make humans quite unique.” Nearly every university robotics department Spiers visits has an anthropomorphic robot hand in development. “This is what the future looks like,” he says, and he sounds a little exasperated. “But there are often better ways.”

The vast majority of people who use a prosthetic limb are unilateral amputees—people with amputations that affect only one side of the body—and they virtually always use their dominant “fleshy” hand for delicate tasks such as picking up a cup. Both unilateral and bilateral amputees also get help from their torsos, their feet, and other objects in their environment; rarely are tasks performed by a prosthesis alone. And yet, the common clinical evaluations to determine the success of a prosthetic are based on using only the prosthetic, without the help of other body parts. Such evaluations seem designed to demonstrate what the prosthetic hand can do rather than to determine how useful it actually is in the daily life of its user. Disabled people are still not the arbiters of prosthetic standards; we are still not at the heart of design.

The Hosmer Hook [left], originally designed in 1920, is the terminal device on a body-powered design that is still used today. A hammer attachment [right] may be more effective than a gripping attachment when hammering nails into wood.Left: John Prieto/The Denver Post/Getty Images; Right: Hulton-Deutsch Collection/Corbis/Getty Images

## Prosthetics in the Real World

To find out how prosthetic users live with their devices, Spiers led a study that used cameras worn on participants’ heads to record the daily actions of eight people with unilateral amputations or congenital limb differences. The study, published last year in IEEE Transactions on Medical Robotics and Bionics, included several varieties of myoelectric hands as well as body-powered systems, which use movements of the shoulder, chest, and upper arm transferred through a cable to mechanically operate a gripper at the end of a prosthesis. The research was conducted while Spiers was a research scientist at Yale University’s GRAB Lab, headed by Aaron Dollar. In addition to Dollar, he worked closely with grad student Jillian Cochran, who coauthored the study.

Watching raw footage from the study, I felt both sadness and camaraderie with the anonymous prosthesis users. The clips show the clumsiness, miscalculations, and accidental drops that are familiar to even very experienced prosthetic-hand users. Often, the prosthesis simply helps brace an object against the body to be handled by the other hand. Also apparent was how much time people spent preparing their myoelectric prostheses to carry out a task—it frequently took several extra seconds to manually or electronically rotate the wrists of their devices, line up the object to grab it just right, and work out the grip approach.The participant who hung a bottle of disinfectant spray on their “hook” hand while wiping down a kitchen counter seemed to be the one who had it all figured out.

In the study, prosthetic devices were used on average for only 19 percent of all recorded manipulations. In general, prostheses were employed in mostly nonprehensile actions, with the other, “intact” hand doing most of the grasping. The study highlighted big differences in usage between those with nonelectric, body-powered prosthetics and those with myoelectric prosthetics. For body-powered prosthetic users whose amputation was below the elbow, nearly 80 percent of prosthesis usage was nongrasping movement—pushing, pressing, pulling, hanging, and stabilizing. For myoelectric users, the device was used for grasping just 40 percent of the time.

More tellingly, body-powered users with nonelectric grippers or split hooks spent significantly less time performing tasks than did users with more complex prosthetic devices. Spiers and his team noted the fluidity and speed with which the former went about doing tasks in their homes. They were able to use their artificial hands almost instantaneously and even experience direct haptic feedback through the cable that drives such systems. The research also revealed little difference in use between myoelectric single-grasp devices and fancier myoelectric multiarticulated, multigrasp hands—except that users tended to avoid hanging objects from their multigrasp hands, seemingly out of fear of breaking them.

“We got the feeling that people with multigrasp myoelectric hands were quite tentative about their use,” says Spiers. It’s no wonder, since most myoelectric hands are priced over \$20,000, are rarely approved by insurance, require frequent professional support to change grip patterns and other settings, and have costly and protracted repair processes. As prosthetic technologies become more complex and proprietary, the long-term serviceability is an increasing concern. Ideally, the device should be easily fixable by the user. And yet some prosthetic startups are pitching a subscription model, in which users continue to pay for access to repairs and support.

Despite the conclusions of his study, Spiers says the vast majority of prosthetics R&D remains focused on refining the grasping modes of expensive, high-tech bionic hands. Even beyond prosthetics, he says, manipulation studies in nonhuman primate research and robotics are overwhelmingly concerned with grasping: “Anything that isn’t grasping is just thrown away.”

TRS makes a wide variety of body-powered prosthetic attachments for different hobbies and sports. Each attachment is specialized for a particular task, and they can be easily swapped for a variety of activities. Fillauer TRS

## Grasping at History

If we’ve decided that what makes us human is our hands, and what makes the hand unique is its ability to grasp, then the only prosthetic blueprint we have is the one attached to most people’s wrists. Yet the pursuit of the ultimate five-digit grasp isn’t necessarily the logical next step. In fact, history suggests that people haven’t always been fixated on perfectly re-creating the human hand.

As recounted in the 2001 essay collection Writing on Hands: Memory and Knowledge in Early Modern Europe, ideas about the hand evolved over the centuries. “The soul is like the hand; for the hand is the instrument of instruments,” Aristotle wrote in De Anima. He reasoned that humanity was deliberately endowed with the agile and prehensile hand because only our uniquely intelligent brains could make use of it—not as a mere utensil but a tool for apprehensio, or “grasping,” the world, literally and figuratively.

More than 1,000 years later, Aristotle’s ideas resonated with artists and thinkers of the Renaissance. For Leonardo da Vinci, the hand was the brain’s mediator with the world, and he went to exceptional lengths in his dissections and illustrations of the human hand to understand its principal components. His meticulous studies of the tendons and muscles of the forearm and hand led him to conclude that “although human ingenuity makes various inventions…it will never discover inventions more beautiful, more fitting or more direct than nature, because in her inventions nothing is lacking and nothing is superfluous.”

Da Vinci’s illustrations precipitated a wave of interest in human anatomy. Yet for all of the studious rendering of the human hand by European masters, the hand was regarded more as an inspiration than as an object to be replicated by mere mortals. In fact, it was widely accepted that the intricacies of the human hand evidenced divine design. No machine, declared the Christian philosopher William Paley, is “more artificial, or more evidently so” than the flexors of the hand, suggesting deliberate design by God.

Performing tasks the cool bionic way, even though it mimicked having two hands, wasn’t obviously better than doing things my way, sometimes with the help of my legs and feet.

By the mid-1700s, with the Industrial Revolution in the global north, a more mechanistic view of the world began to emerge, and the line between living things and machines began to blur. In her 2003 article “ Eighteenth-Century Wetware,” Jessica Riskin, professor of history at Stanford University, writes, “The period between the 1730s and the 1790s was one of simulation, in which mechanicians tried earnestly to collapse the gap between animate and artificial machinery.” This period saw significant changes in the design of prosthetic limbs. While mechanical prostheses of the 16th century were weighed down with iron and springs, a 1732 body-powered prosthesis used a pulley system to flex a hand made of lightweight copper. By the late 18th century, metal was being replaced with leather, parchment, and cork—softer materials that mimicked the stuff of life.

The techno-optimism of the early 20th century brought about another change in prosthetic design, says Wolf Schweitzer, a forensic pathologist at the Zurich Institute of Forensic Medicine and an amputee. He owns a wide variety of contemporary prosthetic arms and has the necessary experience to test them. He notes that anatomically correct prosthetic hands have been carved and forged for the better part of 2,000 years. And yet, he says, the 20th century’s body-powered split hook is “more modern,” its design more willing to break the mold of the human hand.

“The body powered arm—in terms of its symbolism—(still) expresses the man-machine symbolism of an industrial society of the 1920s,” writes Schweitzer in his prosthetic arm blog, “when man was to function as clockwork cogwheel on production lines or in agriculture.” In the original 1920s design of the Hosmer Hook, a loop inside the hook was placed just for tying shoes and another just for holding cigarettes. Those designs, Ad Spiers told me, were “incredibly functional, function over form. All pieces served a specific purpose.”

Schweitzer believes that as the need for manual labor decreased over the 20th century, prostheses that were high-functioning but not naturalistic were eclipsed by a new high-tech vision of the future: “bionic” hands. In 2006, the U.S. Defense Advanced Research Projects Agency launched Revolutionizing Prosthetics, a research initiative to develop the next generation of prosthetic arms with “near-natural” control. The \$100 million program produced two multi-articulating prosthetic arms (one for research and another that costs over \$50,000). More importantly, it influenced the creation of other similar prosthetics, establishing the bionic hand—as the military imagined it—as the holy grail in prosthetics. Today, the multigrasp bionic hand is hegemonic, a symbol of cyborg wholeness.

And yet some prosthetic developers are pursuing a different vision. TRS, based in Boulder, Colo., is one of the few manufacturers of activity-specific prosthetic attachments, which are often more durable and more financially accessible than robotic prosthetics. These plastic and silicone attachments, which include a squishy mushroom-shaped device for push-ups, a ratcheting clamp for lifting heavy weights, and a concave fin for swimming, have helped me experience the greatest functionality I have ever gotten out of a prosthetic arm.

Such low-tech activity prostheses and body-powered prostheses perform astonishingly well, for a tiny fraction of the cost of bionic hands. They don’t look or act like human hands, and they function all the better for it. According to Schweitzer, body-powered prostheses are regularly dismissed by engineers as “arcane” or derisively called “Captain Hook.” Future bionic shoulders and elbows may make a huge difference in the lives of people missing a limb up to their shoulder, assuming those devices can be made robust and affordable. But for Schweitzer and a large percentage of users dissatisfied with their myoelectric prosthesis, the prosthetic industry has yet to provide anything fundamentally better or cheaper than body-powered prostheses.

## The Breakthroughs We Want

Bionic hands seek to make disabled people “whole,” to have us participate in a world that is culturally two-handed. But it’s more important that we get to live the lives we want, with access to the tools we need, than it is to make us look like everyone else. While many limb-different people have used bionic hands to interact with the world and express themselves, the centuries-long effort to perfect the bionic hand rarely centers on our lived experiences and what we want to do in our lives.

We’ve been promised a breakthrough in prosthetic technology for the better part of 100 years now. I’m reminded of the scientific excitement around lab-grown meat, which seems simultaneously like an explosive shift and a sign of intellectual capitulation, in which political and cultural change is passed over in favor of a technological fix. With the cast of characters in the world of prosthetics—doctors, insurance companies, engineers, prosthetists, and the military—playing the same roles they have for decades, it’s nearly impossible to produce something truly revolutionary.

In the meantime, this metaphorical race to the moon is a mission that has forgotten its original concern: helping disabled people acquire and use the tools they want. There are inexpensive, accessible, low-tech prosthetics that are available right now and that need investments in innovation to further bring down costs and improve functionality. And in the United States at least, there is a broken insurance system that needs fixing. Releasing ourselves from the bionic-hand arms race can open up the possibilities of more functional designs that are more useful and affordable, and might help us bring our prosthetic aspirations back down to earth.