# The astounding athletic power of quadcopters | Raffaello D’Andrea

Articles . Blog

Translator: Joseph Geni

Reviewer: Morton Bast So what does it mean

for a machine to be athletic? We will demonstrate the concept

of machine athleticism and the research to achieve it with the help of these flying machines

called quadrocopters, or quads, for short. Quads have been around for a long time. They’re so popular these days

because they’re mechanically simple. By controlling

the speeds of these four propellers, these machines can roll, pitch, yaw, and accelerate

along their common orientation. On board are also a battery, a computer, various sensors and wireless radios. Quads are extremely agile,

but this agility comes at a cost. They are inherently unstable, and they need some form

of automatic feedback control in order to be able to fly. So, how did it just do that? Cameras on the ceiling and a laptop serve as an indoor

global positioning system. It’s used to locate objects in the space that have these reflective

markers on them. This data is then sent to another laptop that is running estimation

and control algorithms, which in turn sends commands to the quad, which is also running estimation

and control algorithms. The bulk of our research is algorithms. It’s the magic that brings

these machines to life. So how does one design the algorithms

that create a machine athlete? We use something broadly

called model-based design. We first capture the physics with a mathematical model

of how the machines behave. We then use a branch of mathematics

called control theory to analyze these models and also to synthesize

algorithms for controlling them. For example, that’s how we can

make the quad hover. We first captured the dynamics

with a set of differential equations. We then manipulate these equations

with the help of control theory to create algorithms

that stabilize the quad. Let me demonstrate

the strength of this approach. Suppose that we want

this quad to not only hover but to also balance this pole. With a little bit of practice, it’s pretty straightforward

for a human being to do this, although we do have the advantage

of having two feet on the ground and the use of our very versatile hands. It becomes a little bit more difficult when I only have one foot on the ground and when I don’t use my hands. Notice how this pole has

a reflective marker on top, which means that it can

be located in the space. (Audience) Oh! (Applause) (Applause ends) You can notice that this quad

is making fine adjustments to keep the pole balanced. How did we design

the algorithms to do this? We added the mathematical

model of the pole to that of the quad. Once we have a model

of the combined quad-pole system, we can use control theory to create

algorithms for controlling it. Here, you see that it’s stable, and even if I give it little nudges, it goes back — to the nice, balanced position. We can also augment the model to include where we want

the quad to be in space. Using this pointer,

made out of reflective markers, I can point to where I want

the quad to be in space a fixed distance away from me. (Laughter) The key to these acrobatic

maneuvers is algorithms, designed with the help

of mathematical models and control theory. Let’s tell the quad to come back here and let the pole drop, and I will next demonstrate the importance of understanding physical models and the workings of the physical world. Notice how the quad lost altitude

when I put this glass of water on it. Unlike the balancing pole, I did not include the mathematical

model of the glass in the system. In fact, the system doesn’t even know

that the glass is there. Like before, I could use

the pointer to tell the quad where I want it to be in space. (Applause) (Applause ends) Okay, you should be asking yourself, why doesn’t the water

fall out of the glass? Two facts. The first is that gravity acts

on all objects in the same way. The second is that the propellers are all pointing in the same direction

of the glass, pointing up. You put these two things together, the net result is that all side forces

on the glass are small and are mainly dominated

by aerodynamic effects, which at these speeds are negligible. And that’s why you don’t need

to model the glass. It naturally doesn’t spill,

no matter what the quad does. (Audience) Oh! (Applause) (Applause ends) The lesson here is that some high-performance tasks

are easier than others, and that understanding

the physics of the problem tells you which ones are easy

and which ones are hard. In this instance, carrying

a glass of water is easy. Balancing a pole is hard. We’ve all heard stories of athletes

performing feats while physically injured. Can a machine also perform

with extreme physical damage? Conventional wisdom says that you need at least four fixed motor

propeller pairs in order to fly, because there are four degrees

of freedom to control: roll, pitch, yaw and acceleration. Hexacopters and octocopters,

with six and eight propellers, can provide redundancy, but quadrocopters are much more popular because they have the minimum number

of fixed motor propeller pairs: four. Or do they? (Audience) Oh! (Laughter) If we analyze the mathematical

model of this machine with only two working propellers, we discover that there’s

an unconventional way to fly it. We relinquish control of yaw, but roll, pitch and acceleration

can still be controlled with algorithms that exploit

this new configuration. Mathematical models tell us

exactly when and why this is possible. In this instance, this knowledge

allows us to design novel machine architectures or to design clever algorithms

that gracefully handle damage, just like human athletes do, instead of building

machines with redundancy. We can’t help but hold our breath when we watch a diver

somersaulting into the water, or when a vaulter is twisting in the air, the ground fast approaching. Will the diver be able

to pull off a rip entry? Will the vaulter stick the landing? Suppose we want this quad here

to perform a triple flip and finish off at the exact same

spot that it started. This maneuver is going

to happen so quickly that we can’t use position feedback

to correct the motion during execution. There simply isn’t enough time. Instead, what the quad can do

is perform the maneuver blindly, observe how it finishes the maneuver, and then use that information

to modify its behavior so that the next flip is better. Similar to the diver and the vaulter, it is only through repeated practice that the maneuver can

be learned and executed to the highest standard. (Laughter) (Applause) Striking a moving ball

is a necessary skill in many sports. How do we make a machine do what an athlete does

seemingly without effort? (Laughter) (Applause) (Applause ends) This quad has a racket

strapped onto its head with a sweet spot roughly the size

of an apple, so not too large. The following calculations

are made every 20 milliseconds, or 50 times per second. We first figure out where

the ball is going. We then next calculate

how the quad should hit the ball so that it flies

to where it was thrown from. Third, a trajectory is planned

that carries the quad from its current state

to the impact point with the ball. Fourth, we only execute 20 milliseconds’

worth of that strategy. Twenty milliseconds later,

the whole process is repeated until the quad strikes the ball. (Applause) Machines can not only perform

dynamic maneuvers on their own, they can do it collectively. These three quads are cooperatively

carrying a sky net. (Applause) (Applause ends) They perform an extremely dynamic

and collective maneuver to launch the ball back to me. Notice that, at full extension,

these quads are vertical. (Applause) In fact, when fully extended, this is roughly five times greater

than what a bungee jumper feels at the end of their launch. The algorithms to do this are very similar to what the single quad used

to hit the ball back to me. Mathematical models are used

to continuously re-plan a cooperative strategy

50 times per second. Everything we have seen so far has been

about the machines and their capabilities. What happens when we couple

this machine athleticism with that of a human being? What I have in front of me

is a commercial gesture sensor mainly used in gaming. It can recognize

what my various body parts are doing in real time. Similar to the pointer

that I used earlier, we can use this as inputs to the system. We now have a natural way of interacting with the raw athleticism

of these quads with my gestures. (Applause) Interaction doesn’t have to be virtual. It can be physical. Take this quad, for example. It’s trying to stay

at a fixed point in space. If I try to move it

out of the way, it fights me, and moves back to where it wants to be. We can change this behavior, however. We can use mathematical models to estimate the force

that I’m applying to the quad. Once we know this force,

we can also change the laws of physics, as far as the quad

is concerned, of course. Here, the quad is behaving

as if it were in a viscous fluid. We now have an intimate way

of interacting with a machine. I will use this new capability to position this camera-carrying quad

to the appropriate location for filming the remainder

of this demonstration. So we can physically interact

with these quads and we can change the laws of physics. Let’s have a little bit of fun with this. For what you will see next, these quads will initially behave

as if they were on Pluto. As time goes on, gravity will be increased until we’re all back on planet Earth, but I assure you we won’t get there. Okay, here goes. (Laughter) (Laughter) (Applause) Whew! You’re all thinking now, these guys are having way too much fun, and you’re probably also asking yourself, why exactly are they building

machine athletes? Some conjecture that the role

of play in the animal kingdom is to hone skills

and develop capabilities. Others think that it has

more of a social role, that it’s used to bind the group. Similarly, we use the analogy

of sports and athleticism to create new algorithms for machines to push them to their limits. What impact will the speed

of machines have on our way of life? Like all our past creations

and innovations, they may be used to improve

the human condition or they may be misused and abused. This is not a technical choice

we are faced with; it’s a social one. Let’s make the right choice, the choice that brings out the best

in the future of machines, just like athleticism in sports

can bring out the best in us. Let me introduce you to the wizards

behind the green curtain. They’re the current members

of the Flying Machine Arena research team. (Applause) Federico Augugliaro, Dario Brescianini, Markus Hehn, Sergei Lupashin,

Mark Muller and Robin Ritz. Look out for them.

They’re destined for great things. Thank you. (Applause)

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