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Good morning. I'm here today to talk about autonomous, flying beach balls. No, agile aerial robots like this one. I'd like to tell you a little bit about the challenges in building these and some of the terrific opportunities for applying this technology. So these robots are related to unmanned aerial vehicles. However, the vehicles you see here are big. They weigh thousands of pounds, are not by any means agile. They're not even autonomous. In fact, many of these vehicles are operated by flight crews that can include multiple pilots, operators of sensors and mission coordinators.

What we're interested in is developing robots like this — and here are two other pictures — of robots that you can buy off the shelf. So these are helicopters with four rotors and they're roughly a meter or so in scale and weigh several pounds. And so we retrofit these with sensors and processors, and these robots can fly indoors without GPS.

The robot I'm holding in my hand is this one, and it's been created by two students, Alex and Daniel. So this weighs a little more than a tenth of a pound. It consumes about 15 watts of power. And as you can see, it's about eight inches in diameter. So let me give you just a very quick tutorial on how these robots work.

So it has four rotors. If you spin these rotors at the same speed, the robot hovers. If you increase the speed of each of these rotors, then the robot flies up, it accelerates up. Of course, if the robot were tilted, inclined to the horizontal, then it would accelerate in this direction. So to get it to tilt, there's one of two ways of doing it. So in this picture you see that rotor four is spinning faster and rotor two is spinning slower. And when that happens there's moment that causes this robot to roll. And the other way around, if you increase the speed of rotor three and decrease the speed of rotor one, then the robot pitches forward.

And then finally, if you spin opposite pairs of rotors faster than the other pair, then the robot yaws about the vertical axis. So an on-board processor essentially looks at what motions need to be executed and combines these motions and figures out what commands to send to the motors 600 times a second. That's basically how this thing operates.

So one of the advantages of this design is, when you scale things down, the robot naturally becomes agile. So here R is the characteristic length of the robot. It's actually half the diameter. And there are lots of physical parameters that change as you reduce R. The one that's the most important is the inertia or the resistance to motion. So it turns out, the inertia, which governs angular motion, scales as a fifth power of R. So the smaller you make R, the more dramatically the inertia reduces. So as a result, the angular acceleration, denoted by Greek letter alpha here, goes as one over R. It's inversely proportional to R. The smaller you make it the more quickly you can turn.

So this should be clear in these videos. At the bottom right you see a robot performing a 360 degree flip in less than half a second. Multiple flips, a little more time. So here the processes on board are getting feedback from accelerometers and gyros on board and calculating, like I said before, commands at 600 times a second to stabilize this robot. So on the left, you see Daniel throwing this robot up into the air. And it shows you how robust the control is. No matter how you throw it, the robot recovers and comes back to him.

So why build robots like this?

What we're interested in is developing robots like this — and here are two other pictures — of robots that you can buy off the shelf. So these are helicopters with four rotors and they're roughly a meter or so in scale and weigh several pounds. And so we retrofit these with sensors and processors, and these robots can fly indoors without GPS.

The robot I'm holding in my hand is this one, and it's been created by two students, Alex and Daniel. So this weighs a little more than a tenth of a pound. It consumes about 15 watts of power. And as you can see, it's about eight inches in diameter. So let me give you just a very quick tutorial on how these robots work.

So it has four rotors. If you spin these rotors at the same speed, the robot hovers. If you increase the speed of each of these rotors, then the robot flies up, it accelerates up. Of course, if the robot were tilted, inclined to the horizontal, then it would accelerate in this direction. So to get it to tilt, there's one of two ways of doing it. So in this picture you see that rotor four is spinning faster and rotor two is spinning slower. And when that happens there's moment that causes this robot to roll. And the other way around, if you increase the speed of rotor three and decrease the speed of rotor one, then the robot pitches forward.

And then finally, if you spin opposite pairs of rotors faster than the other pair, then the robot yaws about the vertical axis. So an on-board processor essentially looks at what motions need to be executed and combines these motions and figures out what commands to send to the motors 600 times a second. That's basically how this thing operates.

So one of the advantages of this design is, when you scale things down, the robot naturally becomes agile. So here R is the characteristic length of the robot. It's actually half the diameter. And there are lots of physical parameters that change as you reduce R. The one that's the most important is the inertia or the resistance to motion. So it turns out, the inertia, which governs angular motion, scales as a fifth power of R. So the smaller you make R, the more dramatically the inertia reduces. So as a result, the angular acceleration, denoted by Greek letter alpha here, goes as one over R. It's inversely proportional to R. The smaller you make it the more quickly you can turn.

So this should be clear in these videos. At the bottom right you see a robot performing a 360 degree flip in less than half a second. Multiple flips, a little more time. So here the processes on board are getting feedback from accelerometers and gyros on board and calculating, like I said before, commands at 600 times a second to stabilize this robot. So on the left, you see Daniel throwing this robot up into the air. And it shows you how robust the control is. No matter how you throw it, the robot recovers and comes back to him.

So why build robots like this?

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