December 3, 2014
Buffalo, New York was absolutely drilled by a massive snowstorm at the beginning of November; it held humans indoors, and stranded others, for days as the snow piled up foot over foot. There was however one sector of the population that could get outdoors, although they aren’t humans. Drones could get up and get out during and after the storm to survey the damage, see just how much snow had fallen, and capture the twisted beauty of the scene.
When I watched this video it brought one question to my mind: how can a drone operate so efficiently in such harsh conditions? Specifically, I wanted to know what it was beyond the durable materials used to create the drone that kept it from getting swept away by massive wind gusts.
In June 2013 Raffaello D’Andrea gave a TED Talk, demonstrating to a crowd the astounding athletic power of a quadcopter, detailing the mathematics at work behind the scenes. They build an indoor set up with cameras on the ceiling hooked up to one laptop, and that system served as an indoor GPS. It’s used to locate objects in the space that have reflective markers on then, which in this case is the drone itself.
The data it records is then sent to a second laptop running estimation and control algorithms, which in turn send commands to the quadcopter simultaneously running its own estimation and control algorithms. That’s what keeps it so steady when D’Andrea violently throws the drone away from his body.
“The bulk of our research is algorithms, it’s the magic that brings these machines to life,” says D’Andrea.
There’s a process called model based design that D’Andrea and his team use to capture the physics of the quadcopter via a mathematical model of how the machine behaves. From there, a branch of mathematics called control theory is used to analyze these models and synthesize algorithms for controlling them; that’s how the quadcopter can hover. The dynamics are captured with a set of differential equations, and those equations are manipulated with the help of control theory to stabilize the quadcopter when it gets thrown off center.
D’Andrea digs deeper by showing how the quadcopter can balance a pole, and even a full glass of water. It’s a fantastic example of just how agile these machines can be, and it helps us solve the mystery of how a drone, or quadcopter, can remain static in harsh conditions.
Here’s the video:
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