Raffaello D’Andrea says that the reason quadcopters are so popular right now is that they’re mechanically simple. He then spends an amazing fifteen minutes demonstrating the complexity that can be brought to a quadcopter using engineering and mathematics. D’Andrea is researching algorithms for robotics, using model based design and control theory.
The dynamics of quadcopter motion are modeled with a set of differential equations, and then processed to create algorithms for stabilization. Roll, pitch, yaw and acceleration can be controlled with sensors, cameras and laptops set up in the TED robotics lab.
The demonstrations in this video are amazing. First the quad hovers at its home altitude, then Raffaello throws the quad and it rights itself, coming back to home position. Raffaello then sets a balancing pole into the quad and the quad controls itself and balances the stick on top of itself by tracking a reflective marker on the pole.
http://www.ted.com/talks/raffaello_d_andrea_the_astounding_athletic_power_of_quadcopters.html
Next a remote control that looks more like a magic wand than an RC handheld controller is pointed at any location in the room and the copter goes to that position. Seeing a quadcopter whiz back and forth with a glass of water on top of it, never tipping the glass or spilling a drop, is amazing.
And then the scissors come out. Raffaello cuts two of the four propeller blades off of the quad. He explains that like an athlete playing with an injury the copter can adapt and still perform without optimal conditions. Through math modeling it was discovered that the machine can still fly with two propellers, yaw control is lost but roll, pitch and acceleration are able to control the vehicle.
The quads learn and adapt to their surroundings. Performing a triple loop or bouncing a ball in mid-air are feats that happen too quickly for the sensors to react. But the sensors can take note of one iteration and then use that data to predict how to better perform the act a second time.
The demonstrations in this TED Talk are mind blowing, and the video should definitely be watched to see the things that the copters can do. More inspiring are the ways that D’Andrea explains the movements and the adaptability in terms of math models and control theory. This gives the feel that the copters are part of a heavily researched and planned experiment instead of an RC hacker chopping away at his machine using trial and error.
http://www.ted.com/talks/raffaello_d_andrea_the_astounding_athletic_power_of_quadcopters.html