The astounding athletic power of quadcopters | Raffaello D'Andrea

Ordinary differential equations? Okay: Just freshman calculus actually is a good start. E.g., for viral growth consider y'(t) = k y(t) ( b - y(t) ) where t is time, y(t) the size at time t, and the rate of growth y'(t) = d/dt y(t) is proportional to both the current size y(t) and the size ( b - y(t) ) yet to be achieved. So, e.g., the growth rate is proportional to the number of present customers talking y(t) and the number of potential customers listening ( b - y(t) ). We assume that the present is time t = 0 and we have the eventual size b and the current size y(0). Then, sure, we have an initial value problem (that is, we know y(0)) for a first order, linear ordinary differential equation. But all that is needed for a solution is just freshman calculus. It's just a routine exercise. Trivial? Once that equation kept FedEx from going out of business. Polished, elegant, insightful, balanced, expert, great first text: Earl A. Coddington, 'An Introduction to Ordinary Differential Equations', Prentice-Hall, Englewood Cliffs, NJ, 1961. For when you want to take some really big next steps up past nearly everyone else in mathematics: Earl A. Coddington and Norman Levinson, 'Theory of Ordinary Differential Equations', McGraw-Hill, New York, 1955. For one of the larger reasons to be interested in ordinary differential equations: Michael Athans and Peter L. Falb, 'Optimal Control: An Introduction to the Theory and Its Applications', McGraw-Hill Book Company, New York, 1966. Also E. B.

Absolutely, as long as they're operating within parameters there's no failing them. I've been running brushless systems in RC cars for the last 7 odd years. The only motor failures has been when It's been subject to extreme abuse, as in the rotor reaching 100+° (internally), going from ~55-60K RPM to 0 in fraction of a second or the rotor being forced through the bearings. For unmanned flight i do agree on multicopters being the best option. See this[1] video for an example of a multicopter flying with disabled props. However, as you see this flightmode isn't appropriate for human beings, humans should keep flying helis for now. The swash plate design even though more complex than a prop mounted on a shaft is still a rather simple design, litterally a bearing mounted on a 2 axis system and rods attached to rotate the blades. Multicopters with swash plates are interesting too as they can be simplified not to tilt the plate but only offset it up and down to alter pitch the same way all around the rotation. If. This exerts less force on the bearing, but considering there's still 4 of them rather than one might increse failure rate. With swash plates on multicopters we could have two motors driving one system that drives the props, and do many amazing things with computer aided controls in case of failure. Idk why i keep on going, TL;DR: Being able to control pitch is key, multirotor or not. I'm not really with Elon Musk on alot of things, but personal human flight is one thing w

I'm kind of surprised they use only 4. There are drones with 6 and 8 rotors, which can still fly if 1 fails, which they use in the film industry to fly heavier, more expensive cameras. There are also ways to get quads to fly on less than 4 rotors if one becomes damaged, although as a human I'm not sure I'd want to be in one doing it. Here's a Ted Talk with a live demo from 2013: [VIDEO]