Take this quad, for example.

For example, that's how we can make the quad hover.

It naturally doesn't spill, no matter what the quad does.

We added the mathematical model of the pole to that of the quad.

Here, the quad is behaving as if it were in a viscous fluid.

Twenty milliseconds later, the whole process is repeated until the quad strikes the ball.

You can notice that this quad is making fine adjustments to keep the pole balanced.

Notice how the quad lost altitude when I put this glass of water on it.

We can use mathematical models to estimate the force that I'm applying to the quad.

Suppose that we want this quad to not only hover but to also balance this pole.

We can also augment the model to include where we want the quad to be in space.

We then manipulate these equations with the help of control theory to create algorithms that stabilize the quad.

I can point to where I want the quad to be in space a fixed distance away from me.

Like before, I could use the pointer to tell the quad where I want it to be in space.

Third, a trajectory is planned that carries the quad from its current state to the impact point with the ball.

We then next calculate how the quad should hit the ball so that it flies to where it was thrown from.

The algorithms to do this are very similar to what the single quad used to hit the ball back to me.

Once we have a model of the combined quad pole system, we can use control theory to create algorithms for controlling it.

Suppose we want this quad here to perform a triple flip and finish off at the exact same spot that it started.

Once we know this force, we can also change the laws of physics, as far as the quad is concerned, of course.

This quad has a racket strapped onto its head with a sweet spot roughly the size of an apple, so not too large.

I will use this new capability to position this camera carrying quad to the appropriate location for filming the remainder of this demonstration.

We share written things, we share images, we share audio, we share video.

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.

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.

We share in their pain we share in their sorrow.

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.

Share application

Share the Work

We can share ideas with other people, and when they discover them, they share with us.

11 Share based Payments

And share my task,

I'll share one story.

They share their designs.

Mitt Romney s Fair Share

I'm willing to share.

And share my task,

We share that view.

It will give us the opportunity to connect with companies that share the values that we share.

There is a share for men and a share for women from what is left by parents and those nearest related, whether, the property be small or large a legal share.

There is a share for men and a share for women from what is left by parents and those nearest related, whether, the property be small or large a legal share.

Men receive a share of what their parents and relatives leave, and women receive a share of what their parents and relatives leave be it little or much a legal share.

Men receive a share of what their parents and relatives leave, and women receive a share of what their parents and relatives leave be it little or much a legal share.

From what is left by parents and those nearest related there is a share for men and a share for women, whether the property be small or large, a determinate share.

From what is left by parents and those nearest related there is a share for men and a share for women, whether the property be small or large, a determinate share.