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Hi, and welcome to the Glue Lectures for control of mobile robots.

This is the last Glue Lecture, Glue Lecture 7.

And I really hope that you guys have enjoyed the course

and learned a lot of awesome things, are super excited about robotics.

I hope you are. So, this Glue Lecture is just going to be.

Basically the course in a nutshell in a very

big nutshell, in the sense of a very broad overview.

Basically what we think from a layman's perspective is like the best

thing you got out of the course, you know, really simple stuff.

Because your quiz is also going to kind of go over what you've done.

All this while etcetera.

So this is what the glue lecture is about. The first

thing that I think was amazing about this entire course is the fact that, you know,

we saw how math can be related to motion. How we can actually visually see.

Equations turn into motion.

So if you guys remember here we have this

pink ball that's moving happily in this corner, you know.

And from the new lectures and the course we saw that the

motion of this ball can actually

be described through equations or through math.

Not only can the motion be described, but we can actually

derive the motion.

Through something called a dynamical model, or dynamical

models in this case, we have this here, right?

Which is also math, and then from this we can

actually get how this ball is moving with time, right.

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So, this was an example we saw in the glue lectures.

Basically, you have a dynamical model that

describes the velocity and where the ball wakes

up at a particular time, and then kind of find

out how the ball is going to change with respect to time.

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Then we also saw that okay, since this course is about robots, right?

So we read a few dynamical

models of the robots.

So this is the most common robot that is there,

basically, or that we deal with, a two-wheel differential drive robot.

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And we saw that, you know what, we can write the model of

this guy through this equation here, or through the set of equations here.

Where you control the angular velocities of the

right and left wheel of the robot, right?

And then we also saw that you can simplify

the model even farther, and make it a unicycle

robot, with just like one wheel, and basically.

This figure here.

And you can control the velocity and the angular velocity of this simplified model.

The good thing about this was the fact that, you

know what, this simplified model can be used for design.

And then we have a beautiful transformation on or relation basically

between these two models that once we design our v and omega for

the simplified model, we can just, you know, put it on to the differential.

Rate model and and find out vr and vi to give to the robots, right?

And actually this week with Dr. Edgarsted you learned another even simpler model.

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Not even a model but a simpler thing called x dot equal to u.

Basically where,

you know, you don't even want to control let's

say the vel, linear velocity and the angular velocity.

Instead you just directly going to control, you know, x dot.

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Equal to u.

And, and then you learn this very nice transformation that allows you

to transform this x star equal to u directly to your reason omegas.

Right?

So, now all of the sudden you don't even

have to design your controller based on this model.

You just design it based off this guy here.

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Another thing that you learned in this

week's lecture was the car-like model where you

have a current, all you do is there is you include this steering angle psi.

Into your correlate model, and then you

can even map that model onto the

simplified model, and the simplified model onto whatever.

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So on and so forth.

You're good to go.

So this was how math translates to motion

and basically what is a dynamical model, or.

How do we start with any robotics problem we

start with the model so this is what that is.

okay.

This is one

excellent thing.

The second thing that we learned in the course was systems, so now that we know

how a model of a, you know robot or anything we want to control is.

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Described through math. Now we want to influence it, right?

We want to control it. We want it to do certain things.

So that's when this whole idea of systems comes in that

okay, we're going to have an input, we're going to have an output.

And we're going to actually describe

our system through these three matrices. A, B and C.

Again, something that we went over extensively in class.

And your system can now again, of course, be a

robot, here it's a Capera robot, here there's a humanoid.

Now robot.

Anything for which you can find your A, B and C matrices.

Now A matrix, just remember.

Is your model, which we just discussed right now,

right? It's something that's given.

Something that's from the physics or from basically the device.

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B matrix is actually something that we construct, that describes the actuators.

Basically, what are the actuators on this model or

on this robot, in particular, that we can control?

And that information is encoded in the B matrix and

then the C matrix of course is, what can we measure?

Or what's

the output?

Wha, what are the sensors on this robot from which we can get our output?

And together, A, B and C will make you make the system.

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And, in this lecture, or sorry, in this course,

basically what we saw was that, you know what,

once we have our model and then we create our

system for the model A, B and C matrices, etcetera,

then, we can in fact make sure that our system.

Robot, with, you know, sensors, actuators, and the, everything, does

not blow up, does not end up doing anything random.

It stays stable.

And we also do this whole controllability, observability analysis,

which is very important in order to make the robot actually do anything.

Before you can even start talking about controlling the robot.

Etcetera.

You need to know that, you know, is it controllable, is it

observable, do I in fact have the ability to do all these things.

We did all this extensively in class.

Another very cool thing that we learned was this whole

automata, our hybrid controls notion, you know, that you can.

For a robot to do some task you can

actually divide up this task into make small, small

behaviors that the robot does and then kind of

mash all these behaviors together and into this automata thing.

And then also we learned that once you do this you know there are undesirable

things like the zeno effect for instance and how do you get rid of it.

And a lot of other things that we saw in this course, right?

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What is great though, was that we did all this with math.

So, by the end of this course, you guys have actually learned about differential

equations, linear algebra, geometry, a lot of these awesome tools that.

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Can you make you, you know, actually do such nice stuff with the robots visually.

Not only just in software simulation but

you actually see it happening. You know, in front of you.

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The now and one guy is doing a cheer leading the

team and the other one is doing a disco dancing routine.

This is Emy Lavier's work when she was a

grad student at George Dake, in our lab and basically

she has a command of this entire thing

based of this course of, of hybrid automators etcetera.

Right in front of you guys we are

actually making robots dance, which is great, right?

And, you can see more amazing videos and stuff about, you know, what

a lab does or what the robots do on the GRITSLab YouTube Channel.