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

Â This is the last Glue Lecture, Glue Lecture 7.

Â And I really hope that you guys have enjoyed the course

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

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

Â Basically the course in a nutshell in a very

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

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

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

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

Â All this while etcetera.

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

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

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

Â Equations turn into motion.

Â So if you guys remember here we have this

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

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

Â motion of this ball can actually

Â be described through equations or through math.

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

Â derive the motion.

Â Through something called a dynamical model, or dynamical

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

Â Which is also math, and then from this we can

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

Â 1:35

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

Â Basically, you have a dynamical model that

Â describes the velocity and where the ball wakes

Â up at a particular time, and then kind of find

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

Â 1:59

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

Â So we read a few dynamical

Â models of the robots.

Â So this is the most common robot that is there,

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

Â 2:17

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

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

Â Where you control the angular velocities of the

Â right and left wheel of the robot, right?

Â And then we also saw that you can simplify

Â the model even farther, and make it a unicycle

Â robot, with just like one wheel, and basically.

Â This figure here.

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

Â The good thing about this was the fact that, you

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

Â And then we have a beautiful transformation on or relation basically

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

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

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

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

Â 3:19

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

Â Basically where,

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

Â say the vel, linear velocity and the angular velocity.

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

Â 3:32

Equal to u.

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

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

Â Right?

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

Â have to design your controller based on this model.

Â You just design it based off this guy here.

Â 4:01

Another thing that you learned in this

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

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

Â Into your correlate model, and then you

Â can even map that model onto the

Â simplified model, and the simplified model onto whatever.

Â 4:20

So on and so forth.

Â You're good to go.

Â So this was how math translates to motion

Â and basically what is a dynamical model, or.

Â How do we start with any robotics problem we

Â start with the model so this is what that is.

Â okay.

Â This is one

Â excellent thing.

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

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

Â 4:52

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

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

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

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

Â And we're going to actually describe

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

Â Again, something that we went over extensively in class.

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

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

Â Now robot.

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

Â Now A matrix, just remember.

Â Is your model, which we just discussed right now,

Â right? It's something that's given.

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

Â 5:37

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

Â Basically, what are the actuators on this model or

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

Â And that information is encoded in the B matrix and

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

Â Or what's

Â the output?

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

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

Â 6:33

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

Â basically what we saw was that, you know what,

Â once we have our model and then we create our

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

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

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

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

Â It stays stable.

Â And we also do this whole controllability, observability analysis,

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

Â Before you can even start talking about controlling the robot.

Â Etcetera.

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

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

Â We did all this extensively in class.

Â Another very cool thing that we learned was this whole

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

Â For a robot to do some task you can

Â actually divide up this task into make small, small

Â behaviors that the robot does and then kind of

Â mash all these behaviors together and into this automata thing.

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

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

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

Â 7:54

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

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

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

Â 8:11

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

Â Not only just in software simulation but

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

Â 8:32

The now and one guy is doing a cheer leading the

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

Â This is Emy Lavier's work when she was a

Â grad student at George Dake, in our lab and basically

Â she has a command of this entire thing

Â based of this course of, of hybrid automators etcetera.

Â Right in front of you guys we are

Â actually making robots dance, which is great, right?

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

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

Â