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Hello and welcome to glue lecture seven. This is the last glue lecture.
We're finishing up the last week of the course and I hope everyone's had, learned
a lot and had a good time. Today in the glue lecture you'll see that,
that quiz seven is a little bit, kind of a mixed bag of all the things we've learned
so far and then really this week has been kind of trying to apply everything you've
seen in the course. [inaudible] Onto some more exciting
problems or sort of high-level take away points.
And so, for this glue lecture, what I'm going to do is just kind of wrap up with
the, my three favorite punchlines of the course.
So take them for what you will, this is not necessarily going to be any tailored
exampled this week. This is just kind of how I my favorite 3
things about what we hope that you learned in the course.
So, the first punchline kind of answers this question of what are systems?
This is a word that in kind of some of the other lectures we've talked about, kind of
gets thrown around in different ways. And so I hope that there's kind of two
views you now have on this word system. One, is that we might, that we have a
system of equations. So we've been calling this a system,
right? And we might even consider, again, here,
that we have some initial condition for these differential equations, right?
But really, this is a system of differential equations, and so we have
this remember that this x, in general, is an x n, and so we might have n equations
that describe these dynamics. We might have n inputs that we can use to
effect these dynamics and then we might have l or some other, you know, number of
outputs. And so, this system is literally a system
of equations that are all related via these matrices, right.
And so these matrices are the, this, we've kind of, kind of had to get a little
comfortable with linear algebra in this course, as really, theses matrices just
encode the relationships of our variables. And we've found that by having these a, b,
and c matrices, we can know a lot about the properties of this system.
Is it controllable, is it observable, is it stable, etc.
So this is a system, right. We also have this view of systems in this
way, where we have this input and this output and those are, those are present
here to, we have the, the output and the input.
And they're related according to these equations, but we also have this view of
systems that's a little higher level, where a system is anything, really, where
we have some input and we get some desired output.
So, in the satellite, we might think of, we have these little thrusters on the
satellite, and as we fire them, the attitude, or the angle of the satellite
changes. But we also have systems where we had
this, this was kind of our go to robot for the course, we had this differential
drive. There the input and output are different
but we can still use the same theory about these A, B, and C matrices to kind of
understand how that might use some controlled input to get some desired
output. And we've also kind of, you know, I want
you to remember that we might have kind of a weirder notion of system.
It might be an entire stock market, right where that could be your system.
Or you might have a, a little humanoid robot that you want to dance.
So I love this flexibility of a system can be anything and we have, you know, if you
can write it down as a system of equations that are related via these A,B and C
matrices, systems theory really let's you do a lot of, of interesting things where
you can be sure of how U and Y will relate to each other.
The second punchline that. Is kind of my favorite, is the idea that
math describes things that move. And I think that sometimes we don't
necessarily see math in that way. And in systems, that's really what we're
most excited about. All these boxes that we like to you know,
the, in this picture here, right? This is something that moves, this box,
this system. And so, Now we've kind of in my lecture
seen this little bouncing ball and, and you've seen more examples of that in
action in Doctor[INAUDIBLE] lectures and I just kind of want us to remember that
these are describing things that move. And we've used things from differential
equations, linear algebra to describe this relationship system of equations.
Geomerty. Figuring out, you know, what direction
should we be driving in given that we have an obstacle in front of us and these
automata that kind of describe the high level, how you should be switching around,
how you should be implementing these different control laws that we developed.
And finally. You know, we can make robots do anything
we want. You know, we have introduced this idea of
an automaton in class. And I think this is really cool where, in
general you know, these states can be anything.
These arrows that go between, you know, how should this robot here a humanoid
robot. How should it be moving?
Well you can make that up Completely. Right?
You can design. Maybe we decide, okay we don't want this
behavior. We want something else.
Right, we can pick the arrows. We can pick this.
We can pick how our system should be evolving.
We're designing that. Now, of course, we've also learned some
very important principles that kind of help us.
Do what we want. Right?
Where we can, you know, we don't want things, to build systems that are unstable
or uncontrollable, we don't want kind of this Zeno phenomenon that we've talked
about. So when your designing these kind of
atomita, there are those thing to consider, but, you know, really the sky is
the limit, and so I'm kind of, I'm going to leave with a little video of From my
research, where I make robots dance. So I, I won't give away the answer yet,
but you can watch these two videos here at the bottom, and see that these robots are
moving in a different way. And, of course.
How they're evolving between each pose is the same, but it's the structure of, of
the poses that is different. And you may replay for a second but this
guy here on the I guess, yeah I guess your left is my left right now right.
So here on the left we have an example of. A behavior I call cheerleading, and on the
right, disco dancing. And all of that comes through a structure
of an object just like this. How should it be constructed to provide
the behavior that we want? So the sky's the limit, and I wish you
luck, in your future endeavors. And I hope that this class, it helps you
achieve those goals. Thank you very much.