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and the reason for that is that, we have not covered praying mantises.
So I'm going to let this be a proxy for all the things we haven't talked about.
Well one thing that we haven't talked about is, what happens when your system
is generally non-linear instead of linear.
So we are now really, really good at dealing with linear control system.
Well, what if it is linear, non-linear? Well we have dealt with some, we've dealt
with the unicycle quite a bit, but there we were kind of lucky that we had a lot
of intuition. What if this is not the unicycle? What if
this is massively non-linear, and strange, and complicated? What do we
actually do? Well, that's called nominal control and it's not in this course but I
encourage you to keep educating yourself and probing further along these lines.
another thing that we didn't deal with is what is called optimal control.
So for us, the name of the game was stability.
Stability, it was performance in the sense of tracking, right, so we want it
to track reference signals, and then we had robustness, but what we didn't have,
explicitly, were things like this. So this is a general, type of cost, where
we're saying, well we want to minimize some cost involving x and u.
This could be, you know, the fuel consumed, or the time it takes to get
there, plus possibly some cost on the final point as well.
This is known as optimal control, and this was also not, in the course.
So this was one grasshopper that we didn't see.
There is another branch of decision theory known as Machine Learning that we
didn't touch upon. The reason why I am putting this as a
another thing that you might want to probe further along is it's useful in
robotics and it's highly related to control in general and optimal control in
particular. So the idea is that.
I'm going to have some costs V and I'm going to have some policy pie which says
what are you going to do when you're at the certain state?
And the cost is just going to be a cost of the different, where I am at time k
and what I'm doing at time k. So this is really U sub k, right? And now
I'm going to sum up this entire cost and if you do that you can write down.
Something known as Bellman's Optimality Equation or Bellman's equation, that
basically characterizes what is the smallest you can make this cost while it
satisfies this kind of weird looking expression.
And the point here is not the math, the point is that we have this equation, and
machine learning is all about finding this V* by exploring.
If I'm at this position, let's try doing u4. if I'm in another position, let's try
doing u9. And while doing this, you're building up
this a, this V* cost function. And when you're done building it up, you
all of the sudden have a complete map or guide to what should you do.
If you encounter a certain state, and that's in a nutshell what machine
learning is about. Another thing that we didn't do much with
is perception and mapping. We had infrared or ultrasonic range
sensors, but a lot of times. We have those.
We have laser scanners. We have cameras.
We did not deal with complicated sensing modalities and we did also not deal with,
okay what do we do with all these sensor data.
How do we actually produce maps of the world? Our world was, here is the, the
robot. Here is an obstacle.
It's a point. Let's just avoid it.
But you know what. This obstacle may not be a point it may
be part of, I don't know, a corridor, and we would like to go in the corridor.
Well then it's good to actually describe what the world looks like.
This is known as mapping. And again, this is a perfect opportunity
for you to probe further, trying to build maps of the world.
There are lots of different methods for doing it.
And finally, the thing that we didn't do at all either is really talk about the
high level artificial intelligence. So, how do you actually decide in the
first place where you should be going. We said, given a goal point, how do we go
there? But where did the goal coin, point come from? Somehow, somewhere, someone is
going to have to make decisions about what at the very high-level the robot
should be doing. And this falls Squarely under the domain
of artificial intelligence. Not covered in this course, I encourage
you to probe further. So, to conclude, there are things that we
haven't done in this class. There are lots of praying mantises that
we didn't cover. And those are good things for you to
probe further. And learn more about.
If you know all of it, you can build an awesome robotic system.
But, beyond that, there are also lots of things we don't know.
So here, Not only praying mantises, but other green creatures.
We have no idea what they look like. We don't know if they exist, we don't
know what they are. It's the same with robotics.
There's a lot of stuff going on that we as a community don't know how to do yet.
So the last thing I want to do is give you the impression that this is a closed
and complete case. We know everything about robotics.
We don't. So, not only in this course are there
praying mantises, but outside of the course there are potential aliens that we
still have not discovered.