We are now extremely close to the end of this entire course and I'm actually done,

believe it or not, with the technical part.

The grand finale was really this idea that we could even make complicated

systems like cars act like unicycles that we now know how to control and navigate

around in complex environments as we've seen both in theory In simulation, and

actually in real experiments. What I want to do in this sub-lecture is

basically probe further. There are lot's of things, believe it or

not, that are actually not in this course, pretaining to other control

robots. Here I have a picture of a praying mantis

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.

To Probe Further

Control of Mobile Robots

Meet the Instructors