So now we feel pretty confident abut our
ability to design controllers that take a
robot to a goal location. In fact we've
seen it in design, we've seen it in
simulation, and we've even seen it in real
life. But we have not discussed the issue
of. Well what if the robot needs to do
something slightly more elaborate than
just get to the point for instance you
typically don't want to hit things on the
way over there so the one behavior that I
want to talk a little bit about is
obstacle avoidance because goal to goal
and obstacle avoidance are really the
dynamic duo of mobile robatics. ,, . We're
going to do more things, of course. But
underneath the hood, there will always be
a goal to goal, and an obstacle avoidance
behavior. And let's think a little bit
about how one should avoid driving into
obstacles. Because going to goal location
was not. Particularly complicated.
Well, we can clearly use the same idea as
we did in go-to-goal by defining a desired
heading, and then simply, you know, steer
in that direction. So, let's say that we
have the following. The robot, well, it's
the blue ball. And then we have this
little red. C, which is the obstacle,
located at xo yo. And the reason that we
know the location of this is because the,
the disc obstraction we talked about, when
we talked about the sensors. Okay, if this
is a goal, we would steer towards it. That
much is clear, now, the question is If it
is an obstacle which direction should we
steer it, when it's not as clear. I mean,
here is a direction we can go in. You
know, let's run away from the obstacle.
But that's a little overly cautious I
think. At least sometimes, if I'm not even
on m way towards the, The red thing. Why
do all of a sudden I have to insist on
going the opposite direction? So. This is
one direction which we can go in, but it
seems a little, how should I put it. It
seems a little skittish, or paranoid. We
should be able to be a little bit more.
Clever, maybe like this. So if we're going
in this general direction, then we should
maybe go perpendicular to the, the
direction to the obstacle. That's one way
in which we could be thinking but there
are other choices we could make. Let's say
that we have a goal. Again, we're not just
avoiding obstacles, we're actually trying
to go somewhere. This obstacle The red
obstacle we see here. Well, it doesn't
seem to matter if I'm going towards the
goal, what do I care about that obstacle.
So, hey we could just ignore it. That's
one direction we could go in. Or we could
somehow combine the direction to the goal
with some way of avoiding an obstacle. So,
we could kind of move away from the
obstacle while somewhat getting towards
it. To goal.
The point here is that there is no obvious
correct answer, going to goal its clear
which direction we want to go in. When
we're avoiding an obstacle its not as
clear, its not obvi, obviously have to go
in this direction and we have choices and
some how some choices are better than
others. So lets, lets look at some of
these choices that we have a little bit.
Okay.
So we have the robot in blue, we have the
obstacle in red. And we have the goal in
yellow. This was choice one. Pi 1 is, I'm
going to call it Pi obst plus Pi. So Pi
obst is this angle, right? So, here is phi
obst. And in fact, Pi obst is we can write
it as arc tangent y obst minus y over x
obst minus x. So this is some way in which
we compute the angle to the obstacle and
then we can say well Pi 1 suggestion one
which is the. The super paranoid robot
who's avoiding obstacles at all cost, it's
adding Pi to the mix. And by the way why
am I adding Pi, and not subtracting Pi?
All right, so, here's the, the, the angle
I want to go to the, this is phi obst.
And, what I'm doing no is adding Pi.
Right, so, this is , well the point is
that it actually doesn't matter if you add
Pi, or subtract Pi, because by now we know
that angles are slightly scary objects.
And, we always take something like r
tangents too, to ensure that we stay
within minus Pi and Pi. Adding Pi or
subtrac ting Pi as long as we take. Some
safety measures, it doesn't matter. So, we
can do the same thing. It doesn't matter
which one we choose. But, that's one way.
Now, this direction is pure in the sense
that I don't care where the goal is. I am
just going to move away from the obstacle
as much as I can. So, I'm going to call
this pure avoidance. No notion of where
I'm supposed to be going. Well, we had
another choice, right? We said, what if we
go perpendicularly to this direction?
Well, so Pi 2 is Pi obstacle plus minus
Pi. Well, what does that mean? It means
that if I do minus Pi over 2, I go in this
direction. If I do plus Pi over 2, I go in
that direction. And there, here it
actually matters if I do plus or minus.
And the question is, which one should we
choose? Well, typically that depends on
where the goal is. So we should pick in
this case minus Pi over 2 because that
moves us closer to the goal, while plus Pi
over 2 moves us further away from the
goal. And the punchline here is really
that this is not a pure strategy, because
we need to know where the goal is.
Instead, what we're doing is we're
actually, I'm calling it blended in, in,
in the sense that we're taking the
direction to the goal into account when we
are figuring out in which direction we
should be going. So it's not a pure
obstacle avoidance. If I just ask you to
avoid an obstacle, you say I can't,
because it needs to know where the goal
is. In that sense, it's not pure. So,
that's one choice. Well, remember this
one? We said, you know what? This obstacle
is no big deal to us, we are just simply
going to go in the direction of the goal.
Well, this is pure goal to goal. We're
just running one behavior. goal to goal,
we don't care about the obstacle. And
what's more interesting is this choice, Fi
4 which is really a combination of the
direction to the goal and the direction to
the obstacle. And the interesting thing
here is that this is clearly a blended
mechanism, somehow we combining go to
goal, type oyds with obstacl e avoidance
of ideas and the punch line here is that
there are really two fundamentally
different ways of combining, avoiding
slimming interstuff and getting to goal
points and these ways of combining things
is called an arbitration Mechanism so we
saw typically in this case two
fundamentally different arbitration
mechanisms one is the winner takes all
approach which is a hard switch when we're
just going straight away from the obstacle
right so here was the obstacle here was
the robot with the robot was going there
we're doing just avoid obstacles. Or, if
the goal was here, right? And we're going
straight to the goal, we're doing just go
to goal. So, these would be two examples
of hard switches. Now, the two other
examples we saw were blended behaviors.
One was, you're combining somehow, the
angle to the goal and the angle to the
obstacle to produce a new desired angle.
and the first blended behavior we saw was
one where we're kind of moving
perpendicularly to the obstacle, but we're
doing it in such a way that we're getting
closer to the goal. And these are two
valid ways of designing arbitration
mechanisms. And in fact, we are going to
have to get systematic and careful about
how to do it. And I should point out that
both Approaches have merit. Now the nice
thing about the winner takes all is that
if go to goal is only going to goal, then
I can analyze that. If obstacle avoidance
is only avoiding obstacles then I can
analyze that, which means that from an
analysis point of view it's easier to deal
with hard switches. However, it's not
necessarily the case that from a
performance point of view hard switches
are to be preferred. Because, it seems
like as I'm walking around I'm kind of
keeping an eye on where I'm going while
not slamming into things. So I'm not
either going towards something or avoiding
slamming into things. So it seems like
performance wise, blending or smoothing
the two behaviors makes a lot of sense.
However, from an analysis point of view
it's harder. So, the question is ho w do
you design your system in such a way that
you can have your cake and eat it meaning
you can analyze what's going on and you
still have good performance. So, we are
going to have to bite this bullet head on,
and in fact we would be very systematic.
And what we have done in this module,
module two is simply introduce mobile
robots. We've looked at some basic models.
We looked at some basic ways in which
we're getting information about the world.
And we designed some basic behaviors, but
to be honest, we haven't been particularly
careful about what we did. Module one, we
were also not particularly careful, but
there the focus was on control theory. So
mobile, mo, , module three is enough chit
chat. Let actually start this course in a
more systematic and formal matter. So,
we're going to return to module one. In
module three and then we're going to
return to module two. And we're going to
see, can we do what we just did, did in a
rather heuristic and ad hoc manner in a
systematic and more formal way. And the
way to do it is to go to the wonderful
abstraction that is linear systems theory.
So, that is the focus of the next module.
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