Obstacle Avoidance

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.

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