The outcome of the last lecture was, in some sense, quite glorious. We ended up with this beautiful hybrid atomaton that solves the general navigation problem. And it had all these cool things in it. Now, the problem is that, after we have solved the general navigation problem i said, but it doesn't work. It was a kind of annoying to be completely honest and today I want to make it work by dealing with some of the practical considerations that we really have to, to think about. the first is that we have this notion of XO everywhere. Now, its hard to see, but this is the distance. Or the point where the obstacle is. Well, obstacles aren't points. And it's not entirely, clear how we should translate these, real world obstacles that aren't points, into something that we can deal with here. The other is what I call fat guards. Here for instance, we're saying that the distance to the obstacle should be exactly equal to delta. Well We're never going to be exactly = to delta, because sensors are noisy. So what we need to do is, we need to say, you know what? The distance is delta + -epsilon. So we basically just need to just fact ta fi the guards, make them larger. So that instead of switching exactly when we're at the distance delta, we're building some slack into the system. [INAUDIBLE]. And then, I have a third bullet here, that I'm calling tweak, tweak, tweak. And the point with that one, is that, even if you have dealt with non point obstacles. And we have fat a fi our goal, guards. There are parameters. There are things like, CGTG. Which is the coefficient in front of the goal to goal behavior. We have things like, delta and epsilons. And there are all these Parameters that we have chosen. That, mathematically, they're all fine. But, in practice, there is no way out of the fact that you need to test, test, test, and tweak your parameters. And this is, in some sense, why robotics is so hard. And that's, how do you actually transition from your beautiful theoretical design, into something that works on the actual robots. Well, lets start with obstacles that aren't points. Green ball is the robot, red thingy is the obstacle, it's not a point. Now the first thing to note is that almost all actual sensors they're really the return points. Point [UNKNOWN], laser scaners, Infrared, ultrasonic sensors, all of them measure distances to things in certain directions. So, here are the points that I'm actually detecting on this obstacle. So now the question is, how do I actually deal with this situation? Where I have not one obstacle, where I have one obstacle but for the purpose of robot these are let's see, 1, 2, 3, 4, 5, 6 obstacle points. So, I have 6 points all of a sudden. Then I somehow need to deal with. So how do I do that. Well, We have some options. One options is, you know what? I'm really not interested in driving into this obstacle, so, the point in my algorithm that I'm going to care about, is simply the closest obstacle. In this case, it's this point, right? So, I'm simply going to say that xo is there, that's actually not bad, it's not a bad idea at all and then this is supposed to be straight line. you avoid obstacle would simply take me in this direction, just straight away from the closest point. That's not bad at all. But you know what, we have all this other information. Why don't we take that information into account a little bit more? So, another option would be to, weigh and add obstacle vectors together, depending on the distances. Right so, here it's closer, so I'm going to get more in this direction. And I'm kind fo far away so I'm going to get little in that direction. And then I'm going to weigh these together and maybe, get something out like this. That's better. So, there are different ways of weighing them. Let's say that I get these weighed or scaled obstacle vectors. And then my obstacle avoidance is simply going to be some scaled version, or weighted and scaled version of that. So this would be, U avoid obstacle now. And what you now need to do, to find x obstacle which we need, is to backtrack this thing, and say that this point here, would be x o. Now x o is not necessarily a point that we're measuring now. It's the scaled and weighted version of the other points but, this is a much better way of Of doing.Now the last thing I should point out this you know what , you should weigh these things depending on the distance.But then you should also weigh depending on the direction of travel, [COUGH] excuse me and what do I mean by that.Well you know what, if I'm really on my way In this direction [NOISE]. What do I care about obstacles behind me. Why should I care about that. I really shouldn't right? So, what I really want to do is weigh it also based on the direction of travel and in that case I would get a weighted obstacle avoidance vector out like this. So this is almost a I would say the best way of doing it. And that's in fact how we're going to do it. Now, the last thing I want to point out, though, you know, there's another option. I should be able to collect all the points I'm getting, building a map of it, so here is the obstacle service. And then, you know what? Instead of just dealing with the questions, like you know, sliding, or snow sliding. Maybe I can, plan my way around this obstacle. Now, what I want to point out , this, in this class, we don't say things like most bestest, because it's grammatical nonsense. we stay with grammatically correct things, which means that Ultra4 is out. what I really want to say is that building maps is an entirely different type of topic, and all that we are learning in this class is still very much applicable. So, I just want to point out that there are ways of building maps and then planning in those maps and then you're goal to goal behavior, for instance, wouldn't aim at the goal point but aim at following planned path based on these obstacle maps. So want to point out option 4 but its really not part of what we're going to pursue in, in the class. Now the last thing or did the second thing I said is we need to allow for fat guards and this is because no sensor is perfect, no actuator is perfect. Robots aren't prefect, right? So if I have this as my navigation hybrid automaton, when I'm doing f1 for some reason until g is negative, then I'm doing f2. And then when g becomes positive I'm doing f1 again. This is not sufficiently fat. Because I may end up actually switching a lot, I may do C note for instance or I may not but, the point is that what I really should do is replace these guys with this, right? Instead of saying G less than 0, I should say G less than negative epsilon. And instead of saying g positive, I should say g greater than epsilon. so Instead of having this as my switching surface, I'm actually building this little corridor here where I'm saying, I'm going to use f1 until I've gone through the entire corridor and so here's f1. And then I'm going to use f2 until I've gone through that corridor. And this factification not only reduces chattering but it also allows us to switch not when we're exactly delta away from an ob, obstacle but in somewhere delta plus minus epsilon. So always build fat guards as a practical precaution against the fact that de, deployed real world is not as clean as the theoretical world on my powerpoint slides. And then, like I said, the final advice, when it comes to practical considerations, is even though you have built a beautiful hybrid automotan, you've thought about everything, you have dealt with practical considerations and that you deal with point obstacles or non point obstacles as susceptible points since [UNKNOWN]. you are using sufficiently [UNKNOWN] guards, you still have to tweak, tweak, tweak. You have to test these parameters. You have to do it over and over again and Like I said, this is what makes robotics hard and why it's a little frustrating at times, but at the end of it, it's also what makes it satisfying when you get it right. So what I'm going to do in the next lecture is not talk at you or to you at all. Instead, what we are going to do is to actually going to build this system that we now have and tweak parameters until we are satisfied with our glorious, great, unifying navigation system.
