We have a model of a robot, we know how the robot can get position information, in this case we used the wheel encoders but there are other ways we talked about compasses and accele accelerometers but the robot also needs to know what the world around. It looks like. And for that you need sensors. And we are not going to be spending too much time modeling different kinds of sensors, and see what is the difference between an infrared and an ultrasonic range sensor. Instead. We're going to come up with an abstraction that captures what a lot of different sensing modalities can do. And, it's going to be based on what's called the, the range sensor skirt. This is the standard sensor suite in a lot, on a lot of robots. And, it's basically a. Collection of sensors that are. The collection that is, gathered around the robot. That measures distances in different directions. So, infra red skirts, ultrasound. LIDAR, which are laser scanners. These are all examples of these range sensors. They're going to show up a lot. Now there are other standard external sensors of course, vision, or tactile sensors, we have bumpers or other ways of physically interacting with the world or "GPS" or I'm putting them in quotation because there are other ways of faking GPS. For instance, in my lab I'm using a motioning, or motion captioning system to pretend that I have GPS. But what we're going to do, mainly. It's assumed that we have this kind of setup. Where a skirt around the robot that can measure distances to, to other to things in the environment. And in fact, here is the Chipera It's a simulation of the Chipera. And the Chipera in this case, has a number of infrared sensors. And Well you see the cones, you have blue and red cones, and then you have red rectangles. The red rectangles are obstacles and what we're going to be able to do is measure the direction and distance to obstacles. So this is what type of information we're going to get out of these range-sensor skirts. over here on the right you see two pictures of the sensing modalities that we had on The self-driving car that was developed at Georgia Tech. And we have laser scanners and radar and vision. but the point is the skirt doesn't always have to be uniform or even homogeneous across the sensors. Here we have a skirt that is heterogeneous across different sensing modalities. But, roughly you have the same kind of abstraction for a car like this, as well as for. Hey, Chipera, little mobile differential drive, robot. Okay, so, that's fine, but we don't actually want to worry about particular sensors. We need to come up with an abstraction of this, sensor skirt, that, that makes sense, that we can reason about when we design our controller. So, what we're going to do is, we're going to do some, or perform what's called a disk abstract. Abstraction. So here's the robot, sitting here in the middle. around it are sensors. And in fact, if you look at this picture here, here are little infrared sensors. And in fact, here are ultrasonic sensors.You see that scattered around this robot are. It's a skirt of range censors. We're, they typically have an effective range, and we're going to extract that and say there is a disk around the robot, of a certain radius, where the robot can see what's going on, right, so this is this, this pinkish disk around the robot and it can detect obstacles that are. Around it. So the two red symbols there are the obstacles. What we can do is we can figure out how far away are the two obstacles. So, D1 is the distance to obstacle one, which is this guy. And this is obstacle two, well, okay. join with ratts of ensure and Pi one is the angle to that obstacle, similarly d2 is the distance to obstacle 2. Phi 2 is the angle to obstacle two. One thing to keep in mind though is that robot has its own coordinate system in the sense that this, if this is the x axis of the robot right now, then Pi one is measure relative to. The robot's x axis, so the robot's heading, right. So we need to take that into account if we want to know globally where the obstacles are. So let's do that. If you have that, and if you know our own pose, so we know x, y and Pi. Then since the measured headings to the obstacles. So this is Pi one which is measuring and we're measuring this relative to our orientation. Lets say that our orientation is this right. So here is phi and here is Pi two say, then of course the actual. direction to obstacle two is going to be Pi 2 plus Pi. So, what we could do, is we could take this into account and compute the global position's of these obstacles if we know where the robot is. So, for instance, the global position for obstacle one x1 and y1. Well, it's the position of the robot plus the distance to that obstacle times cosine and sine of this Pi 1 plus Pi term. So we actually know globally where the obstacles are if we know where The robot actually is. So this is an assumption we're going to make. We're going to assume that we know x, y and Pi. And as a corollary to that, we're going to assume that we know the position of obstacles around this in the environment. So that's the abstraction that we're going to be designing our controllers around. And I just want to show you a. And I'm using an example of this, this is known as the rendezvous problem in multi agent robotics, where you have lots of robots that are supposed to meet at the common location but they're not allowed to talk, they're not allowed to agree on where this would be by chatting instead they have to move in such a way that. They end up meeting in same location and one way of doing this is to assume you have a rain sensor disk around you and then when you see other robots in that disk instead of thinking of them as obsticles we think of them as buddies so what we are going to do is each robot is going to aim toward the center of gravity of all it's neighboors so everyone that is in that disk, Disk, and because of the disk assumption or disk abstraction we just talked about, we can actually compute where the center of gravi ty is of our neighbors. So here's an example of what this looks like. Every robot is shrinking down. Two, all the robots shrink down to meet at the same point, without any communication, simply by taking the disk around them, looking where are my neighbors in that disk, and now we know how to compute that. And, then, computing the center of gravity of my neighbors, and aiming towards said center of gravity. Okay, now we have a robot model. We have a model for figuring out how to know where the robot is, we have a model for how do we know where obstacles and things in environment are. Now we can use these things of course to actually start designing controllers, so that's what we're going to have to do next. I do want to point out though that the model The real encoder, and the disk abstraction. These are but an example of what you can do, and how you should make these kinds of abstractions. But for different kinds of robots, different types of models and abstractions may be appropriate.