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OK.

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In this material, we will try to apply this transformation mattresses, which contains also rotation

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mattresses inside and also, you know, other angles, ends like this into practice by this video,

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I would like to show you how much important and how useful can be the concepts that we have learned

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in this chapter.

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So let's start for in this tutorial.

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I will try to I will try to apply what we have learned or simulate the environment in ROS.

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As you know, I don't know whether you know or not, but it is very important for you to know or else

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or rules because it is used in robotics very widely.

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So you have to know this.

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This is not an option, but you have to know this if you want to simulate or coordinate robots, or

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how can I say or you want to write software for them?

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You have to know this because it contains many of the tools that make your job easier in order to write

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software for robots or programmed them.

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So that's why you have to learn this during the lesson.

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I will apply some concepts in our rules, but I will not teach you the rules.

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So you have to learn it by yourself because otherwise the course would be very long.

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You can learn it in C++, or you can learn it in Python, but I recommend you to learn in Python because

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C++ can be a bit difficult.

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But if you know C++, it would also be good because indeed you can apply different modes in our different

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programming languages and you can communicate between these nodes.

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So, OK, without further ado, let's start to see what first we will do, so we will simulate our program

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inside gazebo.

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So let's first start our environment, or let's start our environment in gazebo.

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So Roseland, first, let me source the environment because this is very important if you don't know

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what I am doing here.

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You can just watch and see that.

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How important is that?

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Otherwise, if you want to know, you can learn or else.

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But the learning curve of arroyos is steep, so it's a bit difficult.

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So I would recommend you to learn the process while also watching this course and programs.

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So let's start first.

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Let's source the environment below.

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Set up the marsh, OK, then roast lunch.

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I think you have to be here and tim about three to two.

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I will use Turtle about three in the simulation.

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OK.

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T. Both three, you have to and it is a start robot, not lunch.

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But OK, let me first launch the environment.

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This will launch otherwise total about three months.

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Three Gazebo.

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So Turtle bought three books, bought lunch.

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I will send you or I will upload this launch file and other programs into GitHub so you can download

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it from there and use.

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OK, first, let's see our environment.

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OK, so we have given a robot, which is Turtle Bot three.

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This is a very famous robot.

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You can what it is differential drive robot.

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And this is our object.

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So what's our purpose?

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OK, this is our object.

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So what's our purpose?

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Our purpose is to make turtle bots.

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Three Robot this robot to follow this object.

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This object is dynamic.

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I mean, we can change its position and we want the turtle bots three to follow this object.

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So if I put it here, it's come to this point.

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If I put it here, it come to this point.

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Yeah, this can be seen a bit stupid, but it's very important because this is called go to goal behavior

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for robots.

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What the what do I mean by go to goal behavior?

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So in many tasks, for example, in navigation or for searching something or doing something very different,

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I don't know.

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We have some.

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Coordinates and we want the robot to go this.

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This is gold, go to gold.

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So go to gold, be here.

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We just make robot to go to that point, so it simulates that behavior.

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So let's start.

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And the first let me see in presentation what we want to do.

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OK, let's start with this one.

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So we are given our robot, which is circle and square.

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Our object, what we want for what we will do.

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First, we will assign transformations.

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Both of these transformations or excuse me, not transformations, but first coordinate frames.

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As we have said before, we first have to assign frames for our objects that we are interested in this

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case, our robot and our object.

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We assign the frames in order to do relations between them.

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OK.

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So communicate between these frames and know the position and orientation of objects relative to the

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robot and the robot relative to object.

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OK, then what we want to do, we want we want to find the which is vector between the centers of these

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two frames and which is also the distance between the robot and the object.

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And also, we want to find Tita why we want to find Peter, because our purpose is first to rotate,

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make the orientation of the robot the same as the object's current frame.

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And so we want rotated degrees in order to face up with the object.

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OK.

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And then what?

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We want to do it, then we want to apply for the velocity to our robot in order to go that point.

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So it's indeed a very easy concept.

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So what we are doing.

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First, we are correcting our heading angle, which is TITA.

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So if our robot watches these side, I mean, if our robot's heading is to decide and the object is

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on this side, we first want our robot to watch to have the same orientation with the object.

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And then we apply forward velocity in order to account for the distance and come near the object.

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So how we will do this task first, we will separate our D vector, or we will project our vector D

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onto X and Y axis.

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OK, not z axis.

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Because as you know, our robot is not a quadcopter or a drone.

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It doesn't move in

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that dimension.

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It moves only in X and Y because it's a differential drive.

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It's not flying.

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So we have only two dimensions, so we will project on the X, a. y.

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And if you remember from our tutorials how we will fund T to A..

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So let's see for in order to find Tita Vivo, we use our time to function.

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OK.

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Item to function.

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Um, well, I have a little talk about this one because we have learned it before, so we will use it

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on to function and we are given from trigonometry.

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You know, we are given d y, d x.

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We can find this tita from other countries, but for some reasons we will use it.

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And two, I have mentioned these reasons in previous tutorials.

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If you want to remember or repeat, you can watch this trial again.

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OK.

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We are funding to our heading NGOs, and we rotate our robot by to degrees in order to face up with

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the AI with our object.

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Then how we will calculate deep.

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It's very easy from trigonometry.

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You know, we will find the this is models of the Vector D. So we are taking a modest more of it, and

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this equals the square root of the X squared plus d y squared.

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This is our formulas that we need to apply then.

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OK, let's come to now.

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Uh, the coding part people.

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I wrote the code before and this I will send it.

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I will attach GitHub link to this so you can download the code and you can analyze by yourself.

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OK.

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First of all, uh, for this one, we will use this sets our interpreter.

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So Python interpreter, because as you know, Python two, there's Python two or Python three and like

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that.

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So we will use Python to.

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OK, so we will import Ross Pay.

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Um, as I said before, I will not explain all of this.

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I will just explain what we have used here, so we will use the n t f to Ross.

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What does t f to t f to is very important in Ross.

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What you do is it means relations creates relations between different frames and also the coke leads

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these homogeneous transformation matriz or not, it causes homogeneous transformation methods, but

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it calculates something like that.

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I mean, it calculates orientation and the distance between these two points.

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So by using T f two Ross, you can find the relation between two frames, which we need in order to

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calculate our T2 and D.

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OK.

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We will use t f conversions.

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I don't know whether we will use.

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I think we will not use OK.

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Excuse me, it's something that we will not need in this case, but we will.

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Let me explain for what is the purpose of this and how we can use this library in this case.

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We will use it if we have given or angles we will use to convert it to cotton use.

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And I think you remember the reasons why we use Quaternary is instead of angles.

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OK.

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Also additionally, Alia's angles are quite earnings are applied to inside are also that's why also

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we are converting everything else to cotton spunk and then we will use geometry messages.

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You will see why we are importing this model or this message.

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OK, then we will use gazebo messages for models.

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This and you will see y will need also.

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OK, let's start from in.

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First of all, we need our mode.

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Then we subscribe to gazebo models, states where we are subs, why we are subscribing this.

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Let's see.

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OK.

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Ross topic?

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Let's see what's our first of all our topics?

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Let's see our topics.

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As you can see, these are topics that are published or subscribe.

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You can subscribe or publish to these topics.

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These are the topics created by this software.

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I'm in the process.

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So, OK, uh, let's see.

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We need here.

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A gazebo model states why we need gazebo models this.

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We need that in order to get the position of our object relative to the autumn frame.

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Autumn frame in this case is like world frame.

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Yeah, yeah.

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There can be some cases in which Adam Frame is different from world frame, and this is changing depending

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on map.

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However, in this case, autumn frame is the same as our world frame.

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As you can see, this is our inertial frame, as we have said before, and these two frames, as you

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can see these frame, this frame is our local frames.

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First is belong to the robot and the second belongs to the object.

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And we want to.

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What we want to do is, first of all, we want to find the object's location relative to the ordem frame

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located so relative to these inertial frame real world frame.

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So that's why we are subscribing to gazebo models, states, gazebo model states.

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As you can see, it lets rules, topic echo, uh, slash gazebo model states gazebo model.

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This Stopit gazebo models this, as you can see, show us the objects on the roof on our Um, how can

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I say on our environment?

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As you can see, this is our box.

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As you can see, this is total about three Berger.

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This is our robot and it gives us their position and orientation.

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This is position and orientation of unit box.

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This is depending on index because the second or first index is four units bookstore.

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The first will be for the position and orientation of unit box.

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And the second index is our robot and this is for our robot.

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Also, it gives us twist.

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Twist Twist is a combination of linear and angular velocity of our objects.

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In this case, we will not need that.

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We will just need the position and orientation of the object.

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We will need only to find the position orientation of objects because turtle bolts three itself.

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We can get its position and orientation from by subscribing, it's all on topic, we will say it.

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Uh, no.

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OK, so we subscribed to this topic.

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And as you can see, we have called back for our subscribers.

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This is called our handle object posts, so we are going to explain this one.

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And this is our callback function, the handle object pause.

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And this accepts message from this topic.

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This is the message that published by this model states topics topic, and we subscribe this topic for

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this message.

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So, OK, first of all, we get are we.

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We get the name of the objects in our environment and we find index of the unit books because we just

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need the unit books object to find its position and orientation.

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So we get its indexed.

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And from this index, we find it's positive x y position.

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OK.

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And this is it's orientation x, y z and W.

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This is in what term you?

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OK.

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This is in cocoa attorney.

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Be careful.

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It is not in other angles, but it's in quaternary.

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OK, so then what?

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What we are doing, then we are publishing this frame.

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So what do I mean by publishing?

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So we get the orientation of this object and position of this object relative to other frame.

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So what we are doing, we are doing what we are doing.

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We are creating this frame as you can see this local frame and publish it.

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So we broadcast it so other objects can see this frame and calculate their position and orientation

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relative to this frame.

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For example, if Turtle bought, our robot wants to find its position and orientation relative to this

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object, it will listen to this frame.

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So this broadcast of frame?

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OK, its local frame, and it will calculate the difference between orientation and position in its,

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uh, the object's local frame and the robot's local frame.

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You know, OK, if you want to understand clearly this because surely I just assume that you know something

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about it, because as as I have said before, I don't want to explain all of these things here.

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I just want to show you how important it is that you can go to the t f to transformation in Ross tutorials,

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official stores, and they have beginner explanation of this.

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You can understand from there, and you can watch again this tutorial and try to understand the code

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by running it yourself.

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OK, then we are creating our frame.

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As you can see, we are creating our frame here and then we will send this frame what we are doing here.

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We first put the stamp of our frame.

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So this frame is taken in.

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This time this is needed for various purposes.

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This can be synchronisation or some other things that it is not needed in this case, but they will

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be needed in something in different situations.

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So we just append the time to it, stamp different stamp of the frame.

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Then this is frame.

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This shows us what is the current frame?

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OK.

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So, um, for example, what do I mean?

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The pound frame?

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We are getting the position and orientation of this frame, OK, but it is relative to what it can be

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relative to our robot.

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It can be relative to some other fixed frame.

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But in this case, this is relative to, I mean, the position and orientation we get by subscribing

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to module states.

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Topic is relative to ordem frame.

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So relative to our world frame, OK?

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So that's why we are writing it here, and this is our child frame.

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What's our child frame?

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Child frame is the local frame of our object.

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We are just so that's why we are giving the name unit box the name of the object to as a child frame.

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Then we are, uh, setting it's x y z, uh, coordinates.

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As you can see there, we put that zero point zero because we are in two dimension.

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Yeah, it's in three dimension if you watch, but the object moves into dimension.

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The robot is also moved to dimension in x y plane, not in that plane because it's not a quadcopter

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drone.

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On something else, if you were controlling a plane, you would then use the zip also.

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And we said also our orientation, as you can see in Quattrone and we then sent this frame or we are

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broadcasting this frame in all the other frames and other objects can listen to this frame and calculate

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their position and orientation relative to this frame.

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OK.

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So this is the final code.

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The distrust by spin is for.

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It is just like, um, just like a loop.

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So our program doesn't finish here and continues until we stop it.

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So let's not write the code for listeners.

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What do I mean listeners saw in the previous code?

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We have broadcasted this frame.

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OK, this local frame now our turtle bought our robot have to listen to this frame and calculate its

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relative, its relative position and orientation to this one.

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OK?

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With respect to local frame of objects.

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So by doing that, we will get our D vector.

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OK?

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We will get our D vector.

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Also, the X, the Y we have from here, I will.

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I can.

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I mean, we will get the X D Y from where we can find Peter and the absolute value of the.

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OK, let's do that.

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So what we are doing here is let's start first.

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We need our load.

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OK.

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This is buffer transformation buffer.

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This is needed in order to get our transformations and listen to them.

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OK.

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And this is listener which we'll use in order to lessen our transformations.

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OK, then we are publishing the C and D.

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Well, what is C and D?

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Will C and D?

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Well, this is common velocity.

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This means common velocity.

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And this message part is twist.

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So we will command velocity.

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I mean, angular velocity and linear velocity to our robot in order to go to that object.

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OK.

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So let's calculate, um, let's first look up transform.

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So we are looking up for transforms from which to reach.

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OK.

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This is very important.

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We want transformation from the frame of our object.

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Let's, uh, from frame of our robot to frame of our object.

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As you can see it, this is we want to find this the.

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Yeah.

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So we have to look for the transforms from robot's frame to objects frame.

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And we are doing that here from Bayes footprint.

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What's based footprint based footprint is local frame of our robot.

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This is given default to this, uh, robot.

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OK?

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The programmers of this robot created that frame.

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It is attached to the our robot, so it is based footprint is local frame of this robot.

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And there we go.

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If we want transformation from base footprint to object.

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OK.

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This is our object.

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Uh, frame.

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OK.

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Um, and then what we are doing after we get this transformation, we are creating new message for twist.

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Our twist message, new message, twist message.

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Then we are setting our angular velocity and our linear velocity.

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Our angle of velocity is proportional as you can see it.

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Or it's equal, let's say, equals the Method eight to as you can see, we calculated by using Item

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two and we get from D, Y and the X by calculating the 8m to we get our T to and we assign it to our

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angular velocity and our, um, linear velocity is we equals it to the distance between these two objects.

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So we are how we calculate by calculating D x squared plus d was squared and we find the square root.

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And this gives us distance.

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However, why we are doing here and we are assigning maximum velocity.

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Maximillian University, why we are doing that because as distance increase.

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Uses our linear velocity increases, and if the distance is too big, it calls some anomalies in the,

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you know, the robot becomes very fast, so it drifts.

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And instead of reaching to the given desired point, it just does something.

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It just drifts and because its velocity is too much.

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So that's why it creates problems.

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So we try to keep its velocity in some range.

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OK, so that's why we are finding minimum of this velocity and between our maximum linear velocity.

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After that, we just publish this comment, this velocity to our robot.

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OK.

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After speaking that much?

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OK, let's create our launch file.

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So we launch here our two nodes, which is our first of all, its object to broadcaster.

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By doing that, we broadcast our local frame of our object.

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00:26:06,240 --> 00:26:12,120
And by doing that, we listen and by launching team bots to lease their node.

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We listened to this transformation and calculated desired heading angle and distance between this object.

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00:26:19,980 --> 00:26:21,930
OK, let's try to run then.

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00:26:22,920 --> 00:26:23,820
Let's do.

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00:26:24,210 --> 00:26:26,010
I hope it will work.

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00:26:26,760 --> 00:26:27,330
OK.

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00:26:27,870 --> 00:26:29,280
Indeed, I have checked before.

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00:26:29,280 --> 00:26:31,320
Surely roast lunch.

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00:26:31,950 --> 00:26:33,750
Let's do that.

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00:26:34,260 --> 00:26:36,000
So what was OK?

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00:26:36,450 --> 00:26:42,160
T both three t f two and the start robot launch?

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00:26:42,310 --> 00:26:52,180
OK, let's bring our here and let's run this book, but let's see what's happening.

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00:26:52,200 --> 00:26:52,710
OK?

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00:26:53,040 --> 00:26:58,080
As you can see, our robot now comes to object and it touches and stop it.

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So if you make it like that, OK, as you can see it, come to this.

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00:27:03,210 --> 00:27:14,540
If you make it in this way, it will all and come closer to object by just calculating the, um uh,

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relative orientation and distance between this object.

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As you can see, this is how important to understand these transformations.

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I mean, the um homogeneous transformation matrix rotation matrix, ail or angles, Quattrone and angles.

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And this is a very simple example of it.

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We will use them as you will see, we will use them in our future left since very, very, very frequently

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00:27:43,650 --> 00:27:47,010
and they are needed in robotics very, very frequently.

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00:27:47,160 --> 00:27:56,030
And if you start to learn our OS or Ross, you will see that they are also used, um, you know, uh,

375
00:27:56,100 --> 00:28:03,190
very, very frequently in our office, in robot programming, because this is something like, um,

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00:28:03,420 --> 00:28:09,720
communication between they are, you know, they are like eyes of the robots and objects.

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00:28:09,720 --> 00:28:15,810
You know, based on these frames, they can calculate what's my position orientation relative this frame,

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00:28:15,810 --> 00:28:19,800
that frame and like that, OK?

379
00:28:20,340 --> 00:28:31,890
I hope that with that tutorial, you can understand how important for us to know the homogeneous transformation

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00:28:31,890 --> 00:28:36,420
mattresses, rotation, mattresses, aler angles, continuous and so on.

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I hope that I will see you in the next lesson.