WEBVTT 00:00.110 --> 00:03.950 To continue studying the features offered by the TF2 Library. 00:04.070 --> 00:10.160 In this lesson, we will explore some tools and nodes that are already developed and available in this 00:10.160 --> 00:17.060 library, offering additional analytical functionalities for the use and management of reference frames. 00:17.360 --> 00:22.100 To use these tools, let's start by launching the visualization of the robot in our office. 00:22.310 --> 00:25.790 So let's open a new terminal and go to the workspace. 00:25.820 --> 00:33.080 Here, let's source the file setup bash and then let's start the robot visualization in our VS. 00:33.320 --> 00:39.290 So let's launch from the Arduino bot description package. 00:39.320 --> 00:41.900 The display dot launch. 00:42.630 --> 00:45.960 So this will enable the visualization in. 00:47.310 --> 00:54.480 And now that we can correctly visualize the robot and the frames, we can use a node that is available 00:54.480 --> 01:01.780 in the TF2 library that allows us to graphically visualize the frame tree and also its connections. 01:01.800 --> 01:08.610 So if we split a terminal, so let's open a new terminal and we take a look at the list of the currently 01:08.610 --> 01:18.060 available topic in Ros2 with the command Ros2 topic list, we can see that among these topics there 01:18.060 --> 01:26.610 are DTF where the dynamic transformations are published and the TF static topic where the static transformation 01:26.610 --> 01:27.540 and published. 01:27.900 --> 01:32.070 Let's see which nodes are currently interacting with these two topics. 01:32.070 --> 01:36.980 So who is publishing this information that is then visualized in Arviz? 01:36.990 --> 01:41.520 We can use the command Ros2 Topic info. 01:41.520 --> 01:51.480 For example, let's take a look at the topic TF and let's also use the verbose flag to see the names 01:51.480 --> 01:52.560 of the nodes. 01:52.860 --> 01:59.670 So now for example, we can see that there is only one node that is publishing and this is exactly the 01:59.670 --> 02:01.380 robot estate publisher node. 02:01.380 --> 02:08.850 So the one that was reading the Urdf model of our robot was interpreting it and is publishing the respective 02:08.880 --> 02:10.020 transformations. 02:11.370 --> 02:17.310 We can also see, which are the messages that currently the robot estate publisher is publishing within 02:17.310 --> 02:25.780 the TF and the TF static topic and we can use the command Ros2 topic echo. 02:26.190 --> 02:29.640 And for example, let's read for the moment the TF topic. 02:30.360 --> 02:32.550 Let's make this one a little bigger. 02:36.360 --> 02:42.360 And so in this topic, we can see that constantly are published messages that define the position of 02:42.360 --> 02:45.690 each reference frame relative to the previous one. 02:45.780 --> 02:49.290 So let's stop this one for a moment for a little bit. 02:49.320 --> 02:52.400 In order to examine the structure of these messages. 02:52.410 --> 02:58.740 So each message that is published within the topic contains a list of transformation. 02:58.740 --> 03:01.680 So here it begins, a new message. 03:01.890 --> 03:05.310 So as we can see, it begins with an header. 03:05.310 --> 03:07.710 And so it has a list of headers. 03:07.710 --> 03:09.960 So there is a list of transformation. 03:10.200 --> 03:17.670 For example, we can see this one that expresses the transformation between the base plate and the base 03:17.670 --> 03:18.330 link. 03:18.330 --> 03:22.320 And so we can also see that here there are the rotation values. 03:22.320 --> 03:30.060 So this is basically the rotation matrix that expresses how the base plate is oriented with respect 03:30.060 --> 03:35.040 to the base link and also the translation that is the translation vector. 03:35.810 --> 03:39.470 We can see that the rotation that is representing the orientation. 03:39.470 --> 03:45.580 So this one has four components that are X, Y, Z, and W. 03:45.590 --> 03:53.480 So actually, this is because the convention that is used in TF2 library and in general in Ros2 is expressing 03:53.480 --> 03:57.920 the orientation of any two reference frames using the quaternion. 03:57.920 --> 04:01.370 And this is a topic that we will study later on in the course. 04:01.790 --> 04:09.260 For the moment, let's use another node from the TF2 Tools library that allows us to graphically visualize 04:09.260 --> 04:12.890 the frames and their connection in a tree structure. 04:13.280 --> 04:20.300 So let's use the command Ros to run and from the TF2 Tools library. 04:20.300 --> 04:24.130 Let's start the node that is called view frames. 04:24.140 --> 04:31.040 So let's press enter and this node will listen for all the frames that are published within the TF and 04:31.040 --> 04:38.370 TF static topic for a few seconds and will generate a graph that contains all the frames and also their 04:38.370 --> 04:39.330 connections. 04:39.330 --> 04:44.400 So once it finished we can see that it created two new files. 04:44.730 --> 04:47.970 So it created these two files. 04:47.970 --> 04:51.810 And also we can take a look at how this file looks likes. 04:51.810 --> 04:54.870 So let's use the evidence. 04:55.080 --> 04:59.820 And as this is a PDF, let's open it in this file. 04:59.820 --> 05:01.620 Let's zoom a little bit back. 05:01.650 --> 05:08.520 We have a simple and immediate and intuitive visualization of all the frames that are currently available 05:08.520 --> 05:09.120 in Ros. 05:09.330 --> 05:14.820 So all the frames that are published both in the TF and in the TF static topic. 05:15.880 --> 05:18.640 For example, we can see that the base link. 05:18.640 --> 05:26.620 So this one is connected to the base plate and that the note that is in charge of publishing this transformation 05:26.620 --> 05:30.130 is publishing it with a rate of ten hertz. 05:30.130 --> 05:33.450 So this is the average rate at which they are published. 05:33.490 --> 05:39.490 Also, we can see that, for example, the transformation between the word and the base link is published 05:39.490 --> 05:42.640 with an incredibly high average rate. 05:42.640 --> 05:46.450 This is because actually this is a static transform. 05:46.450 --> 05:53.500 So as you will see, all the transform that are published in the static topic in this graph will have 05:53.500 --> 05:55.750 an average rate of 10,000. 05:55.930 --> 06:02.950 Let's close this PDF and now let's take a look to another useful tool that is available in the TF2 library 06:02.950 --> 06:04.510 that is called Echo. 06:05.340 --> 06:12.310 This allows us to display the transformation matrix between any two frames in the Tree of Connections. 06:12.330 --> 06:16.470 So to launch it, let's use the command Ros to run. 06:16.680 --> 06:28.140 And from the TF2 Ros package, let's start the TF to echo Node and we need to provide to this node the 06:28.140 --> 06:33.420 names of the two reference frame from which we want to know the transformation matrix. 06:33.420 --> 06:41.850 For example, we want the one from the base link to the horizontal arm. 06:42.150 --> 06:43.980 So let's press enter. 06:43.980 --> 06:50.850 And here in the terminal we can see that the translation and the rotation values of the transformation 06:50.850 --> 06:56.880 between the two frames that we have indicated are continuously printed in the terminal at our regular 06:56.880 --> 06:58.080 time intervals. 06:58.080 --> 07:00.240 And also we can see that the rotation. 07:00.240 --> 07:09.100 So here the rotation is expressed in terms of quaternion, in terms of rpy, both in radians and in 07:09.100 --> 07:12.760 degrees, if we take a look again. 07:13.090 --> 07:15.700 So if we open again the pdf. 07:16.940 --> 07:18.530 That was created. 07:20.280 --> 07:23.610 So this one with Evans. 07:24.000 --> 07:25.770 And let's open the PDF. 07:26.640 --> 07:31.170 We can see that the two frames from which we asked to transform from. 07:31.170 --> 07:38.730 So basically the base link and the horizontal arm, this one and this one are not directly connected 07:38.730 --> 07:40.200 by a transformation. 07:40.500 --> 07:42.270 However, there is a chain. 07:42.480 --> 07:46.820 There is a chain that is connecting the base link and the horizontal arm. 07:46.830 --> 07:52.770 And this chain passes through the base plate, the forward drive arm, and then reaches the horizontal 07:52.770 --> 07:53.070 arm. 07:54.530 --> 08:00.770 This is possible because behind the scenes, the TF2 library and also all the necessary calculations 08:00.770 --> 08:07.490 to compose intermediate transformation matrices and returns the resulting transformation matrix. 08:08.520 --> 08:14.190 As long as there is a chain or a sequence of transformation matrices that connects one reference frame 08:14.190 --> 08:19.650 to another, the TF2 library can calculate the resulting transformation matrix. 08:19.860 --> 08:27.150 So basically, to solve the forward kinematic problem, it becomes as simple as running again the command 08:27.600 --> 08:36.780 TF2 ACO, and this time asking for the transformation between the world reference frame and the low 08:38.940 --> 08:40.810 support reference frame. 08:40.830 --> 08:46.950 So as we press enter, so with this, basically we are solving the forward kinematic problem. 08:46.950 --> 08:50.340 And here we can also see the full transformation matrix. 08:50.340 --> 08:57.120 So this is the rotation, this is the translation vector and this is the full transformation matrix. 08:58.260 --> 09:02.940 Also, we can see that if we take the joint state publisher. 09:02.940 --> 09:05.370 So let's take the joint state publisher. 09:05.730 --> 09:10.010 Let's keep this node running and let's move a little bit. 09:10.020 --> 09:12.330 The robot with the joint state publisher. 09:12.570 --> 09:19.560 We can see that while we move the robot, the values of the transformation are changing and so are constantly 09:19.560 --> 09:20.430 update. 09:20.610 --> 09:28.710 And so if we move the position of the joints, we are moving, of course, the position of the gripper. 09:28.710 --> 09:31.560 And so the transformation is updated. 09:31.560 --> 09:37.590 And so the transformation matrix is recalculated with the new values of the joint angles. 09:38.790 --> 09:45.150 In this way with a bit of mathematics and the help of the TF2 library, we have solved the problem of 09:45.150 --> 09:50.940 the forward kinematics and we can determine at any moment in time the position of the gripper of the 09:50.940 --> 09:52.290 robot in the space.