WEBVTT 00:00.140 --> 00:01.430 Hi robotic enthusiast. 00:01.610 --> 00:08.960 Finally, we now have a real manipulator robot in the simulated environment of gazebo that we can control 00:08.960 --> 00:11.660 using the Ros2 Control library. 00:12.380 --> 00:18.260 However, with the functionalities developed so far in the course, we can only individually control 00:18.260 --> 00:19.820 the robot's joint. 00:20.400 --> 00:27.600 With such an activation system, it becomes extremely difficult to perform complex movements that require 00:27.600 --> 00:33.900 the actuation and the coordination of multiple joints, for example, for picking place applications. 00:34.490 --> 00:41.360 In this section, we will study the mathematics that allows us to control and move the robot without 00:41.390 --> 00:47.150 worrying about the angle of its joint, but focusing only on the position and the orientation of the 00:47.150 --> 00:48.210 robot's gripper. 00:48.230 --> 00:55.250 In the three dimensional space, let me give you an example to justify the study of some mathematics 00:55.250 --> 01:01.760 in this section of the course, specifically a branch of the mathematics called kinematics and will 01:01.820 --> 01:04.400 help us to solve robotics problems. 01:05.180 --> 01:06.610 With the current system. 01:06.620 --> 01:13.730 Actually, we are already able to move the robot by directly and separately controlling its joints. 01:14.300 --> 01:20.360 Now let's assume that we want to use this actuation system so this logic to grasp an object that is 01:20.360 --> 01:22.880 located within the robot's workspace. 01:23.830 --> 01:30.070 To complete this simple operation, we will need to coordinate the movement of the robot's joint to 01:30.070 --> 01:35.110 bring the gripper to the desired position from where it is possible to grasp the object. 01:35.530 --> 01:41.620 Additionally, we also need to coordinate the opening and closing of the gripper to grasp the object. 01:42.210 --> 01:49.260 Indeed, this is a very complex operation, even for a human operator, as it is not trivial to understand 01:49.290 --> 01:54.600 how the robot's gripper is going to move in response to a common sense to its joints. 01:54.990 --> 02:01.860 I invite you to try moving the slider yourself to bring the robot's gripper to a specific position. 02:02.550 --> 02:05.880 But why is this operation so complex? 02:06.620 --> 02:12.770 This happened because the relationship between the cause, which is the rotation of a joint and the 02:12.770 --> 02:19.310 effect which is the movement of the gripper in the space, is a complex relationship and we are not 02:19.310 --> 02:21.970 capable of processing it in real time. 02:21.980 --> 02:28.910 That is, we are not able to calculate in real time whether by moving the joint to, for example, it 02:28.910 --> 02:32.030 will cause a movement of the gripper up or down. 02:32.270 --> 02:37.190 Nor we can determine with certainty how many centimeters it will move. 02:38.020 --> 02:44.170 Moreover, this relationship becomes even more complicated as we increase the number of joints of the 02:44.170 --> 02:44.860 robot. 02:44.950 --> 02:51.430 In this case, it becomes even more complex to understand how the robot's gripper is going to move when 02:51.430 --> 02:53.500 one of its joint rotates. 02:54.400 --> 02:55.300 This also happen? 02:55.300 --> 03:00.800 Because in our minds we are all we used to think in Cartesian frames. 03:00.820 --> 03:07.540 That is, we are used to think about how to move the gripper forward upward, right or left. 03:07.900 --> 03:14.050 However, the overall motion of the gripper in space is due to the composition of the motion of each 03:14.080 --> 03:18.220 arm of the robot that is, of each rotation of each joint. 03:19.240 --> 03:26.320 Fortunately, this relationship is defined by a series of mathematical equations that allows us to relate 03:26.320 --> 03:32.620 the motion of each joint of the robot to the motion of the gripper, and vice versa to relate the motion 03:32.620 --> 03:35.620 of the gripper to the joints that produced it. 03:36.740 --> 03:43.220 This branch of mechanics and mathematics is called kinematics, which is the study of the motion of 03:43.220 --> 03:50.420 a body in the space and deals with calculating the position, velocity and acceleration of a body in 03:50.420 --> 03:52.160 a specific reference frame. 03:53.180 --> 03:55.970 In robotics for manipulator robot. 03:56.000 --> 04:00.200 We use this tool, this kinematic equation for two part process. 04:00.990 --> 04:07.530 The first one is to determine the position of the gripper in the space based on the angle of each joint, 04:07.530 --> 04:10.950 and thus based on the position of each arm. 04:11.760 --> 04:19.260 In this case, we are talking about forward kinematics, referring to the system of equations that specify 04:19.260 --> 04:20.370 this relationship. 04:21.160 --> 04:22.870 For this mathematical problem. 04:22.870 --> 04:28.510 The values of the angle of each joint are known, and we want to calculate the value of the position 04:28.510 --> 04:29.950 of the gripper in the space. 04:30.760 --> 04:37.960 The second purpose for which we use kinematics in robotics manipulator is to determine the angle of 04:37.960 --> 04:39.490 each joint of the robot. 04:39.580 --> 04:46.540 Knowing the position of the gripper in the space, in this case we are talking about inverse kinematics. 04:46.540 --> 04:52.300 And in this mathematical problem we know the position of the gripper in Cartesian coordinates. 04:52.300 --> 04:58.060 And from this we want to know the value of each of the joint angles that have brought the gripper to 04:58.090 --> 04:59.140 that position. 04:59.970 --> 05:07.440 Once we have this tool in our robotics toolbox, we can use it to control the robot in a simpler and 05:07.440 --> 05:12.330 more user friendly way by directly moving the gripper in the Cartesian space. 05:13.080 --> 05:15.120 Automatically the mathematics. 05:15.120 --> 05:22.170 And so the kinematics will calculate the angle by which each joint must rotate to ensure that their 05:22.170 --> 05:26.760 coordinated motion brings the gripper in the desired position.