WEBVTT 00:00.380 --> 00:08.300 The TF2 Library and Erdf model of our robot, where we define the reference frames and connected them 00:08.300 --> 00:13.770 through transformation matrices allowed us to solve the forward kinematics problem. 00:13.790 --> 00:19.370 In other words, they allowed us to know the position and the orientation of the robot's gripper at 00:19.370 --> 00:20.810 any given moment in time. 00:20.810 --> 00:24.770 Given the position and the angle of each joint of the robot. 00:25.640 --> 00:32.180 Now we are ready to face the opposite problem, which is defining the position and the orientation of 00:32.180 --> 00:36.230 the robot's gripper in space and calculating the joint angles. 00:36.260 --> 00:40.400 The motor position that brings the arm to the desired position. 00:40.880 --> 00:45.320 But first, let's recap why we need the inverse kinematics. 00:46.090 --> 00:46.600 Winning. 00:46.600 --> 00:53.020 One of the previous lessons we tried to grasp an object using only these sliders that move the joint 00:53.020 --> 00:53.770 separately. 00:53.800 --> 00:55.990 We encountered some difficulties. 00:56.110 --> 01:03.310 This was because we were trying to lower or raise the gripper or to move it to the right or to the left 01:03.340 --> 01:09.160 without actually having direct control over the gripper movements, but only of the movements of the 01:09.220 --> 01:10.270 robot's joints. 01:11.290 --> 01:18.430 Instead what we would like to do and what would be more intuitive and user friendly is to directly control 01:18.430 --> 01:23.350 the movement of the gripper without worrying about the values of each joint angle. 01:24.040 --> 01:27.460 However, we can't completely ignore these angles. 01:27.460 --> 01:32.590 We cannot overlook their existence because they represent the angle of the motor. 01:32.620 --> 01:35.950 The position commands that we need to send to the robot's motors. 01:36.780 --> 01:40.140 This is where the inverse kinematics comes into play. 01:40.260 --> 01:45.960 Since we would like to think in absolute terms of the position and the orientation of the gripper in 01:45.960 --> 01:51.780 space, but still we need to know the joint angles corresponding to a specific position and orientation 01:51.780 --> 01:52.680 of the robot. 01:52.800 --> 01:56.880 We need a mathematical tool that allows us to make this conversion. 01:57.030 --> 02:00.330 And this is precisely the inverse kinematics. 02:01.200 --> 02:07.500 The problem of the inverse kinematics is much more complex to solve because as you can see from this 02:07.500 --> 02:14.190 illustration taken from the book Robotics by Vico Siciliano, Villani and Oriolo, there can be multiple 02:14.190 --> 02:20.940 configurations, multiple joints combination that result in the robot's gripper being in the same position. 02:21.480 --> 02:28.230 We see how the robot's gripper so the end effector can be in the same position using four different 02:28.230 --> 02:33.060 configurations, namely four different combinations of the joint angles. 02:33.850 --> 02:40.450 While the problem of direct kinematics as a unique solution, the inverse kinematic problem may have 02:40.450 --> 02:44.130 multiple solution not unique and different from each other. 02:44.140 --> 02:49.330 In some cases, there may even be no configuration at all that satisfies the condition. 02:49.330 --> 02:52.900 Or also there might be infinite possible solutions. 02:53.600 --> 02:59.300 For this reason, at least regarding the inverse kinematics, we are not going to study the mathematics 02:59.300 --> 03:06.410 in detail, both because sometimes it is not possible to reach a unique solution and because often numerical 03:06.410 --> 03:11.860 techniques are used to solve the inverse kinematic problem instead of analytical ones. 03:11.870 --> 03:18.620 That is, algorithms that are used for optimization that recursively seek the best solution to an inverse 03:18.620 --> 03:19.850 kinematics problem. 03:20.450 --> 03:26.890 Again, the open source robotics community doesn't leave us alone in facing this problem. 03:26.900 --> 03:34.340 In Russia, there is a library, a software called Movie2, which provides us not only with solvers 03:34.340 --> 03:40.970 for inverse kinematics calculation, but also with a trajectory planning system for manipulator robots. 03:41.570 --> 03:48.440 Move it to, like all the open source libraries needs to be configured and needs to know the urdf model 03:48.440 --> 03:51.890 of the robot and a few other pieces of information. 03:52.460 --> 03:59.780 Then it is capable of solving the inverse kinematic problem for any robot manipulator with any architecture. 04:00.450 --> 04:06.330 Furthermore, it allows us to move the gripper into three dimensional space and automatically calculate 04:06.330 --> 04:12.690 the trajectory that each robot joint must follow to move the gripper from its initial position to the 04:12.690 --> 04:14.970 final one while avoiding obstacles. 04:16.290 --> 04:20.370 In the next lesson, we will configure moving shoe for our robot. 04:20.400 --> 04:23.250 Meaning for the Urdf model of our robot. 04:23.250 --> 04:30.030 And once configured we can use its interface to directly move the gripper in space and send actions 04:30.030 --> 04:31.590 directly to the gripper.