1 00:00:00,750 --> 00:00:06,330 In this section of the course, we are going to see one of the most important concepts in robotics. 2 00:00:06,600 --> 00:00:11,040 This is the dynamic model of the robot, in our case, robotic manipulators. 3 00:00:11,370 --> 00:00:12,660 So let's get started. 4 00:00:14,130 --> 00:00:16,260 What is the dynamic model of the robot? 5 00:00:16,380 --> 00:00:22,950 The dynamic model of the robot provides us a description of the relationship between joint forces, 6 00:00:22,950 --> 00:00:30,780 alteryx and the motion of the structure, namely position, velocity and acceleration of the robot limbs 7 00:00:30,780 --> 00:00:31,710 and joints. 8 00:00:33,450 --> 00:00:39,190 We can separate two kind of robot dynamic model, namely direct model. 9 00:00:39,360 --> 00:00:40,710 And the inverse model. 10 00:00:41,250 --> 00:00:42,660 What is the direct model? 11 00:00:43,350 --> 00:00:44,610 Indirect modeling? 12 00:00:44,730 --> 00:00:51,630 We have the knowledge of joint talks and joint positions and velocities, and we want to determine the 13 00:00:51,630 --> 00:00:53,100 joint accelerations. 14 00:00:53,610 --> 00:01:01,380 As you can see from the equation, F is nothing but a nonlinear function of joint positions, velocities 15 00:01:01,380 --> 00:01:05,440 and talks of the V foreign joint accelerations. 16 00:01:05,460 --> 00:01:13,080 We can integrate it to find new joint positions and velocities in inverse model. 17 00:01:13,110 --> 00:01:16,920 As the name suggests, we do the opposite of the direct model. 18 00:01:17,280 --> 00:01:24,140 So we are given desired joint positions, velocities and accelerations, and we want to calculate join 19 00:01:24,150 --> 00:01:30,360 talks for forces that must be applied in order to get the desired motion. 20 00:01:30,990 --> 00:01:32,970 These are joint accelerations. 21 00:01:32,970 --> 00:01:39,000 Velocities and positions are obtained by choosing desired trajectory to be tracked. 22 00:01:40,260 --> 00:01:48,060 It will be more clear to you when we see trajectory planning during modelling, we will make some assumptions 23 00:01:48,060 --> 00:01:50,070 in order to simplify the problem. 24 00:01:50,370 --> 00:01:57,780 First of all, we will discard the flexibilities in robot manipulator and accept each part of it as 25 00:01:57,780 --> 00:01:58,710 a rigid body. 26 00:01:59,100 --> 00:02:07,110 Secondly, we will consult the joints almost ideal, so there is no backlash or any other issues, except 27 00:02:07,110 --> 00:02:10,320 we will take into account only joint frictions. 28 00:02:12,790 --> 00:02:19,380 Okay, at this moment, you may ask, or maybe not, why it's interesting for us to get a dynamic model 29 00:02:19,380 --> 00:02:20,430 of the manipulator. 30 00:02:21,240 --> 00:02:25,000 This will be more clear to you further in the course. 31 00:02:25,020 --> 00:02:27,300 But let me briefly give you some points. 32 00:02:28,080 --> 00:02:34,350 First, we use it for simulation of robots, which is very important because the robots are precious 33 00:02:34,350 --> 00:02:38,880 and we want first to simulate them and then apply in the real world. 34 00:02:39,450 --> 00:02:45,810 During simulation, we will need joint positions, velocities and acceleration to provide correct motion 35 00:02:45,810 --> 00:02:46,620 to our robot. 36 00:02:47,100 --> 00:02:50,680 We will need to work to simulate further advanced concepts. 37 00:02:51,570 --> 00:02:56,910 Then we will use the robot dynamic model excessively in design of control algorithms, which we will 38 00:02:56,910 --> 00:02:58,320 see in future topics. 39 00:02:58,860 --> 00:03:04,860 Control algorithms are very fundamental concepts for robotics because in order to do any user field 40 00:03:04,860 --> 00:03:09,630 work with robots, we have to first be able to control them properly. 41 00:03:10,230 --> 00:03:19,140 During this phase, you will see how important is robot dynamic model for us and also for analysis of 42 00:03:19,140 --> 00:03:20,520 manipulator structures. 43 00:03:20,640 --> 00:03:29,700 Because by robot dynamic model, we can get the talks that are induced in joins due to contact forces 44 00:03:29,700 --> 00:03:30,810 with the environment. 45 00:03:31,260 --> 00:03:38,070 Internal stress and Taubes endurance and so on, which are important for us during design phase of gears 46 00:03:38,310 --> 00:03:39,870 drivers and so on. 47 00:03:40,920 --> 00:03:49,180 We can obtain dynamic model of robot by using two very popular methods, namely a little Lagrange and 48 00:03:49,280 --> 00:03:54,390 Newton formulation in Illinois Lagrange mode method. 49 00:03:54,450 --> 00:04:01,860 The robot is considered as a whole, so because of that, we cannot get internal forces and stress in 50 00:04:01,860 --> 00:04:02,370 joints. 51 00:04:03,120 --> 00:04:05,370 But this method is more initiative. 52 00:04:05,880 --> 00:04:12,810 You can inspect and understand physical meaning of each element in the robot dynamic model because model 53 00:04:12,810 --> 00:04:14,580 is obtained analytically. 54 00:04:14,950 --> 00:04:22,530 However, the method is not computationally efficient because you get model in symbolic form and then 55 00:04:22,530 --> 00:04:30,120 do replacements to get a numerical result, which is time consuming in yet a major method. 56 00:04:30,170 --> 00:04:37,170 Each link is considered as a rigid body and by using free body diagram and forward and backward recursion 57 00:04:37,170 --> 00:04:39,690 method, the model is obtained. 58 00:04:40,080 --> 00:04:41,250 However, be careful. 59 00:04:41,370 --> 00:04:42,930 This model is numerical. 60 00:04:43,260 --> 00:04:49,680 Namely, you get numerical results at the end instead of symbolic, as in a little like range method. 61 00:04:50,430 --> 00:04:53,910 Because of that, this algorithm is much efficient. 62 00:04:54,270 --> 00:04:58,920 Additionally, you can get internal forces and stress between each limb. 63 00:04:59,490 --> 00:04:59,870 Howard. 64 00:04:59,960 --> 00:05:06,260 This method of modeling is not initiative in order to grasp the physical meaning of each term. 65 00:05:07,040 --> 00:05:13,520 The last thing I want to note is that while these two methods are completely different, the result 66 00:05:13,520 --> 00:05:21,950 obtained is the same, so you can use either a little grounds or need some method based on the task 67 00:05:21,950 --> 00:05:22,820 requirements.