1 00:00:00,720 --> 00:00:09,300 We have seen the inverse dynamics in Syria, so let's now apply it in practice focus or in MATLAB. 2 00:00:09,660 --> 00:00:15,860 So first of all, how we will do it, we will first import the model of the desire to the robot manipulator. 3 00:00:15,870 --> 00:00:22,050 In our case, I will just import at the model of you are five robotic manipulator, then justified the 4 00:00:23,220 --> 00:00:26,790 PD gains, which are required. 5 00:00:27,210 --> 00:00:32,560 And this is the time span to execute the whole process. 6 00:00:32,610 --> 00:00:41,100 OK, so let's we just call the smoothing file and simulate the smerling file, and then we open the 7 00:00:41,100 --> 00:00:42,420 scopes in order to see them. 8 00:00:42,420 --> 00:00:48,870 So when you execute this one, it will be executed, and at the end you will see automatically the results 9 00:00:48,870 --> 00:00:51,390 from the scopes. 10 00:00:51,390 --> 00:00:54,870 But I will not do that because it will take a bit of time. 11 00:00:56,010 --> 00:00:58,440 I have done this before and I will show you the results. 12 00:00:58,680 --> 00:01:01,350 But let's first analyze the simulation file. 13 00:01:01,350 --> 00:01:04,860 As you can see again, we have here our robot manipulator. 14 00:01:04,860 --> 00:01:15,720 Again, this accept talks and gives out as GIS give out back the cute and cuddly, which are configuration, 15 00:01:16,050 --> 00:01:19,470 velocity and acceleration, but even not actually if you will not need acceleration. 16 00:01:19,470 --> 00:01:24,860 So we put the Terminator here in order to avoid the burning in the lab. 17 00:01:25,200 --> 00:01:28,370 I'm sorry, I'm a bit of sick, so I am sick. 18 00:01:28,380 --> 00:01:31,560 So that's why my throat is a bit bad. 19 00:01:32,280 --> 00:01:33,180 I'm sorry for that. 20 00:01:33,960 --> 00:01:36,500 Anyway, this is our desired trajectory. 21 00:01:36,530 --> 00:01:41,880 OK, here is our desired orientation, velocity and acceleration. 22 00:01:41,880 --> 00:01:48,840 As you can see, we have used we have used three or three of them, OK, we use configuration, velocity 23 00:01:48,840 --> 00:01:49,710 and acceleration. 24 00:01:50,010 --> 00:01:57,990 We have used velocity to calculator in order to calculate the input for the controller and excuse me, 25 00:01:57,990 --> 00:02:01,570 configuration for peak controller velocity for the controller. 26 00:02:01,590 --> 00:02:02,190 OK. 27 00:02:02,460 --> 00:02:06,720 And we used also velocity acceleration feed forward. 28 00:02:06,750 --> 00:02:07,170 OK. 29 00:02:07,470 --> 00:02:08,490 Please remember this. 30 00:02:08,760 --> 00:02:11,590 We use also acceleration feed forward. 31 00:02:11,610 --> 00:02:12,120 OK. 32 00:02:12,570 --> 00:02:13,000 OK. 33 00:02:13,020 --> 00:02:20,160 And as you can see what we have done, we have to calculate the inverse dynamics here and we give it 34 00:02:21,000 --> 00:02:24,360 to our robot, the main operator, OK, as an input torque. 35 00:02:24,480 --> 00:02:34,440 So what we have done, we have tried to compensate for the terms in the modeling of the robotic manipulator 36 00:02:34,440 --> 00:02:36,210 again, not just for the gravity term. 37 00:02:38,010 --> 00:02:39,150 OK, let's see. 38 00:02:39,150 --> 00:02:50,580 And again, here you have the try to visualize what's our error configuration error and what's our velocity 39 00:02:50,580 --> 00:02:50,940 error? 40 00:02:50,970 --> 00:02:51,420 OK? 41 00:02:51,660 --> 00:02:56,020 Let's check if the voltage desired configuration or not. 42 00:02:56,040 --> 00:02:56,400 OK. 43 00:02:56,430 --> 00:03:00,600 This is so if you press run button, you will see the results, but I will not do that. 44 00:03:00,840 --> 00:03:08,280 That's just directly check, as you can see, as you can see, no, our error is much, much smaller. 45 00:03:08,310 --> 00:03:13,600 OK, let's check this is ten or minus three, OK? 46 00:03:13,620 --> 00:03:15,630 As you can see these, our error is very small. 47 00:03:15,810 --> 00:03:20,760 OK, from here, take this OK, and let's zoom it and let's check. 48 00:03:20,850 --> 00:03:21,470 OK. 49 00:03:21,510 --> 00:03:28,980 As you can see, the error at the end is 10 to the minus four, which is very, very small. 50 00:03:28,980 --> 00:03:32,560 As you can see the almost zero 10 to the minus five. 51 00:03:32,580 --> 00:03:33,660 OK, it's almost zero. 52 00:03:34,020 --> 00:03:37,710 This controller is better than shear lipide controller. 53 00:03:37,710 --> 00:03:38,130 OK? 54 00:03:38,370 --> 00:03:40,200 This is better than PD controller. 55 00:03:40,470 --> 00:03:42,090 And let's so we did. 56 00:03:42,240 --> 00:03:44,930 We reached the desired configuration. 57 00:03:44,940 --> 00:03:46,950 Let's see what's happening with the velocity. 58 00:03:47,280 --> 00:03:49,340 As you can see, this is our velocity. 59 00:03:49,350 --> 00:03:53,670 And as you can see at the end, we have reached the velocity error of zero. 60 00:03:53,970 --> 00:04:00,570 And we this is the velocity of zero because at the end, we have to reach the velocity of zero if our 61 00:04:00,570 --> 00:04:01,330 robot stops. 62 00:04:01,350 --> 00:04:08,820 OK, so it start from the zero velocity or any initial velocity, it doesn't matter. 63 00:04:10,590 --> 00:04:15,840 However, at the end it reaches the desired configuration, so it stops and the velocity becomes zero, 64 00:04:15,840 --> 00:04:18,270 or it can reach even the desired velocity. 65 00:04:18,270 --> 00:04:21,300 So the velocity error will be zero. 66 00:04:21,510 --> 00:04:25,030 It depends just that it changed because of the task. 67 00:04:25,050 --> 00:04:25,380 OK. 68 00:04:26,310 --> 00:04:32,160 Or as you can see, we have reached the error of zero, both in terms of velocity tracking and configuration 69 00:04:32,160 --> 00:04:32,770 tracking. 70 00:04:32,790 --> 00:04:40,380 And again, you can just do some manipulation with b d gains and you can check what's happening with 71 00:04:40,380 --> 00:04:42,960 the result and figures.