1 00:00:00,450 --> 00:00:07,290 OK, after we have seen the theory of gravity compensation, let's see how it will be applied in practice 2 00:00:07,290 --> 00:00:10,650 or in how it will be simulated, and let's see the results. 3 00:00:11,230 --> 00:00:11,620 OK? 4 00:00:11,660 --> 00:00:19,480 As we have the first imported model of our robot manipulator, in this case, you are five robot manipulator. 5 00:00:19,500 --> 00:00:21,850 Then we will define just PD gains. 6 00:00:21,870 --> 00:00:22,290 OK. 7 00:00:22,740 --> 00:00:29,160 You can tune this OK as in tuning of PD controllers, OK? 8 00:00:29,460 --> 00:00:29,880 You can. 9 00:00:29,880 --> 00:00:33,000 Just by changing the values you can practice at the results. 10 00:00:33,540 --> 00:00:35,820 I mean, you can visualize the results in this practice. 11 00:00:36,120 --> 00:00:38,700 This is the time span to execute the whole process. 12 00:00:38,970 --> 00:00:42,360 And here we start to simulate the simulated file. 13 00:00:42,360 --> 00:00:48,630 And then at the end, we just open the result of the scopes automatically in order to see what, what, 14 00:00:48,630 --> 00:00:55,410 what, in order to visualize the configuration errors or position error if we reached at the end the 15 00:00:55,410 --> 00:00:58,140 desired configuration or not and our velocity. 16 00:00:58,230 --> 00:01:01,020 OK, let's see this link file. 17 00:01:01,380 --> 00:01:03,220 As you can see, this is very simple. 18 00:01:03,490 --> 00:01:05,010 Simple link is very simple. 19 00:01:05,160 --> 00:01:09,050 Excuse me, not similar, but very simple controller we have here. 20 00:01:09,060 --> 00:01:16,560 Our plan, which is our robot manipulator, which accepts the input and gives output as and the actual 21 00:01:16,560 --> 00:01:21,330 Veloce, excuse me, position, configuration, velocity and acceleration. 22 00:01:21,360 --> 00:01:25,430 OK, then we are just applying PD plus gravity compensation. 23 00:01:25,650 --> 00:01:32,130 So as our velocity is zero, we just give the actual our desired velocity input to the wheels. 24 00:01:32,880 --> 00:01:34,350 But these are those is zero. 25 00:01:34,350 --> 00:01:42,090 We just input for the key determine just the actual velocity, as you can see for the capital and the 26 00:01:42,840 --> 00:01:43,410 input. 27 00:01:43,530 --> 00:01:54,120 Um, the configuration or position, or as you can see V by QTL, the V just plot here the position 28 00:01:54,120 --> 00:01:57,600 and wrote OK and the position error is come, uh, came from here. 29 00:01:57,870 --> 00:01:59,520 So this is the desired. 30 00:01:59,850 --> 00:02:01,140 This is the desired position. 31 00:02:01,140 --> 00:02:05,400 And this this is the actual position or configuration. 32 00:02:05,410 --> 00:02:06,510 Let me say it's more correct. 33 00:02:07,200 --> 00:02:11,320 And as you can see, this is our gravity compensation term, OK? 34 00:02:11,340 --> 00:02:16,860 This computes the gravity torque, and as the gravity only depends on the configuration, the on input 35 00:02:16,860 --> 00:02:17,400 is Q. 36 00:02:17,670 --> 00:02:25,560 And we also add here the gravity torque to their PD torque and overall the input the all the input is 37 00:02:25,560 --> 00:02:27,120 given to our robot manipulator. 38 00:02:27,180 --> 00:02:28,980 And here we visualize the velocity. 39 00:02:29,370 --> 00:02:32,950 So it's easy to adjust, uh, to see. 40 00:02:32,980 --> 00:02:35,520 In order to visualize the result, you have to just run the script. 41 00:02:35,620 --> 00:02:38,500 I will not do that now because it takes a bit of time. 42 00:02:38,520 --> 00:02:40,800 You can do it by changing these values. 43 00:02:40,800 --> 00:02:42,300 You can see different results. 44 00:02:42,540 --> 00:02:43,470 But let's see. 45 00:02:43,470 --> 00:02:45,750 I have done beforehand, so I have figures. 46 00:02:45,750 --> 00:02:46,680 I saved the figures. 47 00:02:46,680 --> 00:02:47,240 So let's see. 48 00:02:47,250 --> 00:02:50,940 This is our configuration position. 49 00:02:51,300 --> 00:02:51,630 OK? 50 00:02:51,660 --> 00:02:56,550 As you can see, the position error is at the end is almost zero. 51 00:02:56,580 --> 00:02:58,150 Very, very small. 52 00:02:58,170 --> 00:02:58,500 OK. 53 00:02:58,800 --> 00:02:59,190 OK. 54 00:02:59,360 --> 00:03:00,140 Not on the zero. 55 00:03:00,140 --> 00:03:01,430 OK, but it's very small. 56 00:03:01,440 --> 00:03:02,670 Let's just zoom in. 57 00:03:02,670 --> 00:03:03,270 OK? 58 00:03:03,330 --> 00:03:04,380 Zoom in the error. 59 00:03:04,380 --> 00:03:04,920 OK? 60 00:03:05,040 --> 00:03:06,900 And the here is our error. 61 00:03:07,860 --> 00:03:13,230 As you can see, it is not zero, but it is 10 to the minus something. 62 00:03:13,470 --> 00:03:15,990 You will see this when you calculate it. 63 00:03:16,350 --> 00:03:22,260 Excuse me, when you run the script file OK here, because I have said it before and it doesn't seem 64 00:03:22,260 --> 00:03:27,650 here, then it is 10 to the negative which amount? 65 00:03:27,660 --> 00:03:31,930 OK, but you will see that, but it is 10 to the negative of something. 66 00:03:31,980 --> 00:03:32,230 OK. 67 00:03:32,250 --> 00:03:34,760 It's very it's small error, as you can see. 68 00:03:34,770 --> 00:03:40,710 So with PD control, LAPD plus gravity compensation controller, which is not that advanced controller, 69 00:03:41,760 --> 00:03:46,920 even with that controller, we can reach to the desired configuration. 70 00:03:46,950 --> 00:03:47,370 OK. 71 00:03:48,420 --> 00:03:51,940 So let's now see the velocity term, OK? 72 00:03:51,960 --> 00:03:56,220 As you can see, the velocity at the beginning was zero because we have initially started with zero, 73 00:03:56,220 --> 00:04:00,090 and at the end the velocity is also zero because we reach the desired configuration. 74 00:04:00,090 --> 00:04:03,840 So the robot reached the desired configuration and stopped. 75 00:04:04,200 --> 00:04:04,590 OK. 76 00:04:04,890 --> 00:04:07,230 So at the end, we had the velocity of zero. 77 00:04:07,560 --> 00:04:13,500 Again, I have said, as I say, I have said before, I highly recommend to change in this p and values 78 00:04:14,160 --> 00:04:14,820 experiment. 79 00:04:14,820 --> 00:04:15,910 What will be the result? 80 00:04:15,930 --> 00:04:16,320 OK. 81 00:04:16,510 --> 00:04:20,910 Sure, the oscillations will change, so the state response will change oscillations. 82 00:04:20,910 --> 00:04:22,150 Peak values will change. 83 00:04:22,170 --> 00:04:22,560 OK. 84 00:04:22,860 --> 00:04:27,180 You can change this as in the tuning of PD controllers.