1 00:00:00,560 --> 00:00:07,730 ‫So this is the code here, and by the way, in the next section, I'm going to explain the code to you 2 00:00:07,730 --> 00:00:09,460 ‫in a more detailed way. 3 00:00:09,830 --> 00:00:17,780 ‫However, right now, I just want to show you how the drone behaves when I play around with my polls 4 00:00:18,680 --> 00:00:25,730 ‫so I can choose my polls here, polls for the extermination, polls for the why dimension and also polls 5 00:00:25,730 --> 00:00:26,950 ‫for the Z dimension. 6 00:00:27,680 --> 00:00:32,750 ‫And so my Lunda one is going to be minus one in my lamda. 7 00:00:32,750 --> 00:00:37,430 ‫Two is going to be minus two for all three dimensions. 8 00:00:38,510 --> 00:00:46,930 ‫And you can see that the drone is able to track the trajectory quite well. 9 00:00:48,150 --> 00:00:53,080 ‫So here you have the X dimension, Y dimension and then the Z dimension. 10 00:00:53,100 --> 00:00:59,520 ‫So the blue is the reference trajectory and then the red is the true value. 11 00:01:00,650 --> 00:01:07,410 ‫And then here you have the fly and then the Seeta and BPCI angles. 12 00:01:07,940 --> 00:01:13,910 ‫So, again, Blue is the reference trajectory and then the red is the true trajectory. 13 00:01:14,520 --> 00:01:18,650 ‫So you can see the drone is able to follow the trajectory quite well. 14 00:01:19,940 --> 00:01:22,070 ‫So this is the examination here. 15 00:01:22,550 --> 00:01:29,600 ‫You can see how the drone was able to follow specifically the X dimension and also the X dot dimension. 16 00:01:29,780 --> 00:01:36,190 ‫So this is the time derivative of the X dimension and you can see how it is able to follow that as well. 17 00:01:36,920 --> 00:01:40,280 ‫The same thing for why and why dot values. 18 00:01:40,940 --> 00:01:42,350 ‫You can see the tracking. 19 00:01:43,320 --> 00:01:47,040 ‫And here you have Z and then the Z dot values. 20 00:01:48,130 --> 00:01:55,630 ‫Here you have the angles and then here you have the control, he puts you one, you to you three and 21 00:01:55,630 --> 00:02:03,790 ‫then you four, and then here you have the Omega Omega one, omega two, omega three and Omega four. 22 00:02:05,140 --> 00:02:13,450 ‫And now let's look at a more complicated trajectory, but still with these polls, you can see that 23 00:02:13,450 --> 00:02:17,290 ‫the drone is able to track the trajectory quite well. 24 00:02:18,190 --> 00:02:23,490 ‫This is the X dimension here, the Y dimension and then the Z dimension. 25 00:02:23,980 --> 00:02:25,930 ‫And these are the angles. 26 00:02:27,310 --> 00:02:35,500 ‫So you can see that the feedback lionization controller is constantly feeding different angles to the 27 00:02:35,620 --> 00:02:42,490 ‫NPC controller as reference values, and then the NPC controller is trying to track that. 28 00:02:43,330 --> 00:02:50,500 ‫But those reference values, what the feedback lionization controller gives to the NPC controller, 29 00:02:51,310 --> 00:02:59,710 ‫they originate from the polls that we have chosen, Lunda one minus one and then Lunda two minus two. 30 00:03:00,490 --> 00:03:05,980 ‫And that will, of course, make your K one value in your differential equation. 31 00:03:06,970 --> 00:03:15,340 ‫This K one value for X, Y and Z dimension minus two, and then K two values will be minus three. 32 00:03:16,600 --> 00:03:17,950 ‫And so that's how it is. 33 00:03:18,920 --> 00:03:23,920 ‫So that's how it has been able to track the entire trajectory quite well. 34 00:03:25,010 --> 00:03:26,750 ‫That's your X dimension. 35 00:03:27,810 --> 00:03:29,670 ‫That's your y dimension. 36 00:03:30,720 --> 00:03:35,580 ‫That's your Z dimension, and these are your angles here. 37 00:03:36,730 --> 00:03:44,830 ‫You see, if you zoom in, then you will see that the inner loop is running at a faster rate at the 38 00:03:44,830 --> 00:03:53,290 ‫higher frequency, so the red line changes several times compared to the blue line, which is the reference 39 00:03:53,290 --> 00:04:05,440 ‫values given to the NPC controller by the feedback controller that originated from our choice with regards 40 00:04:05,440 --> 00:04:06,580 ‫to our polls. 41 00:04:07,570 --> 00:04:15,950 ‫And, of course, the Passi reference angle, well, that's generated by the planner, but the finance 42 00:04:15,950 --> 00:04:21,580 ‫and Seeta reference angles, they're generated by the feedback lionization controller. 43 00:04:22,580 --> 00:04:29,570 ‫And well, here you have your control inputs, you one year to Q3 and Q4, and here you have Omega's 44 00:04:30,080 --> 00:04:31,550 ‫radians per second. 45 00:04:32,620 --> 00:04:45,040 ‫But now let's do something else, let's take this poll in the X dimension and let's say that the two 46 00:04:45,070 --> 00:04:54,880 ‫still equals minus two, but let's make Lumb the one zero point zero one. 47 00:04:55,850 --> 00:05:03,650 ‫So a very small, positive poll and let's see what's going to happen so you can see that it is starting 48 00:05:03,650 --> 00:05:06,260 ‫to track the reference line. 49 00:05:06,870 --> 00:05:09,020 ‫Well, however. 50 00:05:10,120 --> 00:05:18,010 ‫The red line is getting further apart from the blue line in this dimension, you see, it's not doing 51 00:05:18,010 --> 00:05:18,670 ‫so well. 52 00:05:19,390 --> 00:05:25,250 ‫The Y dimension is doing well, the Z dimension is doing well, but not the X dimension. 53 00:05:26,110 --> 00:05:27,430 ‫And look at the result. 54 00:05:28,030 --> 00:05:29,790 ‫The difference is growing. 55 00:05:30,670 --> 00:05:32,860 ‫You see, that's your X dimension here. 56 00:05:33,400 --> 00:05:40,330 ‫And you can see that the error, which is the difference between the blue line and the red line, because 57 00:05:40,330 --> 00:05:46,990 ‫the blue line is the reference value and then the red line is the true value that belongs to the real 58 00:05:46,990 --> 00:05:47,560 ‫drawn. 59 00:05:48,720 --> 00:05:52,050 ‫You see that this error is growing. 60 00:05:53,300 --> 00:05:58,020 ‫So if you give it a lot more time, then this error is going to grow a lot. 61 00:05:59,000 --> 00:06:03,500 ‫You don't have that problem in the Y dimension nor in the Z dimension. 62 00:06:04,880 --> 00:06:09,480 ‫And the controller is also doing a good job in. 63 00:06:10,720 --> 00:06:18,280 ‫Tracking the reference values that the feedback Latinization controller gives it, however, when it 64 00:06:18,280 --> 00:06:27,100 ‫comes to the extent mentioned in the feedback, lionization controller gives bad reference values to 65 00:06:27,100 --> 00:06:28,300 ‫the NPC controller. 66 00:06:29,490 --> 00:06:36,210 ‫Those reference values are not enabling the drone to follow its trajectory in the X dimension. 67 00:06:37,340 --> 00:06:41,180 ‫And these are your control inputs and your omega's. 68 00:06:42,390 --> 00:06:45,870 ‫And the reason is what we have talked about before. 69 00:06:47,000 --> 00:06:55,700 ‫So if this is your general solution here, then, yes, you have a big negative Lunda, too, you have 70 00:06:55,700 --> 00:06:56,290 ‫it here. 71 00:06:56,300 --> 00:06:59,060 ‫That's your minus two here. 72 00:06:59,780 --> 00:07:03,830 ‫However, you have a small positive Lunda, one zero point zero one. 73 00:07:04,870 --> 00:07:13,610 ‫And because of that, when your time goes to infinity, then over time this term will approach zero. 74 00:07:14,200 --> 00:07:23,980 ‫But this term will approach infinity and so you will have infinity, plus zero will be infinity. 75 00:07:24,280 --> 00:07:34,030 ‫So your total error or the distance between the blue and the red line, that's your error here. 76 00:07:34,390 --> 00:07:42,430 ‫Error as a function of time from this equation, you see that it's going to grow up until infinity as 77 00:07:42,430 --> 00:07:44,620 ‫your time goes to infinity. 78 00:07:45,070 --> 00:07:53,140 ‫In other words, in real life, it means that this error is going to grow and it's going to grow until 79 00:07:53,140 --> 00:07:54,290 ‫your drone crashes. 80 00:07:55,300 --> 00:08:03,980 ‫So you see even a small positive lambda can mess up this big negative other Londa. 81 00:08:04,840 --> 00:08:07,720 ‫So both Londis need to be negative.