1 00:00:00,690 --> 00:00:07,220 ‫Now, how about this variable here, both on the score and X on score, Y equals zero. 2 00:00:08,230 --> 00:00:20,080 ‫Well, this is your drone here, but how can you know which side is positive body frame, x axis and 3 00:00:20,080 --> 00:00:23,330 ‫which side is positive body frame, y axis? 4 00:00:24,190 --> 00:00:28,470 ‫Which one is which and which one is positive and which one is negative? 5 00:00:29,380 --> 00:00:39,190 ‫In this simulation, the body frame x axis is the red one and then the body frame y axis is the green 6 00:00:39,190 --> 00:00:39,490 ‫one. 7 00:00:40,060 --> 00:00:45,460 ‫But again, how do you know which one is positive and which one is negative? 8 00:00:46,390 --> 00:00:57,190 ‫So if I make this variable one here and then if I run the simulation, then you see that one side becomes 9 00:00:57,190 --> 00:00:58,180 ‫very long. 10 00:00:59,110 --> 00:01:04,310 ‫So now it's quite obvious which one is the positive side and which one is the negative side. 11 00:01:05,140 --> 00:01:14,350 ‫So the long red side is the positive x axis and then the long green side is the positive Y axis. 12 00:01:15,340 --> 00:01:24,100 ‫So you see the positive body frame y axis points to the center of the spiral and then the positive body 13 00:01:24,100 --> 00:01:29,240 ‫frame x axis points in the direction of the flight. 14 00:01:30,160 --> 00:01:33,670 ‫So this is just an extra feature for convenience. 15 00:01:34,740 --> 00:01:40,380 ‫Then this valuable sub underscore loop equals five, that's for animation purposes. 16 00:01:41,380 --> 00:01:44,080 ‫It's to make the animation smoother. 17 00:01:45,380 --> 00:01:55,130 ‫And now let's talk about this same underscore version variable, if I make this variable, too, then 18 00:01:55,130 --> 00:01:57,730 ‫the animation here looks like this. 19 00:01:58,580 --> 00:02:08,510 ‫Here you see the tracking of the X, Y and Z dimensions and also the tracking of the Phi Theta and PSI 20 00:02:08,520 --> 00:02:09,320 ‫Dimensions. 21 00:02:10,160 --> 00:02:17,000 ‫However, I also want to see how my control inputs you want you to use three and you four evolve in 22 00:02:17,000 --> 00:02:17,540 ‫time. 23 00:02:18,600 --> 00:02:27,230 ‫For that, I'm going to put here one, and so if I run it again, then you see that I have new shop 24 00:02:27,270 --> 00:02:35,390 ‫windows here and here you have the control inputs you have you want you to Q3 and Q4. 25 00:02:36,120 --> 00:02:39,240 ‫And by the way, I don't want my drone to be that long anymore. 26 00:02:39,240 --> 00:02:43,920 ‫So I'm going to make this variable zero POS underscore X or Y. 27 00:02:44,700 --> 00:02:47,030 ‫And so my drone looks normal now. 28 00:02:47,820 --> 00:02:50,260 ‫And so these are your control inputs here. 29 00:02:50,460 --> 00:02:54,870 ‫However, notice that you have two more sub windows here. 30 00:02:55,710 --> 00:03:06,330 ‫These two windows show you the orientation of the body frame, Exide, the red one and the orientation 31 00:03:06,330 --> 00:03:10,000 ‫of the body frame y side, the green one. 32 00:03:10,830 --> 00:03:15,960 ‫So this red one, this is like this red beam and then this green one. 33 00:03:15,960 --> 00:03:23,730 ‫This is like the green bean note that these are not actual beams, though, because these links, they 34 00:03:23,730 --> 00:03:26,420 ‫are not the lengths of the beams themselves. 35 00:03:27,150 --> 00:03:29,460 ‫So they are not the actual beams. 36 00:03:29,880 --> 00:03:36,330 ‫They are just here to show the orientation of the red beam and the green beam. 37 00:03:37,080 --> 00:03:42,390 ‫But the length of this line here is not equal to the length of this red beam. 38 00:03:43,260 --> 00:03:48,690 ‫And the length of this green line is not equal to the length of this green beam. 39 00:03:49,530 --> 00:03:57,390 ‫And so in the red case, the left side of the beam is the positive Exide. 40 00:03:58,300 --> 00:04:06,610 ‫That's the forward beam and then the Z dimension is up, and in the green case, it is reversed, the 41 00:04:06,610 --> 00:04:10,520 ‫positive Y is on the right side here. 42 00:04:10,540 --> 00:04:13,270 ‫So this one, this is your positive Y side. 43 00:04:14,230 --> 00:04:19,950 ‫This side points into the spiral and then the Z dimension is still up. 44 00:04:20,920 --> 00:04:28,180 ‫If you make this viable one again, then it will become apparent which side is which. 45 00:04:29,150 --> 00:04:37,790 ‫So you see this long red side here, there's this on the left side, so that's your positive body frame, 46 00:04:37,790 --> 00:04:45,310 ‫X-axis and then this one here, that's your positive body frame y axis. 47 00:04:45,320 --> 00:04:48,500 ‫So you see that it's here on the right side. 48 00:04:49,680 --> 00:05:00,690 ‫So I have to turn off the lone beam feature and so this red line here, it gives you a feeling about 49 00:05:00,690 --> 00:05:01,910 ‫the theater angle. 50 00:05:03,000 --> 00:05:11,520 ‫This red line here, that's your rotation about the body frame y axis and then the green line gives 51 00:05:11,520 --> 00:05:20,790 ‫you a feeling about the fire angle because that's rotation about the body frame x axis, since the fire 52 00:05:21,220 --> 00:05:29,100 ‫angles are very small here, in order to see some kind of movement in terms of orientation, you can 53 00:05:29,100 --> 00:05:35,460 ‫see that the horizontal and then the vertical axis, they are not up to scale. 54 00:05:36,150 --> 00:05:39,790 ‫If they were, it would be very hard to see the orientation here. 55 00:05:40,740 --> 00:05:47,120 ‫And so notice that the green one has its positive side down. 56 00:05:47,550 --> 00:05:48,930 ‫Why is it like that? 57 00:05:49,650 --> 00:05:53,080 ‫Well, you want your drone to go in circles, right? 58 00:05:53,880 --> 00:05:56,190 ‫So you need centripetal force for that. 59 00:05:57,140 --> 00:06:03,230 ‫And you get it by tilting the UVs body from positive y axis down. 60 00:06:04,320 --> 00:06:12,390 ‫So if you imagine that this is the side of your drone and so your thrust force is then in this direction 61 00:06:13,230 --> 00:06:19,290 ‫and in this direction here, because your drone is tilted, they can be decomposed like this. 62 00:06:20,260 --> 00:06:27,370 ‫This is the vertical component of this thrust force, and this one is the horizontal component of this 63 00:06:27,370 --> 00:06:30,450 ‫thrust force and the same thing here. 64 00:06:31,330 --> 00:06:39,670 ‫And so the horizontal component here, that's your centripetal force and that component forces your 65 00:06:39,670 --> 00:06:41,350 ‫drone to go in circles.