1 00:00:00,440 --> 00:00:10,640 ‫And so now let's make our Drak switch one again, let's include drag and also let's choose trajectory 2 00:00:10,640 --> 00:00:11,330 ‫six. 3 00:00:12,380 --> 00:00:20,990 ‫And so this is the animation, however, now I want to look at the fire and see two angles separately. 4 00:00:22,010 --> 00:00:26,150 ‫So here you have it, you have your fire angle and then you have your angle. 5 00:00:27,130 --> 00:00:33,940 ‫So the fire angle, as you can see here, becomes negative over time, that's the angle that causes 6 00:00:34,060 --> 00:00:40,600 ‫centripetal acceleration and then the third angle becomes positive over time. 7 00:00:41,200 --> 00:00:48,930 ‫That's the red beam tilting down to produce force in the direction of the forward flight. 8 00:00:49,930 --> 00:00:51,760 ‫So let's check the conventions. 9 00:00:52,800 --> 00:01:01,050 ‫So this is your drone here, the top of you, that's your body frame, X-axis here, that's your body 10 00:01:01,050 --> 00:01:02,280 ‫frame, Y-axis. 11 00:01:03,090 --> 00:01:10,440 ‫So this is your model one and then this is your model, too, and this is your trajectory on the X Y 12 00:01:10,440 --> 00:01:10,920 ‫plane. 13 00:01:10,920 --> 00:01:11,250 ‫Right. 14 00:01:11,280 --> 00:01:13,310 ‫So this is your spiral. 15 00:01:14,130 --> 00:01:22,290 ‫So the X Y plane, you move like this, so you're following this turning trajectory and so you get the 16 00:01:22,650 --> 00:01:26,850 ‫angle if you rotate about the body frame x axis. 17 00:01:27,900 --> 00:01:31,980 ‫So if you want to tilt this side down. 18 00:01:33,010 --> 00:01:41,380 ‫You're looking at the drone from the top, so if you want this site to go down this M2, then you have 19 00:01:41,380 --> 00:01:45,100 ‫to rotate about the negative body frame x axis. 20 00:01:46,070 --> 00:01:52,640 ‫So this is your hand, these are your knuckles and your thumb points in this direction, in the negative 21 00:01:52,640 --> 00:02:01,900 ‫body from X direction, and then your M to side tilts down, giving you that centripetal acceleration. 22 00:02:02,600 --> 00:02:11,870 ‫And since you are some points down, which is the negative body from X direction, your fi angle becomes 23 00:02:12,050 --> 00:02:12,770 ‫negative. 24 00:02:13,580 --> 00:02:16,400 ‫And that's what you see here in the graph. 25 00:02:17,210 --> 00:02:24,860 ‫Your angle becomes more and more negative, which means that this side tilts down more and more, giving 26 00:02:24,860 --> 00:02:31,670 ‫you more and more centripetal acceleration because your radius here increases in time. 27 00:02:32,550 --> 00:02:41,940 ‫And that means that this part of the equation here increases faster than this part of the equation overall, 28 00:02:41,940 --> 00:02:44,760 ‫giving you greater centripetal acceleration. 29 00:02:45,690 --> 00:02:54,570 ‫However, if you want to take this side down this more one side, you want this side to go down, then 30 00:02:54,570 --> 00:03:00,450 ‫that means that you have to rotate about the positive body frame y axis. 31 00:03:01,230 --> 00:03:10,560 ‫Your side now is in the positive body frame y axis, and so your angle becomes positive as you tilt 32 00:03:10,560 --> 00:03:12,660 ‫your end one down. 33 00:03:13,690 --> 00:03:19,300 ‫And you can also see it here in this graph, you can see that your theater becomes more and more positive 34 00:03:19,300 --> 00:03:20,110 ‫over time. 35 00:03:21,040 --> 00:03:25,360 ‫So that means that our conventions match and that's very good. 36 00:03:26,530 --> 00:03:35,920 ‫So here you can see that your fire angle reaches around minus zero point one radiance in the end and 37 00:03:35,920 --> 00:03:42,240 ‫your FITA angle reaches about zero point zero four radians in the end. 38 00:03:42,760 --> 00:03:44,260 ‫But let's go crazy now. 39 00:03:45,250 --> 00:03:54,790 ‫Let's make this drag coefficient CDs of you ten point five, and let's do the same with C, D, sub 40 00:03:54,800 --> 00:03:57,050 ‫V also let's make it ten point five. 41 00:03:58,000 --> 00:04:01,180 ‫So now these drag coefficients are 10 times higher. 42 00:04:02,110 --> 00:04:03,580 ‫That's the animation. 43 00:04:04,610 --> 00:04:12,020 ‫As you can see, your fire angle is still around minus zero point one radians in the end, and it makes 44 00:04:12,020 --> 00:04:12,530 ‫sense. 45 00:04:13,640 --> 00:04:18,620 ‫Let's bring to our velocity, that's the velocity in the body frame, Y-axis. 46 00:04:19,660 --> 00:04:23,300 ‫So these are the values for the velocity, as you can see. 47 00:04:23,320 --> 00:04:29,890 ‫They range from zero point three to zero point five to again zero point three meters per second. 48 00:04:30,760 --> 00:04:33,950 ‫So it's not zero, but it is quite small. 49 00:04:34,990 --> 00:04:43,660 ‫So the 10 times higher force in the V direction almost plays no role and therefore Angle is not affected 50 00:04:43,660 --> 00:04:44,890 ‫by that almost at all. 51 00:04:45,790 --> 00:04:52,870 ‫So if I make my drag coefficients one point five again and put my velocity again. 52 00:04:54,050 --> 00:05:00,170 ‫Then you can see that the velocities become bigger, which makes sense because now you have less drag. 53 00:05:01,170 --> 00:05:09,300 ‫But the change is very small, and so if I make it ten point five again, that means that your angle 54 00:05:09,300 --> 00:05:14,630 ‫is not affected by this increase in drag almost at all. 55 00:05:15,660 --> 00:05:22,670 ‫This angle here is affected by the fact that the radius of the spiral is increasing. 56 00:05:23,670 --> 00:05:31,980 ‫So the radius of your spiral gets bigger and bigger, which means that every second you have to cover 57 00:05:31,980 --> 00:05:33,300 ‫more distance. 58 00:05:34,080 --> 00:05:39,870 ‫At the beginning, maybe you had to cover this distance in one second. 59 00:05:40,800 --> 00:05:51,840 ‫And now you have to cover maybe this distance in one second, which means that your velocity here must 60 00:05:51,840 --> 00:05:54,090 ‫be bigger than here. 61 00:05:54,630 --> 00:05:55,230 ‫All right. 62 00:05:56,320 --> 00:06:02,140 ‫This will last and needs to be bigger than here, because here in one second, you need to cover more 63 00:06:02,140 --> 00:06:07,140 ‫distance than here, and that plays itself out here. 64 00:06:08,170 --> 00:06:10,990 ‫And that makes your centripetal acceleration bigger. 65 00:06:11,770 --> 00:06:16,480 ‫Of course, your radius also increases and that makes your centripetal acceleration smaller. 66 00:06:16,660 --> 00:06:24,970 ‫But in this case, this thing becomes bigger, faster than this thing here. 67 00:06:25,850 --> 00:06:32,620 ‫So we conclude that the triangle is not very much affected by the increase in drag. 68 00:06:33,640 --> 00:06:41,610 ‫However, due to 10 times higher drag force in the new direction, you using this more? 69 00:06:41,620 --> 00:06:49,930 ‫One needs to tilt down a lot more to produce the horizontal force to overcome that massive drag. 70 00:06:50,890 --> 00:06:56,410 ‫And it does tilt more now instead of zero point zero four radians. 71 00:06:56,410 --> 00:07:02,650 ‫In the end, you finish the maneuver with a three to four zero point twenty one radians approximately. 72 00:07:03,550 --> 00:07:07,510 ‫And now I'm going to go back to my one point five drag coefficients. 73 00:07:08,380 --> 00:07:13,960 ‫And now I want to show you trajectory three here. 74 00:07:13,960 --> 00:07:22,560 ‫You have a bit of spiral and then you go up exponentially until like 700 meters. 75 00:07:23,470 --> 00:07:32,050 ‫So now you mostly go in the body frame axis and so your W velocity becomes pretty large. 76 00:07:32,590 --> 00:07:41,140 ‫So you can see that on the X Y plane, you move from minus two to eight meters and then in the Z dimension 77 00:07:41,500 --> 00:07:45,550 ‫you go from zero meters to almost seven hundred meters. 78 00:07:46,570 --> 00:07:54,480 ‫And by the way, if you look at the length of these beams here, the red beam and then the green beam, 79 00:07:55,300 --> 00:08:00,120 ‫then again, they don't represent the real length of the drone. 80 00:08:01,030 --> 00:08:03,580 ‫They just help you visualize the drone. 81 00:08:04,360 --> 00:08:12,220 ‫If I had put here the drone with its real dimensions, then it would be a very small drone here and 82 00:08:12,220 --> 00:08:14,080 ‫it would be very hard for you to see it. 83 00:08:14,830 --> 00:08:23,050 ‫And so since your upward velocity is pretty large now, that means that you have a drag force in the 84 00:08:23,050 --> 00:08:27,030 ‫downward direction, mainly to overcome that. 85 00:08:27,070 --> 00:08:34,380 ‫You see that you're you want control, you put your control force becomes pretty huge at some point. 86 00:08:35,340 --> 00:08:42,630 ‫And also, all your Omega's that give you that you want control force, they become pretty large at 87 00:08:42,630 --> 00:08:51,540 ‫some point and it makes sense because they have to produce this massive thrust up to accelerate you 88 00:08:51,540 --> 00:08:59,520 ‫up force and to overcome this massive drag that increases as a function of time because you go up faster 89 00:08:59,520 --> 00:09:00,210 ‫and faster. 90 00:09:01,080 --> 00:09:08,570 ‫And so this has been trajectory three and in total, you have nine trajectories here to choose from, 91 00:09:09,420 --> 00:09:11,310 ‫and that's the place where you choose them. 92 00:09:12,240 --> 00:09:17,820 ‫You just pick a number from one to nine and it cannot be anything else. 93 00:09:17,820 --> 00:09:19,350 ‫It has to be from one to nine. 94 00:09:20,070 --> 00:09:24,390 ‫And then you run your program and then you have one more valuable here. 95 00:09:24,720 --> 00:09:27,010 ‫No plots equals zero. 96 00:09:27,810 --> 00:09:34,470 ‫So if you only want to see the animation and you don't want to see the plots that come after that, 97 00:09:35,280 --> 00:09:37,910 ‫then you make this variable one like this. 98 00:09:38,880 --> 00:09:44,240 ‫So here you have your animation and then if you close it, it's going to be the end of the program. 99 00:09:44,940 --> 00:09:51,420 ‫But if you do want to see the plots afterwards, then you're going to put here zero and then you run 100 00:09:51,420 --> 00:09:52,070 ‫the program. 101 00:09:52,830 --> 00:09:54,680 ‫So you have your animation here. 102 00:09:54,870 --> 00:10:03,030 ‫And then if you close it, then you will have a plot, then another plot in the next dimension and then 103 00:10:03,060 --> 00:10:11,160 ‫another one in the Y dimension, in the Z dimension, then the angles and then the control inputs. 104 00:10:12,120 --> 00:10:21,120 ‫Along with their Omega's, and if you close that, then your program finishes and so all these variables 105 00:10:21,120 --> 00:10:26,570 ‫here in this init function are stored in this self that constants variable. 106 00:10:27,390 --> 00:10:32,800 ‫And so this list, this vector is then sent to the main file. 107 00:10:33,690 --> 00:10:35,300 ‫So this is your main file here. 108 00:10:35,310 --> 00:10:45,000 ‫And if the main file calls this function from the support file class, then the main file gets this 109 00:10:45,150 --> 00:10:46,510 ‫list in return. 110 00:10:47,100 --> 00:10:50,670 ‫OK, and now let's go back to our main file.