1 00:00:00,610 --> 00:00:01,390 ‫Welcome back. 2 00:00:01,870 --> 00:00:10,510 ‫So let's just recap what we have done here in the case of an autonomous vehicle, you first had your 3 00:00:10,510 --> 00:00:20,510 ‫equations of motion in the lateral direction, then you reformulated it to get your non-linear state 4 00:00:20,560 --> 00:00:21,700 ‫space equations. 5 00:00:22,690 --> 00:00:31,210 ‫Then, thanks to the small BPCI angle approximation in the autonomous vehicle, you got your system 6 00:00:31,630 --> 00:00:41,980 ‫in the LTI form, you had your constant A, B, C and D matrices, then you decided to do it and you 7 00:00:41,980 --> 00:00:45,430 ‫got your discrete A, B, C and D matrices. 8 00:00:46,150 --> 00:00:56,500 ‫And then you applied the NPC strategy to your descriptivist LTI system where you worked with your discrete 9 00:00:56,500 --> 00:01:05,860 ‫A, B, C and D matrices, and then you sent your control inputs into your plant and then the plant 10 00:01:05,860 --> 00:01:14,050 ‫would produce new states and then those new states would go back into the controller to compute the 11 00:01:14,050 --> 00:01:15,670 ‫new control inputs. 12 00:01:16,030 --> 00:01:18,060 ‫And so it would go in a loop. 13 00:01:18,370 --> 00:01:25,780 ‫However, your discrete A, B, C and D matrices, they would be constant throughout the entire maneuver. 14 00:01:26,650 --> 00:01:35,500 ‫And you have a similar case with your UA V at the beginning, you had your equations of motion, your 15 00:01:35,890 --> 00:01:37,110 ‫degree of freedom. 16 00:01:37,480 --> 00:01:39,010 ‫Newton oilor equations. 17 00:01:40,020 --> 00:01:50,040 ‫Then you transform them in the non-linear states space equations, then you make a small phi and theta 18 00:01:50,070 --> 00:01:58,080 ‫angle approximation, you would assume that they would equal to zero radians. 19 00:01:59,010 --> 00:02:04,050 ‫That made your transfer matrix equal to an identity matrix. 20 00:02:04,950 --> 00:02:12,870 ‫Then from your nonlinear state based equations, you took only those equations that were relevant to 21 00:02:12,870 --> 00:02:18,030 ‫your additive control, and then you got your nonlinear state based equations. 22 00:02:18,360 --> 00:02:25,710 ‫But with these variables, phi that theta that inside that, then you reformulated them and you put 23 00:02:25,710 --> 00:02:31,400 ‫them in the HPV form, then you democratised your Lopevi form. 24 00:02:32,250 --> 00:02:36,480 ‫You apply your discreetness form to your NPC controller. 25 00:02:37,510 --> 00:02:43,990 ‫Now, in the case of an autonomous vehicle, your MPAC controller gave you a steering wheel angled Deltans, 26 00:02:43,990 --> 00:02:45,070 ‫your control input. 27 00:02:46,100 --> 00:02:54,670 ‫But now you send you to U3 and EUFOR into your plans and then your plant will give you new states, 28 00:02:55,520 --> 00:03:03,890 ‫so out of those new states, you take your P, Q and R variables and you put them through a transfer 29 00:03:03,890 --> 00:03:12,590 ‫matrix and then you get your file that, that and BPCI that and then find out and setar that will go 30 00:03:12,590 --> 00:03:15,410 ‫back into your continuous LP form. 31 00:03:16,310 --> 00:03:26,450 ‫And this HPV update happens every inner circle, every zero point one second, and so note that we assumed 32 00:03:26,480 --> 00:03:34,760 ‫that our transfer matrix equals the identity matrix here, not here, but here. 33 00:03:35,630 --> 00:03:43,970 ‫We do this assumption one time and then we get a simplified, non-linear state based equation form with 34 00:03:43,980 --> 00:03:50,360 ‫final thought that implied that as its variables and in order to be complete. 35 00:03:50,780 --> 00:03:58,790 ‫I should also say that one of the variables in this nonlinear equation is Omega. 36 00:03:58,790 --> 00:04:02,350 ‫But Omega is not a state in our situation. 37 00:04:03,080 --> 00:04:06,270 ‫So this small angle approximation happened here. 38 00:04:06,740 --> 00:04:17,880 ‫However, when you now actually use this LP form, then here you do not have the small ÀNGEL approximation. 39 00:04:17,930 --> 00:04:18,530 ‫All right. 40 00:04:19,220 --> 00:04:28,400 ‫Here you still take your pick your states and then you use the real transfer matrix with all its angles 41 00:04:28,550 --> 00:04:37,580 ‫in order to get your updated find that theta that and decide that in order to get more correct values. 42 00:04:37,790 --> 00:04:48,260 ‫And then these values, specifically Phi Dot and Theta, that will enter the LP system along with your 43 00:04:48,260 --> 00:04:55,310 ‫omega variable, which is not a state, but still it gets updated every zero point one second.