1 00:00:00,150 --> 00:00:00,540 OK. 2 00:00:00,840 --> 00:00:06,840 Before switching to Adaptive Controller, let's remind ourselves, why did we learn the robust control 3 00:00:07,440 --> 00:00:10,230 they have seen model based control techniques before? 4 00:00:10,470 --> 00:00:18,630 But the problem was that the robot model that we have came up with was not very correct and this was 5 00:00:19,260 --> 00:00:25,830 deteriorating the effectiveness or performance of model based control techniques we have seen before. 6 00:00:26,370 --> 00:00:32,700 Other than that, we didn't consider many other effects during modeling such such as friction. 7 00:00:33,090 --> 00:00:38,760 All these and other external disturbances were creating a problem in the control of the robot. 8 00:00:39,330 --> 00:00:44,820 In order to solve these issues or more technical, it reject these disturbances. 9 00:00:45,090 --> 00:00:47,160 We have to come up with a robot. 10 00:00:47,160 --> 00:00:53,490 We have come up with robust control, which was using high direct control, more like switching action 11 00:00:53,730 --> 00:00:55,080 to reject disturbances. 12 00:00:55,530 --> 00:01:01,320 But this switching like action, especially due to chattering, is not good for the robot manipulator 13 00:01:01,320 --> 00:01:08,610 structure, and it also create noise if you want to avoid these problems by using smoother control technique. 14 00:01:08,910 --> 00:01:12,940 And here it is, they can achieve this using adaptive control. 15 00:01:12,960 --> 00:01:21,360 So let's see it as we have saved for robust control, we have some problems with model based techniques 16 00:01:21,570 --> 00:01:27,300 that we have seen before, namely the large uncertainty on the robot dynamic model. 17 00:01:27,480 --> 00:01:35,190 So robot dynamic parameters, because essential part of the robot dynamics are dynamic parameters that 18 00:01:35,190 --> 00:01:38,070 we either don't know or they are known poorly. 19 00:01:38,550 --> 00:01:43,500 These uncertain dynamic parameters cause uncertain dynamic or efficiency. 20 00:01:43,920 --> 00:01:51,210 Then we have poor knowledge about inertial payload to the body that we are, namely the body we are 21 00:01:51,420 --> 00:01:58,380 hunting using a robot manipulator, as we have seen before, when the gripper grabs some object, it 22 00:01:58,390 --> 00:02:01,650 becomes part of the last link and objects. 23 00:02:01,650 --> 00:02:11,430 Inertial parameters combines with robots, robots, inertial parameters and cause the cause the change 24 00:02:11,430 --> 00:02:16,180 in dynamic coefficient as we don't know what is the payload. 25 00:02:16,200 --> 00:02:18,300 This cause uncertainty in the model. 26 00:02:18,690 --> 00:02:25,890 So again, the well-known question how to solve these issues without writing a robot like a horse in 27 00:02:25,890 --> 00:02:27,300 case of robots control. 28 00:02:27,750 --> 00:02:33,390 So named the boat so named by adapting to the changes instead of resisting them. 29 00:02:33,840 --> 00:02:39,990 So the key steps are firstly, estimate the value of unknown parameters online. 30 00:02:40,470 --> 00:02:48,150 We know how we can do that and then adapt the control parameters to these estimations. 31 00:02:48,390 --> 00:02:55,320 So namely, be aware of the disturbances and adapt the robot's parameters to these disturbances to achieve 32 00:02:55,320 --> 00:03:00,540 its aim, namely trajectory, trajectory and checking. 33 00:03:00,990 --> 00:03:03,810 Like we humans do in difficult situations. 34 00:03:07,380 --> 00:03:15,120 There are two kinds of adaptive control, namely direct adaptive control and indirect adaptive control. 35 00:03:15,570 --> 00:03:17,400 Indirect adaptive control. 36 00:03:17,460 --> 00:03:25,170 We make trajectory tracking errors go to zero asymptotically by adopting, by adapting to the changes 37 00:03:25,170 --> 00:03:26,760 in the dynamic coefficients. 38 00:03:27,150 --> 00:03:33,960 However, it's not needed for us to get correct values for the dynamic estimations of the dynamic coefficients. 39 00:03:34,410 --> 00:03:42,240 So while tracking errors, while tracking errors will converge to zero dynamic coefficients, estimation 40 00:03:42,240 --> 00:03:45,600 error will not convert to zero, but they will be bound. 41 00:03:45,600 --> 00:03:53,100 That the exact opposite is true for in the adaptive controller, where we not only make trajectory tracking 42 00:03:53,100 --> 00:03:59,610 error go to zero asymptotically, but also dynamic coefficients to convert their true values. 43 00:04:00,810 --> 00:04:06,690 This is more difficult to achieve, and the thrust is that we don't need correct values of dynamic coefficients 44 00:04:06,690 --> 00:04:16,200 if we can achieve the same control without estimating them correctly, so we will use a direct adaptive 45 00:04:16,200 --> 00:04:16,800 control. 46 00:04:18,000 --> 00:04:21,480 So let's see the dynamic parameters that cause problem. 47 00:04:22,230 --> 00:04:24,780 We can categorize this dynamic parameters. 48 00:04:25,200 --> 00:04:34,650 Namely, we have the ones that we are know that we know, namely the parameters which namely, excuse 49 00:04:34,650 --> 00:04:39,000 me, the H parameters, which are for parameters for each link. 50 00:04:39,300 --> 00:04:49,860 So namely for M for the whole robot and then link lengths, which are in total and uncertain, but constant 51 00:04:49,860 --> 00:04:55,820 parameters that can be identified off-line, namely dynamic coefficients. 52 00:04:55,830 --> 00:04:59,490 And if you remember, there are p times the. 53 00:04:59,980 --> 00:05:05,560 Each weigh less than 10 and total parameters and slowly varying parameters. 54 00:05:05,800 --> 00:05:13,600 These are fiction elements as fiction parameters as the robot works, its lubrication changes which 55 00:05:13,600 --> 00:05:21,010 effect friction, surely, and the parameters that are changing abruptly and we don't have any knowledge 56 00:05:21,010 --> 00:05:21,700 about them. 57 00:05:22,060 --> 00:05:27,130 These are the objects that we are handling and we don't know their parameters. 58 00:05:27,610 --> 00:05:33,340 So after detecting the problems and the cause of these problems, we have to determine what's our goal. 59 00:05:33,700 --> 00:05:40,630 Our goal with adaptive control is to execute the given trajectory by achieving asymptotic convergence 60 00:05:40,630 --> 00:05:42,010 in tracking errors. 61 00:05:42,400 --> 00:05:49,420 So both position and velocity errors have to go to the zero asymptotically and we have to provide global 62 00:05:49,420 --> 00:05:50,200 stability. 63 00:05:50,230 --> 00:05:53,290 It means we have to achieve our goal. 64 00:05:53,530 --> 00:06:00,340 What whatever the amount of deviation of dynamic parameters from their true values and whatever is the 65 00:06:00,340 --> 00:06:02,260 initial trajectory errors. 66 00:06:02,590 --> 00:06:07,660 So we are not bounded with small amount of deviations and initial tracking errors. 67 00:06:07,900 --> 00:06:14,470 In this case, it would be logical that stability, but we want global stability. 68 00:06:14,920 --> 00:06:22,420 And finally, we do need convergence to the correct parameter values, as we have said before. 69 00:06:23,470 --> 00:06:29,680 The key concept to achieve this adaptation is utilizing linear parameterization of the robot dynamics, 70 00:06:29,690 --> 00:06:31,540 and we have seen this before. 71 00:06:31,870 --> 00:06:39,640 As you remember, we can ride this robot dynamics equation of robot manipulator in this way where Vivo's 72 00:06:39,640 --> 00:06:43,420 regression matrix and alpha was that dynamic or efficient. 73 00:06:43,840 --> 00:06:49,660 However, as we have said before, we have partial knowledge about dynamic parameters, so coefficients. 74 00:06:49,990 --> 00:06:52,930 So we can write dynamic equations in this way. 75 00:06:52,930 --> 00:07:01,660 Instead, the terms of it had to represent estimations of the terms, namely method is estimation of 76 00:07:01,660 --> 00:07:03,430 term M and so on. 77 00:07:04,000 --> 00:07:08,290 So overhead is estimation of dynamic parameters of alpha. 78 00:07:09,160 --> 00:07:15,940 We need to find appropriate update rules for dynamic parameters, estimation of alpha in order to make 79 00:07:15,940 --> 00:07:17,710 the controller we have seen. 80 00:07:18,670 --> 00:07:24,640 In order to make the controller, we have seen Adaptive, which controllers we have seen before, and 81 00:07:24,640 --> 00:07:32,140 we have seen control feet for birth control and feedback minimization in the Universe Dynamics Control. 82 00:07:32,500 --> 00:07:39,310 We can get good model based controllers by combination of these like inverse dynamics, feedforward 83 00:07:39,310 --> 00:07:45,460 controller, PD control action and nonlinear control that's based on feedback to negotiation. 84 00:07:45,730 --> 00:07:51,550 Let's analyze these two control methods and discuss whether we can make them adaptive. 85 00:07:52,060 --> 00:07:57,400 Let's start with inverse dynamics forward feedforward plus PD control. 86 00:07:58,030 --> 00:08:01,290 You can see the two parts call it differently. 87 00:08:01,780 --> 00:08:08,140 The good thing about this controller is that as the feedforward term contains only desired values, 88 00:08:08,410 --> 00:08:13,750 it can be calculated off-line, which increases sure the speed of the control algorithm. 89 00:08:14,200 --> 00:08:19,930 However, as you can see in the control algorithm, we have used the exact term values. 90 00:08:20,440 --> 00:08:26,680 In this case, we can get asymptotic stability in terms of tracking errors, but we do not know exact 91 00:08:26,680 --> 00:08:28,090 values of these terms. 92 00:08:28,390 --> 00:08:35,530 So the right control algorithm, with terms indicated by hand saw not exactly obvious, but their estimations. 93 00:08:35,980 --> 00:08:42,850 Now we have a problem when we use estimation of the terms, we cannot get decoupling and initialization 94 00:08:42,850 --> 00:08:45,940 we have achieved before with inverse dynamics. 95 00:08:46,420 --> 00:08:52,450 Please review inverse dynamics if you can not remember the linear regression process and also the copy 96 00:08:53,230 --> 00:08:55,970 before with its exact values of terms. 97 00:08:55,990 --> 00:09:03,050 We were able to get M.C terms as common terms outside and get rid of and G terms. 98 00:09:03,790 --> 00:09:10,840 But with estimated values, we cannot do the same because terms with heart are not the same with the 99 00:09:10,840 --> 00:09:15,160 ones we thought had as we can look to these cancellations. 100 00:09:15,160 --> 00:09:22,210 We cannot achieve decoupling and initialization, and we have these aerodynamics, which is stable as 101 00:09:22,210 --> 00:09:29,980 kidI and CPP gains are positive definite, but they convert not zero, but ETA, which is nonlinear 102 00:09:29,980 --> 00:09:32,860 function of unknown, uncertain parameters. 103 00:09:34,630 --> 00:09:36,250 Let's analyze the second one. 104 00:09:37,060 --> 00:09:44,050 Indeed, as you can see, this control algorithm contains feedback minimization not feedforward as previous 105 00:09:44,050 --> 00:09:45,360 case with PD. 106 00:09:45,940 --> 00:09:53,500 Again, we have to write it with estimated terms instead of exact loans, and the same thing happens 107 00:09:53,500 --> 00:09:54,310 in error. 108 00:09:55,810 --> 00:09:59,320 It doesn't convert to zero, even if it's stable. 109 00:09:59,950 --> 00:10:06,460 This is normal that aerodynamics don't convert to the zero because of uncertainties, and we knew that 110 00:10:06,460 --> 00:10:07,090 beforehand. 111 00:10:07,750 --> 00:10:14,260 Love, you have to make these two algorithms adaptive by finding appropriate dynamic parameter updates 112 00:10:14,260 --> 00:10:14,680 rule. 113 00:10:15,400 --> 00:10:22,510 If you find this rule, then dynamic model can adapt to these changes, and aerodynamics can converge 114 00:10:22,510 --> 00:10:24,580 to zero asymptotically. 115 00:10:25,420 --> 00:10:33,070 The issue with these algorithms is that the process of making these control algorithms adaptive is not 116 00:10:33,070 --> 00:10:35,560 trivial because of below reasons. 117 00:10:36,040 --> 00:10:41,670 During a transient estimation of inertia, matter is can be non positive or single. 118 00:10:42,040 --> 00:10:49,150 It can happen because we define an updated rule, and we don't put some constraints to this update. 119 00:10:49,480 --> 00:10:53,260 It will try to adapt the changes by whatever way it can. 120 00:10:53,800 --> 00:11:02,950 This will cause problems during inverse dynamics because inverse dynamics, as you can remember, so 121 00:11:03,310 --> 00:11:09,970 inverse dynamics control, I mean, because inverse dynamics control, as you remember, we have to 122 00:11:09,970 --> 00:11:11,920 find inverse of inertia matrix. 123 00:11:12,070 --> 00:11:19,200 If inertial metrics become similar, then this will create a problem during inversion, then instability. 124 00:11:19,200 --> 00:11:26,660 It can be the problem because as inertia matrix becomes non positive, it will cause non positive PD 125 00:11:26,680 --> 00:11:30,460 gains, which will surely cause instability in aerodynamics. 126 00:11:30,850 --> 00:11:38,720 You can see this from the second control algorithms, namely M Times CP and M Times Cadee. 127 00:11:38,740 --> 00:11:44,740 Terms will be new PD games, which can be negative so cause instability. 128 00:11:46,660 --> 00:11:54,970 Finally, a complex analysis is needed to determine bound on PD gains in the first control algorithm. 129 00:11:55,630 --> 00:12:01,840 So because of these reasons, we will try to choose another control method which doesn't contain these 130 00:12:01,840 --> 00:12:05,140 issues and make the process of adaptation easier. 131 00:12:05,710 --> 00:12:13,030 Then we will find correct then, if I correct update for the dynamic coefficient. 132 00:12:13,870 --> 00:12:18,400 But let's stop here and continue on further in the second part.