0 00:00:00,000 --> 00:00:30,000 Dear viewer, these subtitles were generated by a machine via the service Trint and therefore are (very) buggy. If you are capable, please help us to create good quality subtitles: https://c3subtitles.de/talk/345 Thanks! 1 00:00:09,720 --> 00:00:10,720 So 2 00:00:12,180 --> 00:00:14,459 the stock will be on the experimental 3 00:00:14,460 --> 00:00:16,979 rover project and we had some problems, 4 00:00:16,980 --> 00:00:18,420 but here are the slides. 5 00:00:20,190 --> 00:00:21,809 So I'm going to start with a little 6 00:00:21,810 --> 00:00:24,029 introduction and tell you why 7 00:00:24,030 --> 00:00:25,709 this project might eventually become 8 00:00:25,710 --> 00:00:28,019 interesting and why we are doing it 9 00:00:28,020 --> 00:00:30,119 and then talk us separate 10 00:00:30,120 --> 00:00:31,439 into two main parts. 11 00:00:31,440 --> 00:00:33,359 And the first part I am going to talk 12 00:00:33,360 --> 00:00:35,219 about walking in simulation. 13 00:00:35,220 --> 00:00:37,439 That is we take a physics engine, 14 00:00:37,440 --> 00:00:39,689 build a model of the rover and try 15 00:00:39,690 --> 00:00:42,539 to get it to walk in the 16 00:00:42,540 --> 00:00:44,639 simplified physics with a few simplifying 17 00:00:44,640 --> 00:00:45,719 assumptions. 18 00:00:45,720 --> 00:00:47,579 And then in the second part of talk, 19 00:00:47,580 --> 00:00:49,739 Felix will tell you about how we might 20 00:00:49,740 --> 00:00:51,209 eventually move from simulation to 21 00:00:51,210 --> 00:00:52,210 reality. 22 00:00:54,240 --> 00:00:56,309 So this project is about 23 00:00:56,310 --> 00:00:59,369 building a life sized humanoid robot. 24 00:00:59,370 --> 00:01:01,529 And for the next 25 00:01:01,530 --> 00:01:03,449 year at least, we are going to focus on 26 00:01:03,450 --> 00:01:06,029 the legs. So arms might come eventually, 27 00:01:06,030 --> 00:01:07,110 but only much later. 28 00:01:09,360 --> 00:01:12,089 There are, as was mentioned already, 29 00:01:12,090 --> 00:01:13,949 quite a few projects that are already 30 00:01:13,950 --> 00:01:15,809 working on this, but none of them are 31 00:01:15,810 --> 00:01:17,849 really a fully open. 32 00:01:17,850 --> 00:01:20,399 So we try to make a fully free 33 00:01:20,400 --> 00:01:21,959 project, which is both open source 34 00:01:21,960 --> 00:01:23,549 software and hardware. 35 00:01:24,850 --> 00:01:27,609 Also, we try to completely document 36 00:01:27,610 --> 00:01:29,079 the development process. 37 00:01:30,290 --> 00:01:32,299 The goal will be to have on state of the 38 00:01:32,300 --> 00:01:34,609 art software as fast as possible, because 39 00:01:34,610 --> 00:01:36,469 software, of course, is easy to copy. 40 00:01:36,470 --> 00:01:38,809 And for the hardware, we try to focus 41 00:01:38,810 --> 00:01:41,179 on something that is manufactured 42 00:01:41,180 --> 00:01:42,519 with moderate resources. 43 00:01:45,630 --> 00:01:47,369 Well, why would one want to have a 44 00:01:47,370 --> 00:01:49,499 humanoid robot at all, and 45 00:01:49,500 --> 00:01:51,829 we are, of course, in 46 00:01:51,830 --> 00:01:53,459 dedicated environment, so if you are on 47 00:01:53,460 --> 00:01:55,589 the street, you're not going to be the 48 00:01:55,590 --> 00:01:57,929 wheeled robot no matter what you do. 49 00:01:57,930 --> 00:01:59,939 On the other hand, human environment such 50 00:01:59,940 --> 00:02:02,219 as this room are really limited 51 00:02:02,220 --> 00:02:03,329 if you are on wheels. 52 00:02:03,330 --> 00:02:04,859 So, for example, there are stairs over. 53 00:02:04,860 --> 00:02:06,629 There are there are stairs you couldn't 54 00:02:06,630 --> 00:02:08,999 get on the stage without 55 00:02:09,000 --> 00:02:10,109 climbing stairs. 56 00:02:10,110 --> 00:02:12,299 So there are many reasons why Wheelz 57 00:02:12,300 --> 00:02:14,249 might not be so ideal. 58 00:02:14,250 --> 00:02:16,379 If service robots eventually do 59 00:02:16,380 --> 00:02:18,299 become commonplace, these environments 60 00:02:18,300 --> 00:02:19,379 may change. 61 00:02:19,380 --> 00:02:21,149 But at least if everything goes wrong and 62 00:02:21,150 --> 00:02:23,519 there is a disaster, you 63 00:02:23,520 --> 00:02:25,499 really need to have some alternative to 64 00:02:25,500 --> 00:02:26,909 Wheelz. 65 00:02:26,910 --> 00:02:28,289 But of course, I mean, for us, the real 66 00:02:28,290 --> 00:02:30,209 reason is that we saw these videos from 67 00:02:30,210 --> 00:02:32,399 Boston Dynamics and you 68 00:02:32,400 --> 00:02:33,539 all saw them and you thought, that's 69 00:02:33,540 --> 00:02:34,589 really cool. 70 00:02:34,590 --> 00:02:36,359 It's unfortunate that the military is 71 00:02:36,360 --> 00:02:36,989 doing it. 72 00:02:36,990 --> 00:02:38,159 Let's try to do something 73 00:02:39,330 --> 00:02:40,970 similar ourselves. 74 00:02:43,670 --> 00:02:46,129 Well, it seems that the progress 75 00:02:46,130 --> 00:02:48,679 on humanoid robots after several decades 76 00:02:48,680 --> 00:02:50,869 is finally heating up and on the other 77 00:02:50,870 --> 00:02:52,999 hand, the big company players like Boston 78 00:02:53,000 --> 00:02:54,949 Dynamics and Traffic, which are now both 79 00:02:54,950 --> 00:02:57,409 owned by Google, are really secretive. 80 00:02:57,410 --> 00:02:59,779 So they published YouTube videos. 81 00:02:59,780 --> 00:03:01,709 Make you that excited? 82 00:03:01,710 --> 00:03:03,439 That I really exciting, but don't really 83 00:03:03,440 --> 00:03:05,659 tell you anything and seem to be no 84 00:03:05,660 --> 00:03:07,179 scientific papers or anything. 85 00:03:08,400 --> 00:03:10,769 There are also university projects 86 00:03:10,770 --> 00:03:12,839 that do publish papers, but 87 00:03:12,840 --> 00:03:14,339 still they don't they don't actually 88 00:03:14,340 --> 00:03:16,499 publish usually sars-cov-2, they 89 00:03:16,500 --> 00:03:18,689 don't publish the drawings 90 00:03:18,690 --> 00:03:20,669 and they are not really intended for you 91 00:03:20,670 --> 00:03:22,499 to copy their hardware. 92 00:03:22,500 --> 00:03:24,389 They are scientists and they write papers 93 00:03:24,390 --> 00:03:26,139 and that's about it. 94 00:03:26,140 --> 00:03:28,029 And the other problem is, of course, that 95 00:03:28,030 --> 00:03:29,799 existing robots cost on the order of 96 00:03:29,800 --> 00:03:31,869 several hundred thousand dollars, which 97 00:03:31,870 --> 00:03:34,059 is completely unaffordable for hobbyists 98 00:03:34,060 --> 00:03:35,949 now a dream at the moment, just to get 99 00:03:35,950 --> 00:03:38,289 this down to maybe a few thousand euros, 100 00:03:38,290 --> 00:03:40,629 which is still a lot, but 101 00:03:40,630 --> 00:03:42,789 possibly affordable for a small group 102 00:03:42,790 --> 00:03:43,359 of people. 103 00:03:43,360 --> 00:03:44,360 Hackerspace also. 104 00:03:45,320 --> 00:03:46,849 I would also like to mention that 105 00:03:47,960 --> 00:03:49,999 this first part of the talk where we do a 106 00:03:50,000 --> 00:03:52,129 physics based character animation, that's 107 00:03:52,130 --> 00:03:53,569 actually a big topic in computer 108 00:03:53,570 --> 00:03:56,239 animation, that they don't seem to focus 109 00:03:56,240 --> 00:03:58,099 on putting this idea some real on real 110 00:03:58,100 --> 00:04:00,199 robots to use physics as a tool 111 00:04:00,200 --> 00:04:02,419 to get get 112 00:04:02,420 --> 00:04:03,559 realistic animation. 113 00:04:06,600 --> 00:04:08,219 So what are you going to do in a first 114 00:04:08,220 --> 00:04:09,299 talk? 115 00:04:09,300 --> 00:04:11,279 The idea is to take a simplified physics 116 00:04:11,280 --> 00:04:13,529 model and try 117 00:04:13,530 --> 00:04:15,719 to simulate a robot and then to develop 118 00:04:15,720 --> 00:04:17,338 a controller that will keep it from 119 00:04:17,339 --> 00:04:18,339 falling down. 120 00:04:19,220 --> 00:04:21,439 The idea is, despite 121 00:04:21,440 --> 00:04:24,079 actually working on the controller 122 00:04:24,080 --> 00:04:26,179 to actually inform design choices for the 123 00:04:26,180 --> 00:04:28,339 later projecto dissimulation will 124 00:04:28,340 --> 00:04:30,229 ideally tell us what kind of maltose we 125 00:04:30,230 --> 00:04:32,149 need, how fast they have to be, what kind 126 00:04:32,150 --> 00:04:34,369 of years we need, how 127 00:04:34,370 --> 00:04:36,619 well we can cope with Ansun 128 00:04:36,620 --> 00:04:38,059 uncertainty and so on. 129 00:04:40,360 --> 00:04:42,489 We are going to use a dedicated dynamic's 130 00:04:42,490 --> 00:04:44,559 toolkit that we brought ourselves 131 00:04:44,560 --> 00:04:46,699 from algorithms that are published, 132 00:04:46,700 --> 00:04:49,089 but we also use the open dynamics engine 133 00:04:49,090 --> 00:04:50,739 that was already briefly mentioned in the 134 00:04:50,740 --> 00:04:52,869 last talk just to make sure that we 135 00:04:52,870 --> 00:04:55,339 don't exploit any implementation 136 00:04:55,340 --> 00:04:57,399 backs in our own engine to our 137 00:04:57,400 --> 00:04:59,559 advantage that we have an external engine 138 00:04:59,560 --> 00:05:01,689 that kind of lets us know that 139 00:05:01,690 --> 00:05:04,119 this works with our, you know, the 140 00:05:04,120 --> 00:05:06,789 assumptions we might unconsciously 141 00:05:06,790 --> 00:05:07,790 make. 142 00:05:08,840 --> 00:05:11,179 So how do you let a robot at this point, 143 00:05:11,180 --> 00:05:12,799 and this is really the basics of all the 144 00:05:12,800 --> 00:05:15,079 game physics engines that you may know, 145 00:05:15,080 --> 00:05:17,749 such as the bullet and so on, 146 00:05:17,750 --> 00:05:19,849 and the center concepts that of a 147 00:05:19,850 --> 00:05:22,249 rigid body, which is a physical 148 00:05:22,250 --> 00:05:24,049 body that is assumed to be completely 149 00:05:24,050 --> 00:05:25,699 unreformable. So it can't bend. 150 00:05:25,700 --> 00:05:26,700 It can flex. 151 00:05:27,920 --> 00:05:29,909 And as a result of this, the massive 152 00:05:29,910 --> 00:05:31,999 situation is completely convinced of 10 153 00:05:32,000 --> 00:05:34,339 parameters and this thing has six 154 00:05:34,340 --> 00:05:36,529 degrees of freedom, and except for 155 00:05:36,530 --> 00:05:38,389 the ten parameters, the simulation engine 156 00:05:38,390 --> 00:05:40,129 doesn't really care about how the mass is 157 00:05:40,130 --> 00:05:41,189 distributed. 158 00:05:41,190 --> 00:05:42,319 It is only natural for collision 159 00:05:42,320 --> 00:05:44,059 detection, but not for actually for 160 00:05:44,060 --> 00:05:45,060 actual dynamics. 161 00:05:46,580 --> 00:05:48,649 The next step up in realism would be 162 00:05:48,650 --> 00:05:50,839 the so-called soft body 163 00:05:50,840 --> 00:05:52,849 shown here, a picture from Wikipedia, 164 00:05:52,850 --> 00:05:54,769 probably most commonplace example of a 165 00:05:54,770 --> 00:05:55,770 flexing beam. 166 00:05:56,960 --> 00:05:58,609 Then suddenly you need the complete 167 00:05:58,610 --> 00:06:00,589 details of mass distribution and so on, 168 00:06:00,590 --> 00:06:02,149 which essentially means you have to make 169 00:06:02,150 --> 00:06:04,249 a character or you have to design 170 00:06:04,250 --> 00:06:05,449 your robot. You have to decide what 171 00:06:05,450 --> 00:06:07,279 materials to use and so on. 172 00:06:07,280 --> 00:06:09,169 And even then, this thing has infinitely 173 00:06:09,170 --> 00:06:10,759 many degrees of freedom. 174 00:06:10,760 --> 00:06:13,879 It's become a lot after democratization. 175 00:06:13,880 --> 00:06:15,289 So this is numerically much more 176 00:06:15,290 --> 00:06:16,999 expensive to simulate. 177 00:06:17,000 --> 00:06:18,649 The method would be called the so-called 178 00:06:18,650 --> 00:06:19,879 finite element method. 179 00:06:21,310 --> 00:06:23,409 If you can and 180 00:06:23,410 --> 00:06:25,139 you don't want to do this at the moment, 181 00:06:25,140 --> 00:06:26,949 our robot to simulate it as a collection 182 00:06:26,950 --> 00:06:27,950 of rigid bodies, 183 00:06:29,050 --> 00:06:31,069 this is the model we use at the moment. 184 00:06:31,070 --> 00:06:33,609 It consists of six rigid bodies, 185 00:06:33,610 --> 00:06:36,159 the torso, which is just one piece 186 00:06:36,160 --> 00:06:37,480 and two legs. 187 00:06:38,500 --> 00:06:39,859 You have six degrees of freedom. 188 00:06:39,860 --> 00:06:42,489 Peleg three in the hip, 189 00:06:42,490 --> 00:06:45,429 one in the knee and two in the ankle. 190 00:06:45,430 --> 00:06:47,649 Four six degrees of freedom, total polec. 191 00:06:47,650 --> 00:06:49,959 And the advantage of this is that the 192 00:06:49,960 --> 00:06:52,239 body that is the foot also 193 00:06:52,240 --> 00:06:53,559 has six degrees of freedom. 194 00:06:53,560 --> 00:06:55,299 So in this country duration, we can 195 00:06:55,300 --> 00:06:57,219 essentially control the position and the 196 00:06:57,220 --> 00:06:59,319 orientation of both feet, 197 00:06:59,320 --> 00:07:00,320 but not more. 198 00:07:02,870 --> 00:07:05,329 At the moment, so this is sufficient 199 00:07:05,330 --> 00:07:06,330 for what we want to do. 200 00:07:07,820 --> 00:07:09,879 Now, let's come to control our design. 201 00:07:09,880 --> 00:07:11,449 Why is this even a hard problem? 202 00:07:11,450 --> 00:07:13,879 I mean, if you've seen 3-D animated 203 00:07:13,880 --> 00:07:15,379 films, you might think that this will be 204 00:07:15,380 --> 00:07:17,529 easy, at least reasonably easy. 205 00:07:20,400 --> 00:07:22,479 He is an industrial robot 206 00:07:22,480 --> 00:07:24,429 and a biped, and there's really a lot of 207 00:07:24,430 --> 00:07:26,739 work on industrial robots, we last talked 208 00:07:26,740 --> 00:07:28,029 about this. 209 00:07:28,030 --> 00:07:29,709 What's the main difference? 210 00:07:29,710 --> 00:07:30,999 Well, the main difference, as you see 211 00:07:31,000 --> 00:07:33,249 here, is that the industrial robot is 212 00:07:33,250 --> 00:07:35,529 bolted to the ground with rather large 213 00:07:35,530 --> 00:07:36,549 bolts. 214 00:07:36,550 --> 00:07:38,259 And it is obviously impossible for a 215 00:07:38,260 --> 00:07:40,359 biped because it can't screw 216 00:07:40,360 --> 00:07:41,979 its foot on the ground every time it 217 00:07:41,980 --> 00:07:42,889 wants to take a step. 218 00:07:42,890 --> 00:07:43,890 That's impossible. 219 00:07:44,830 --> 00:07:46,959 And this is what this is 220 00:07:46,960 --> 00:07:48,419 what makes this problem hard. 221 00:07:51,820 --> 00:07:53,379 The thing is that for the industrial 222 00:07:53,380 --> 00:07:55,719 robot to control all degrees of freedom, 223 00:07:55,720 --> 00:07:57,969 this is called fully actuated 224 00:07:57,970 --> 00:07:59,919 and this means that any trajectory can be 225 00:07:59,920 --> 00:08:00,979 followed. 226 00:08:00,980 --> 00:08:02,589 This, of course, not completely true for 227 00:08:02,590 --> 00:08:04,059 industrial robots. You then start to 228 00:08:04,060 --> 00:08:05,799 worry about things like collision 229 00:08:05,800 --> 00:08:07,129 avoidance and so on. 230 00:08:07,130 --> 00:08:09,219 But if I mean, if the 231 00:08:09,220 --> 00:08:11,469 problem were as simple as for walking 232 00:08:11,470 --> 00:08:13,149 robot, then collision avoidance is 233 00:08:13,150 --> 00:08:14,679 usually not a big problem if you're on 234 00:08:14,680 --> 00:08:15,919 even ground. 235 00:08:15,920 --> 00:08:17,949 So it would be trivial or this would seem 236 00:08:17,950 --> 00:08:19,899 to be trivial, but it's actually made 237 00:08:19,900 --> 00:08:22,499 complicated by the fact that you have to 238 00:08:22,500 --> 00:08:24,369 just stand for it, which is not fixed to 239 00:08:24,370 --> 00:08:26,679 the ground, and therefore 240 00:08:26,680 --> 00:08:28,719 the intrinsic dynamics begin to matter. 241 00:08:28,720 --> 00:08:30,669 It actually matters how fast you execute 242 00:08:30,670 --> 00:08:33,069 a direct trajectory and so on, 243 00:08:33,070 --> 00:08:35,229 and you really can't take any trajectory 244 00:08:35,230 --> 00:08:36,230 any longer. 245 00:08:36,880 --> 00:08:38,769 And I'm going to show you a little demo 246 00:08:38,770 --> 00:08:39,770 for this. 247 00:08:40,880 --> 00:08:42,249 Which is a thing here, 248 00:08:43,250 --> 00:08:45,169 though, this is what we would what we 249 00:08:45,170 --> 00:08:47,929 might like to get 250 00:08:47,930 --> 00:08:50,149 is a model of a robot with no 251 00:08:50,150 --> 00:08:52,219 physics engine and we might want 252 00:08:52,220 --> 00:08:53,209 to get this. 253 00:08:53,210 --> 00:08:54,139 It just walks. 254 00:08:54,140 --> 00:08:55,459 I mean, just doesn't look particularly. 255 00:08:55,460 --> 00:08:57,529 Well, that seems OK. 256 00:08:58,690 --> 00:09:00,849 So now if you take this and connect 257 00:09:00,850 --> 00:09:02,139 an natural physics engine. 258 00:09:05,660 --> 00:09:07,690 Then we see something disappointing. 259 00:09:09,360 --> 00:09:11,179 Namely, that. 260 00:09:13,290 --> 00:09:15,059 It just falls over. 261 00:09:18,910 --> 00:09:20,709 The thing is, the trajectory tracking 262 00:09:20,710 --> 00:09:22,899 actually works, so you can see 263 00:09:22,900 --> 00:09:25,119 that at the joint angles 264 00:09:25,120 --> 00:09:27,369 in the robot, they actually more or less 265 00:09:27,370 --> 00:09:29,529 tracked the trajectories they 266 00:09:29,530 --> 00:09:31,509 had in the last simulation. 267 00:09:31,510 --> 00:09:33,309 But the big problem is that the foot 268 00:09:33,310 --> 00:09:35,259 which we cannot control, just loses 269 00:09:35,260 --> 00:09:36,309 contact with the ground. 270 00:09:37,390 --> 00:09:39,159 And this is exactly the kind of problem 271 00:09:39,160 --> 00:09:41,079 you need to worry about if you want to 272 00:09:41,080 --> 00:09:43,149 design a controller for a walking 273 00:09:43,150 --> 00:09:45,610 robot, see it just fight over. 274 00:09:49,690 --> 00:09:51,819 So let's do a little 275 00:09:51,820 --> 00:09:54,039 bit of physics here and talk 276 00:09:54,040 --> 00:09:55,659 about contact forces. 277 00:09:55,660 --> 00:09:57,099 Now, contact is in principle a 278 00:09:57,100 --> 00:09:59,259 complicated microscopic phenomenon. 279 00:09:59,260 --> 00:10:00,939 But there's one thing that's actually 280 00:10:00,940 --> 00:10:01,929 quite simple. 281 00:10:01,930 --> 00:10:03,459 Namely, that context is usually non 282 00:10:03,460 --> 00:10:04,839 sticky. 283 00:10:04,840 --> 00:10:06,999 And I illustrate this as this cartoon 284 00:10:07,000 --> 00:10:09,279 of picking up a box of 285 00:10:09,280 --> 00:10:11,339 a place, a box or something 286 00:10:11,340 --> 00:10:12,069 and have a box. 287 00:10:12,070 --> 00:10:14,089 But this pullover will do that places on 288 00:10:14,090 --> 00:10:16,719 the table and it's actually put towards 289 00:10:16,720 --> 00:10:18,189 towards the center of the earth by 290 00:10:18,190 --> 00:10:20,319 gravity. And the reaction force from the 291 00:10:20,320 --> 00:10:22,599 table just compensates for 292 00:10:22,600 --> 00:10:23,979 the resulting force of zero. 293 00:10:23,980 --> 00:10:26,479 So by Newton, it doesn't move. 294 00:10:26,480 --> 00:10:28,539 If I try to lift it up, I don't quite 295 00:10:28,540 --> 00:10:29,950 succeed then. 296 00:10:31,510 --> 00:10:34,209 Well, the lifting force compensates 297 00:10:34,210 --> 00:10:36,249 a bit of gravity and the rest is 298 00:10:36,250 --> 00:10:37,250 compensated by 299 00:10:39,130 --> 00:10:40,239 by the reaction force 300 00:10:41,320 --> 00:10:43,629 or contact force and the resulting 301 00:10:43,630 --> 00:10:44,709 from the station. 302 00:10:44,710 --> 00:10:46,759 So this is a so-called constrained force 303 00:10:46,760 --> 00:10:49,419 that just takes the value it needs to 304 00:10:49,420 --> 00:10:51,309 stop this from accelerating. 305 00:10:51,310 --> 00:10:53,469 But finally, if I pull up what was 306 00:10:53,470 --> 00:10:55,929 a large lifting force, then 307 00:10:55,930 --> 00:10:57,369 the contact force would have to be 308 00:10:57,370 --> 00:10:58,809 negative in this picture. 309 00:10:58,810 --> 00:11:01,029 And this this would happen if it were 310 00:11:01,030 --> 00:11:02,029 glued to the table. 311 00:11:02,030 --> 00:11:03,889 But if it's just the normal contact and 312 00:11:03,890 --> 00:11:05,859 it can't and it would just actually 313 00:11:05,860 --> 00:11:08,369 accelerate upwards and pick it up, 314 00:11:08,370 --> 00:11:10,689 it is really the central concept that 315 00:11:10,690 --> 00:11:12,549 happened to the poor robot in the last 316 00:11:12,550 --> 00:11:13,550 simulation. 317 00:11:14,740 --> 00:11:16,389 Now, let's consider multiple contact 318 00:11:16,390 --> 00:11:17,390 points. 319 00:11:18,160 --> 00:11:20,469 Of course. I mean, this is, 320 00:11:20,470 --> 00:11:22,569 again, a cartoon, and in reality, you 321 00:11:22,570 --> 00:11:24,009 could have very, very many contact 322 00:11:24,010 --> 00:11:26,649 points. But let's suppose we have four 323 00:11:26,650 --> 00:11:28,389 and this is supposed to be a cartoon of 324 00:11:28,390 --> 00:11:29,390 the foot. 325 00:11:30,790 --> 00:11:32,919 Now, at each contact 326 00:11:32,920 --> 00:11:35,169 point, there is a 327 00:11:35,170 --> 00:11:36,279 contact force acting 328 00:11:37,360 --> 00:11:38,949 and we can now define the so-called 329 00:11:38,950 --> 00:11:40,989 center of pressure as the weighted 330 00:11:40,990 --> 00:11:43,090 average of all the contact points. 331 00:11:45,490 --> 00:11:47,349 And we weight them just by their 332 00:11:47,350 --> 00:11:49,179 contribution to the normal component of 333 00:11:49,180 --> 00:11:51,429 the contact force of 334 00:11:51,430 --> 00:11:53,769 X2. This, if all the contact 335 00:11:53,770 --> 00:11:55,959 force come from the next to an X, 336 00:11:55,960 --> 00:11:58,149 C is going to move closer to X two and so 337 00:11:58,150 --> 00:11:59,150 on. 338 00:11:59,650 --> 00:12:01,689 We can write this with these weighting 339 00:12:01,690 --> 00:12:03,879 factors, alpha, and 340 00:12:03,880 --> 00:12:06,099 then the fact that the normal that these 341 00:12:06,100 --> 00:12:08,439 events are larger than zero implies 342 00:12:08,440 --> 00:12:10,179 that the others have to live between zero 343 00:12:10,180 --> 00:12:11,180 and one. 344 00:12:11,950 --> 00:12:13,689 Mathematically, this is quite a convex 345 00:12:13,690 --> 00:12:14,499 some. 346 00:12:14,500 --> 00:12:16,779 But even if you don't know what that is, 347 00:12:16,780 --> 00:12:18,909 it's really quite obvious that if we take 348 00:12:18,910 --> 00:12:21,279 weighted average of these four points 349 00:12:21,280 --> 00:12:22,899 with weighting factors between zero and 350 00:12:22,900 --> 00:12:25,029 one, then the average can move outside of 351 00:12:25,030 --> 00:12:25,959 the box. 352 00:12:25,960 --> 00:12:28,089 That's really all there is to it, 353 00:12:28,090 --> 00:12:29,559 at least for the case of a box. 354 00:12:31,450 --> 00:12:32,739 Now, this seems to depend on the 355 00:12:32,740 --> 00:12:34,539 microscopic details, and that would make 356 00:12:34,540 --> 00:12:36,489 it completely useless because we can't 357 00:12:36,490 --> 00:12:38,229 hope to model this. 358 00:12:38,230 --> 00:12:40,179 We don't actually know the microscopic 359 00:12:40,180 --> 00:12:41,200 structure of the ground. 360 00:12:43,120 --> 00:12:45,449 But there is a magic trick in a way, 361 00:12:45,450 --> 00:12:47,619 and that is if you sum all 362 00:12:47,620 --> 00:12:49,659 the contact forces into total contact 363 00:12:49,660 --> 00:12:51,909 force and a total contact talk, 364 00:12:51,910 --> 00:12:53,829 and there is this equation, phoniness in 365 00:12:53,830 --> 00:12:57,009 this state, let us calculate 366 00:12:57,010 --> 00:12:58,719 the center of pressure just from the 367 00:12:58,720 --> 00:13:01,159 total contact force and the total contact 368 00:13:01,160 --> 00:13:02,160 talk. 369 00:13:02,620 --> 00:13:04,570 This is really nice because 370 00:13:05,950 --> 00:13:08,139 we can now look at walking and usually 371 00:13:08,140 --> 00:13:09,990 the stands of stationary. 372 00:13:11,050 --> 00:13:13,659 So in this case, the contact forces 373 00:13:13,660 --> 00:13:15,729 have to compensate the reaction force to 374 00:13:15,730 --> 00:13:16,730 some robot body. 375 00:13:18,460 --> 00:13:19,959 And then we can just calculate the 376 00:13:19,960 --> 00:13:22,299 contact for the reaction forces 377 00:13:22,300 --> 00:13:24,529 from the robot body and get 378 00:13:24,530 --> 00:13:27,049 necessary conditions so that distance 379 00:13:27,050 --> 00:13:30,099 for it a chance at remaining stationary. 380 00:13:30,100 --> 00:13:31,929 And these conditions are well, first of 381 00:13:31,930 --> 00:13:33,339 all, the center of pressure has to remain 382 00:13:33,340 --> 00:13:34,579 inside the foot. 383 00:13:34,580 --> 00:13:36,759 And second of all, it can't just 384 00:13:36,760 --> 00:13:38,859 pull up at Stanford like so 385 00:13:38,860 --> 00:13:40,959 for the total, total, normal 386 00:13:40,960 --> 00:13:43,299 component has to be positive as much 387 00:13:43,300 --> 00:13:44,300 as the sign 388 00:13:45,370 --> 00:13:46,689 turns out that these conditions are 389 00:13:46,690 --> 00:13:48,669 sufficient for those lift constraints. 390 00:13:48,670 --> 00:13:50,859 So if you don't wish you can slip on 391 00:13:50,860 --> 00:13:53,049 ground like this, then is that even 392 00:13:53,050 --> 00:13:54,009 sufficient? 393 00:13:54,010 --> 00:13:55,479 And usually this is sufficient in 394 00:13:55,480 --> 00:13:57,549 practice. If you fail, you fail in the 395 00:13:57,550 --> 00:13:59,019 way you saw in the last demo. 396 00:14:00,550 --> 00:14:02,169 And now you can actually say 397 00:14:02,170 --> 00:14:03,879 quantitatively you've either lost them or 398 00:14:03,880 --> 00:14:05,379 fails because this is the center of 399 00:14:05,380 --> 00:14:06,769 pressure that would be required. 400 00:14:06,770 --> 00:14:08,619 And you see, if it does this kind of 401 00:14:08,620 --> 00:14:10,509 work, it would require feet that are 402 00:14:10,510 --> 00:14:13,809 huge, almost 70 centimeters. 403 00:14:13,810 --> 00:14:15,909 This is not only unrealistic, this 404 00:14:15,910 --> 00:14:16,959 can't work. 405 00:14:16,960 --> 00:14:17,960 That would collide. 406 00:14:19,450 --> 00:14:21,009 So this lets you know what really 407 00:14:21,010 --> 00:14:22,449 happens, of course, is at the center of 408 00:14:22,450 --> 00:14:24,429 pressure goes to the dotted line and then 409 00:14:24,430 --> 00:14:26,679 stays there via the foot, starts 410 00:14:26,680 --> 00:14:27,680 to rotate. 411 00:14:28,810 --> 00:14:29,830 So this can't work. 412 00:14:30,970 --> 00:14:33,369 So our new control strategy should focus 413 00:14:33,370 --> 00:14:35,299 on contact forces. 414 00:14:35,300 --> 00:14:36,849 Here's an idea. Imagine the robot 415 00:14:36,850 --> 00:14:38,529 floating in space and you know, from 416 00:14:38,530 --> 00:14:40,509 school it totally now and angular 417 00:14:40,510 --> 00:14:41,799 momentum are conserved. 418 00:14:41,800 --> 00:14:43,569 And this implies that your center of 419 00:14:43,570 --> 00:14:45,919 gravity trajectory cannot be influenced. 420 00:14:45,920 --> 00:14:47,979 John, as an astronaut in space and you're 421 00:14:47,980 --> 00:14:50,109 floating away from your space station 422 00:14:50,110 --> 00:14:51,339 and there is nothing that you can do 423 00:14:51,340 --> 00:14:53,559 about it because the center of 424 00:14:53,560 --> 00:14:56,439 gravity or center of Mars in this case 425 00:14:56,440 --> 00:14:57,699 is moving away. 426 00:14:57,700 --> 00:15:00,039 And no matter what you do with your arms, 427 00:15:00,040 --> 00:15:01,200 you can change things 428 00:15:02,680 --> 00:15:03,759 on ground. 429 00:15:03,760 --> 00:15:05,889 Fortunate that you can do something about 430 00:15:05,890 --> 00:15:07,419 it, but you can only do something about 431 00:15:07,420 --> 00:15:09,549 it through contact forces. 432 00:15:09,550 --> 00:15:11,709 That is obviously a relay or 433 00:15:11,710 --> 00:15:13,419 not. Obviously, that is the relationship 434 00:15:13,420 --> 00:15:15,159 between linear, angular momentum change 435 00:15:15,160 --> 00:15:17,379 on the one hand and the contact forces 436 00:15:17,380 --> 00:15:19,569 transmitted through the foot or the feet 437 00:15:19,570 --> 00:15:20,570 on the other side. 438 00:15:22,210 --> 00:15:24,609 So we make a simplifying 439 00:15:24,610 --> 00:15:26,679 restriction and we assume that 440 00:15:26,680 --> 00:15:28,629 a total angular momentum of the robot is 441 00:15:28,630 --> 00:15:29,679 just zero. 442 00:15:29,680 --> 00:15:31,959 The simplifies the equation 443 00:15:31,960 --> 00:15:33,909 and then we're just left with the center 444 00:15:33,910 --> 00:15:35,859 of mass trajectory and we can completely 445 00:15:35,860 --> 00:15:37,749 determine the contact forces from the 446 00:15:37,750 --> 00:15:39,070 center of mass victory. 447 00:15:40,210 --> 00:15:42,489 In particular, a joint Ango trajectories 448 00:15:42,490 --> 00:15:44,499 only matter insofar as they influence the 449 00:15:44,500 --> 00:15:46,300 center of gravity trajectory. 450 00:15:48,370 --> 00:15:50,889 We still have six contact forces, that is 451 00:15:50,890 --> 00:15:52,989 six forces, three forces 452 00:15:52,990 --> 00:15:55,209 and three Turks, and 453 00:15:55,210 --> 00:15:57,369 we have six equations, namely that 454 00:15:57,370 --> 00:15:59,199 the angular momentum has not changed. 455 00:15:59,200 --> 00:16:00,969 We have the center of pressure and we 456 00:16:00,970 --> 00:16:02,739 have the height of the center of mass. 457 00:16:04,430 --> 00:16:06,309 Then you can solve a so-called boundary 458 00:16:06,310 --> 00:16:08,479 of your problem to find a center of mass 459 00:16:08,480 --> 00:16:10,869 checkley. This idea is from a 460 00:16:10,870 --> 00:16:12,409 PhD thesis from Munich 461 00:16:13,670 --> 00:16:15,559 Illustrated here. 462 00:16:15,560 --> 00:16:17,209 So we assume that the center of Mars is 463 00:16:17,210 --> 00:16:18,320 just a constant right. 464 00:16:19,370 --> 00:16:21,529 Now we specify a center 465 00:16:21,530 --> 00:16:23,629 of pressure. This is the blue line. 466 00:16:23,630 --> 00:16:25,789 We specify this so that it changes 467 00:16:25,790 --> 00:16:27,859 inside a legal region. 468 00:16:27,860 --> 00:16:29,479 And then solving the boundary of your 469 00:16:29,480 --> 00:16:31,409 problem gives us the green curve. 470 00:16:31,410 --> 00:16:33,799 And if you track this center of 471 00:16:33,800 --> 00:16:36,319 Mars or center of gravity, 472 00:16:36,320 --> 00:16:38,659 then it will generate 473 00:16:38,660 --> 00:16:40,819 these contact forces which are, as we 474 00:16:40,820 --> 00:16:42,710 chose them to be legal. 475 00:16:44,210 --> 00:16:46,579 Now, there's one slight problem, though, 476 00:16:46,580 --> 00:16:48,649 because we would usually have three 477 00:16:48,650 --> 00:16:50,299 boundary conditions, but only a second 478 00:16:50,300 --> 00:16:51,590 order differential equation, 479 00:16:53,690 --> 00:16:56,059 because Adelfa are usually 480 00:16:56,060 --> 00:16:57,569 we are already walking. 481 00:16:57,570 --> 00:17:00,109 So we have the center of mass position 482 00:17:00,110 --> 00:17:01,789 and velocity at the beginning. 483 00:17:01,790 --> 00:17:03,439 And we would also like to specify the 484 00:17:03,440 --> 00:17:05,838 center of mass position 485 00:17:05,839 --> 00:17:07,159 at the end so that it doesn't go 486 00:17:07,160 --> 00:17:08,160 completely off 487 00:17:09,349 --> 00:17:10,848 and we fix this. 488 00:17:10,849 --> 00:17:13,189 So we get the third degree of freedom, 489 00:17:13,190 --> 00:17:15,709 but just allowing our chosen 490 00:17:15,710 --> 00:17:17,449 center of pressure trajectory to be 491 00:17:17,450 --> 00:17:18,709 slightly modified. 492 00:17:19,930 --> 00:17:22,118 The problem now is that the center 493 00:17:22,119 --> 00:17:24,368 of pressure constrained by then become 494 00:17:24,369 --> 00:17:25,369 violated. 495 00:17:26,400 --> 00:17:28,149 What this is really saying is that 496 00:17:28,150 --> 00:17:29,559 sometimes you need to sidestep. 497 00:17:29,560 --> 00:17:31,089 So if you're walking in, someone pushes 498 00:17:31,090 --> 00:17:33,339 you. You can't just keep placing 499 00:17:33,340 --> 00:17:34,569 your feet like you want them to. 500 00:17:34,570 --> 00:17:36,589 You have to take a sidestep. 501 00:17:36,590 --> 00:17:37,590 And this is really what? 502 00:17:38,480 --> 00:17:40,279 This mathematical strain to tell you 503 00:17:40,280 --> 00:17:41,280 here, 504 00:17:42,740 --> 00:17:44,719 however, usually so if you're not pushed, 505 00:17:44,720 --> 00:17:46,369 for example, this approach works quite 506 00:17:46,370 --> 00:17:48,829 well in the next 507 00:17:48,830 --> 00:17:51,059 in the last step, we just take our 508 00:17:51,060 --> 00:17:53,239 robot with its 12 joints, basic use 509 00:17:53,240 --> 00:17:55,129 of freedom and use so-called inverse 510 00:17:55,130 --> 00:17:57,349 dynamics to just control the contact 511 00:17:57,350 --> 00:17:59,569 forces. And by this track, the center 512 00:17:59,570 --> 00:18:00,570 of gravity. 513 00:18:01,640 --> 00:18:03,679 Now, two cases, just four completely. 514 00:18:03,680 --> 00:18:04,879 The next life will be a demo. 515 00:18:04,880 --> 00:18:05,880 Don't worry. 516 00:18:06,980 --> 00:18:09,019 So if there's only one leg on the ground 517 00:18:09,020 --> 00:18:11,089 and we have six contact forces, again, 518 00:18:11,090 --> 00:18:13,189 six, three, four, three 519 00:18:13,190 --> 00:18:15,289 talks, and we also 520 00:18:15,290 --> 00:18:17,389 have to swing like just on the air and we 521 00:18:17,390 --> 00:18:19,549 have to test six generalized 522 00:18:19,550 --> 00:18:20,550 accelerations. 523 00:18:21,560 --> 00:18:23,239 Again, three translation, three 524 00:18:23,240 --> 00:18:24,240 translation. As for your. 525 00:18:25,520 --> 00:18:27,379 And each case will if you have two legs 526 00:18:27,380 --> 00:18:28,649 on the ground, then you have to contact 527 00:18:28,650 --> 00:18:29,929 forces, one for each leg. 528 00:18:29,930 --> 00:18:32,089 In each case, you have 12 equations for 529 00:18:32,090 --> 00:18:33,890 12 joints, degrees of freedom. 530 00:18:36,100 --> 00:18:38,199 Now, this approach is 531 00:18:38,200 --> 00:18:39,519 actually implemented here, 532 00:18:41,020 --> 00:18:44,229 and I just need to slightly 533 00:18:44,230 --> 00:18:46,299 play with my computer sci. 534 00:18:51,840 --> 00:18:53,909 So this is the 535 00:18:53,910 --> 00:18:54,910 first demo. 536 00:18:56,670 --> 00:18:59,009 And this is now actually a physics 537 00:18:59,010 --> 00:19:02,679 simulation with contact enabled, 538 00:19:02,680 --> 00:19:04,949 so this, as far as the physics engine 539 00:19:04,950 --> 00:19:06,659 is concerned, is physically possible. 540 00:19:06,660 --> 00:19:08,429 There are still some assumptions, but at 541 00:19:08,430 --> 00:19:10,200 least the contact is actually 542 00:19:11,460 --> 00:19:13,649 is actually respected on the order 543 00:19:13,650 --> 00:19:15,569 of hundred Newton meters, which is really 544 00:19:15,570 --> 00:19:17,699 a lot. And this is 545 00:19:17,700 --> 00:19:19,709 going to be the main problem really in 546 00:19:19,710 --> 00:19:21,839 the realization talk. 547 00:19:21,840 --> 00:19:23,899 But we also need quite a lot of power. 548 00:19:23,900 --> 00:19:25,379 So we need on the order of two hundred 549 00:19:25,380 --> 00:19:26,459 watts per joint. 550 00:19:30,120 --> 00:19:32,759 This will be a topic in the second part. 551 00:19:32,760 --> 00:19:34,439 So let's just summarize what we've just 552 00:19:34,440 --> 00:19:35,399 seen. 553 00:19:35,400 --> 00:19:37,589 And we've tried to design a confort 554 00:19:37,590 --> 00:19:39,749 for a controlled strategy based 555 00:19:39,750 --> 00:19:41,789 on contact force management. 556 00:19:41,790 --> 00:19:43,889 The performance is quite OK. 557 00:19:43,890 --> 00:19:45,209 I mean, there are better results in 558 00:19:45,210 --> 00:19:46,849 simulation, but it's a start. 559 00:19:48,360 --> 00:19:50,579 One thing is that the foot positions for 560 00:19:50,580 --> 00:19:51,959 this controller actually fixed in 561 00:19:51,960 --> 00:19:52,949 advance. 562 00:19:52,950 --> 00:19:54,569 So this could be used by a higher level 563 00:19:54,570 --> 00:19:56,639 controller to make it walk upstairs, 564 00:19:56,640 --> 00:19:57,539 for example. 565 00:19:57,540 --> 00:19:59,129 But it also limits the options we have 566 00:19:59,130 --> 00:20:00,609 for push recovery. 567 00:20:00,610 --> 00:20:02,879 And the idea to take a smart sidestep 568 00:20:02,880 --> 00:20:04,979 is just not implemented in this kind 569 00:20:04,980 --> 00:20:07,469 of controller, although it is simplifying 570 00:20:07,470 --> 00:20:09,419 this friction at a total angular momentum 571 00:20:09,420 --> 00:20:11,849 has to be zero because of this weird 572 00:20:11,850 --> 00:20:13,469 Tozzo motion that you've seen in the 573 00:20:13,470 --> 00:20:15,539 video and could try to fix 574 00:20:15,540 --> 00:20:17,579 this by adding arms and make this 575 00:20:17,580 --> 00:20:19,799 stereotypical walking style to keep 576 00:20:19,800 --> 00:20:21,329 the angular momentum zero. 577 00:20:22,860 --> 00:20:25,049 But at the moment, it doesn't do 578 00:20:25,050 --> 00:20:27,209 so much harm. So we just could just leave 579 00:20:27,210 --> 00:20:28,210 it like this. 580 00:20:30,950 --> 00:20:33,019 So regarding this 581 00:20:33,020 --> 00:20:35,119 last dynamic's part, we could, of 582 00:20:35,120 --> 00:20:36,799 course, just take the physics engine and 583 00:20:36,800 --> 00:20:39,319 treat this as a it's a black box 584 00:20:39,320 --> 00:20:41,599 and then use black box function 585 00:20:41,600 --> 00:20:44,269 and version to get our inverse dynamics. 586 00:20:44,270 --> 00:20:46,579 But it is highly inefficient and also 587 00:20:46,580 --> 00:20:48,349 numerically, it's a nightmare. 588 00:20:48,350 --> 00:20:50,539 So what we do is we take this nice, very 589 00:20:50,540 --> 00:20:53,029 nice book and look at some dynamics, 590 00:20:53,030 --> 00:20:54,799 algorithms that are actually intended for 591 00:20:54,800 --> 00:20:55,800 use in robotics. 592 00:20:56,940 --> 00:20:59,099 And we implement them 593 00:20:59,100 --> 00:21:01,649 and well, in a small 594 00:21:01,650 --> 00:21:03,749 library that will be released 595 00:21:03,750 --> 00:21:05,909 pretty soon now together 596 00:21:05,910 --> 00:21:07,589 with the controller, so that everyone can 597 00:21:07,590 --> 00:21:09,719 play this one 598 00:21:09,720 --> 00:21:11,729 nice feature of the of the legs of our 599 00:21:11,730 --> 00:21:13,469 robot is that they are analytical, 600 00:21:13,470 --> 00:21:14,439 inverse kinematics. 601 00:21:14,440 --> 00:21:16,439 So you can actually calculate without 602 00:21:16,440 --> 00:21:18,659 using iterative methods 603 00:21:18,660 --> 00:21:21,059 for joint angles, you need to position 604 00:21:21,060 --> 00:21:23,249 the foot in a certain way. 605 00:21:23,250 --> 00:21:25,439 This is just a nice feature that somewhat 606 00:21:25,440 --> 00:21:27,239 simplifies the controller. 607 00:21:29,070 --> 00:21:30,900 Now, in the longer term, 608 00:21:32,310 --> 00:21:34,169 this kind of hand traffic controllers 609 00:21:34,170 --> 00:21:36,000 that we had are OK for walking. 610 00:21:37,260 --> 00:21:39,029 But if you're really if you push really 611 00:21:39,030 --> 00:21:41,129 hard of the two and get really rough 612 00:21:41,130 --> 00:21:42,629 or if you want to do acrobatics or 613 00:21:42,630 --> 00:21:44,759 whatever, then it's 614 00:21:44,760 --> 00:21:46,589 going to then is kind of simplifying 615 00:21:46,590 --> 00:21:49,139 assumptions eventually break down. 616 00:21:49,140 --> 00:21:51,389 And there is actually a large body 617 00:21:51,390 --> 00:21:53,459 of resolve that people just use 618 00:21:53,460 --> 00:21:55,169 large scale simulation. 619 00:21:55,170 --> 00:21:57,119 So basically, you tell the roll to the 620 00:21:57,120 --> 00:21:59,129 computer, this is your starting status, 621 00:21:59,130 --> 00:22:01,829 your goal state, get me there 622 00:22:01,830 --> 00:22:03,429 and decide this. 623 00:22:03,430 --> 00:22:05,729 This uses this works offline 624 00:22:05,730 --> 00:22:07,289 quite well. It doesn't work so well if 625 00:22:07,290 --> 00:22:09,629 you have real time constraints, because, 626 00:22:09,630 --> 00:22:10,829 I mean, if you push, you can actually 627 00:22:10,830 --> 00:22:11,999 stop to think, of course. 628 00:22:13,770 --> 00:22:15,779 So there are many interesting results and 629 00:22:15,780 --> 00:22:18,179 eventually we are going to 630 00:22:18,180 --> 00:22:19,649 look into that as well. 631 00:22:19,650 --> 00:22:21,749 But as the goal 632 00:22:21,750 --> 00:22:24,329 for now is to just walk on even ground, 633 00:22:25,410 --> 00:22:27,689 well, it's probably 634 00:22:27,690 --> 00:22:29,579 easier to stay with these handcrafted 635 00:22:29,580 --> 00:22:31,559 approaches, not least because they're 636 00:22:31,560 --> 00:22:33,389 easier to debark. 637 00:22:33,390 --> 00:22:35,489 You can look at it and check 638 00:22:35,490 --> 00:22:37,619 if your assumptions are still valid and 639 00:22:37,620 --> 00:22:38,620 if everything works. 640 00:22:41,250 --> 00:22:43,559 So that's it for my side. 641 00:22:43,560 --> 00:22:45,809 I summarize this 642 00:22:45,810 --> 00:22:48,719 crowded site again, and 643 00:22:48,720 --> 00:22:50,669 these are now the requirements that Felix 644 00:22:50,670 --> 00:22:52,499 will have to deal with. 645 00:22:52,500 --> 00:22:53,500 Yes. 646 00:23:03,120 --> 00:23:05,489 Yes, now it showed you 647 00:23:05,490 --> 00:23:07,649 the simulation gives us 648 00:23:07,650 --> 00:23:09,929 requirements for 649 00:23:09,930 --> 00:23:12,059 yeah, for talk, so 650 00:23:12,060 --> 00:23:14,429 our freak talk is in the order 651 00:23:14,430 --> 00:23:17,099 of hundred meters, which is quite large. 652 00:23:17,100 --> 00:23:19,799 It gives us velocity 653 00:23:19,800 --> 00:23:20,849 requirements. 654 00:23:20,850 --> 00:23:22,949 So about 20 655 00:23:22,950 --> 00:23:25,649 radians per second and, uh, 656 00:23:25,650 --> 00:23:28,109 a power requirement, 250 657 00:23:28,110 --> 00:23:30,719 watts. So if you do the math, 658 00:23:30,720 --> 00:23:32,549 um, that won't match. 659 00:23:32,550 --> 00:23:34,869 That is because the peak velocity and 660 00:23:34,870 --> 00:23:37,049 the peak torque won't show up at 661 00:23:37,050 --> 00:23:38,050 the same time. 662 00:23:38,910 --> 00:23:41,429 So on the outside, 663 00:23:41,430 --> 00:23:43,589 the mainstream option there is brushless 664 00:23:43,590 --> 00:23:44,590 motors 665 00:23:45,900 --> 00:23:48,419 because we cannot afford industrial grade 666 00:23:48,420 --> 00:23:50,579 motors. We go 667 00:23:50,580 --> 00:23:53,969 to our favorite, our sea side 668 00:23:53,970 --> 00:23:56,459 Cheapside shiny stuff 669 00:23:56,460 --> 00:23:59,009 and uh, found this two kilowatts 670 00:23:59,010 --> 00:24:01,079 brushless motor for thirty 671 00:24:01,080 --> 00:24:03,179 dollars. It is quite heavy 672 00:24:03,180 --> 00:24:04,289 but manageable. 673 00:24:04,290 --> 00:24:06,449 Five grams but 674 00:24:06,450 --> 00:24:09,189 overpowered but slow, uh, 675 00:24:09,190 --> 00:24:10,169 to 70. 676 00:24:10,170 --> 00:24:12,779 Cavey Cave stands for uh 677 00:24:12,780 --> 00:24:15,029 yeah. Basically how 678 00:24:15,030 --> 00:24:17,309 fast the motor would turn in 679 00:24:17,310 --> 00:24:19,229 idle per volt. 680 00:24:19,230 --> 00:24:21,329 Uh if you do the math again. 681 00:24:21,330 --> 00:24:23,549 Eight hundred fifty irradiance 682 00:24:23,550 --> 00:24:26,309 at thirty volts and uh 683 00:24:26,310 --> 00:24:28,709 approximately uh three 684 00:24:28,710 --> 00:24:30,959 Knewton meter at 685 00:24:30,960 --> 00:24:32,739 ninety amps. 686 00:24:32,740 --> 00:24:35,009 Uh so that gives us 687 00:24:35,010 --> 00:24:38,279 a gear ratio of one to 50. 688 00:24:38,280 --> 00:24:40,889 Um we get 689 00:24:40,890 --> 00:24:43,529 to the gas later on because 690 00:24:43,530 --> 00:24:46,199 uh, if you have a brushless 691 00:24:46,200 --> 00:24:48,269 motor from the RCA 692 00:24:48,270 --> 00:24:50,429 environment, you usually power your plane 693 00:24:50,430 --> 00:24:52,619 with it so you can control 694 00:24:52,620 --> 00:24:54,929 direction and maybe speed with the 695 00:24:54,930 --> 00:24:57,269 usual affordable brushless controllers, 696 00:24:57,270 --> 00:24:58,589 but not position. 697 00:24:58,590 --> 00:25:00,869 And we want position control here. 698 00:25:00,870 --> 00:25:02,939 So we implemented our 699 00:25:02,940 --> 00:25:06,059 own, uh, brushless controller, 700 00:25:06,060 --> 00:25:08,429 uh, which is encoder based. 701 00:25:08,430 --> 00:25:10,529 So there is a sensor on the 702 00:25:10,530 --> 00:25:12,779 rotation axis and 703 00:25:12,780 --> 00:25:14,639 it uses a thing called space vector 704 00:25:14,640 --> 00:25:16,829 modulation, which is like this 705 00:25:16,830 --> 00:25:19,019 light says basically three 706 00:25:19,020 --> 00:25:21,299 face AC face locked 707 00:25:21,300 --> 00:25:22,889 to the motor rotation. 708 00:25:22,890 --> 00:25:25,919 Uh, think of it like microstamping 709 00:25:25,920 --> 00:25:27,959 for Stepa Motors. 710 00:25:27,960 --> 00:25:30,029 And uh, as we are 711 00:25:30,030 --> 00:25:32,409 switching, uh, high courant's, they're 712 00:25:32,410 --> 00:25:34,679 nighttime's we are using, 713 00:25:34,680 --> 00:25:36,749 um, four eighty 714 00:25:36,750 --> 00:25:37,829 five. 715 00:25:37,830 --> 00:25:40,079 Uh, because, um, yeah, it's 716 00:25:40,080 --> 00:25:41,080 differential. 717 00:25:42,630 --> 00:25:44,819 The power stage is 718 00:25:44,820 --> 00:25:47,279 actually from a cheap 719 00:25:47,280 --> 00:25:48,939 Chinese pressure controller. 720 00:25:48,940 --> 00:25:51,089 They were kind enough to put us 721 00:25:51,090 --> 00:25:51,989 on it to. 722 00:25:51,990 --> 00:25:54,239 Mm. Uh, pitch 723 00:25:54,240 --> 00:25:56,429 but had us and you can just 724 00:25:56,430 --> 00:25:58,649 unplug it from the ship 725 00:25:58,650 --> 00:26:00,719 as I elapse microcontroller 726 00:26:00,720 --> 00:26:03,169 and use a SDM thirty two 727 00:26:03,170 --> 00:26:05,369 uh and build 728 00:26:05,370 --> 00:26:07,349 a nice new baseboard for it. 729 00:26:07,350 --> 00:26:09,479 And uh if it ever breaks 730 00:26:09,480 --> 00:26:11,729 or burns just pay twenty 731 00:26:11,730 --> 00:26:13,529 bucks, get a new one. 732 00:26:13,530 --> 00:26:16,349 Uh and hope they don't change the design. 733 00:26:16,350 --> 00:26:18,929 So as 734 00:26:18,930 --> 00:26:20,970 we are trying to, to uh 735 00:26:22,290 --> 00:26:24,749 uh to control the talk 736 00:26:24,750 --> 00:26:26,429 and the talk is proportional to the 737 00:26:26,430 --> 00:26:28,769 current, uh, we need to measure 738 00:26:28,770 --> 00:26:31,049 the current of all faiths or 739 00:26:31,050 --> 00:26:32,729 at least two phases because you can 740 00:26:32,730 --> 00:26:35,579 calculate the, uh, um, 741 00:26:35,580 --> 00:26:37,529 the current for the third phase. 742 00:26:37,530 --> 00:26:39,779 And so we use, 743 00:26:39,780 --> 00:26:42,239 uh, one hundred fifty amps 744 00:26:42,240 --> 00:26:44,429 hall effects. And, uh, 745 00:26:44,430 --> 00:26:46,799 it's it's a nice model from Allegro 746 00:26:46,800 --> 00:26:48,899 Microsystems eight seven five nine. 747 00:26:48,900 --> 00:26:51,059 If you ever need, uh, current, 748 00:26:51,060 --> 00:26:52,739 just use them. 749 00:26:52,740 --> 00:26:54,989 And this, 750 00:26:54,990 --> 00:26:57,749 uh, graph shows how fast 751 00:26:57,750 --> 00:26:59,639 the precision tracking is actually 752 00:26:59,640 --> 00:27:01,709 working. And, um, 753 00:27:01,710 --> 00:27:03,809 it basically shows on 754 00:27:03,810 --> 00:27:06,059 the Y axis the position in the sensor 755 00:27:06,060 --> 00:27:08,309 units. Uh, and on the 756 00:27:08,310 --> 00:27:09,569 X axis, it's time. 757 00:27:09,570 --> 00:27:11,639 And you see tracking is quite 758 00:27:11,640 --> 00:27:13,829 nice. Blue line is the 759 00:27:13,830 --> 00:27:15,719 opposition. Green Line is the desired 760 00:27:15,720 --> 00:27:16,649 position. 761 00:27:16,650 --> 00:27:19,169 And no major overshoots, 762 00:27:19,170 --> 00:27:22,359 uh, despite the the Mean 763 00:27:22,360 --> 00:27:23,360 Square WAF. 764 00:27:24,270 --> 00:27:26,849 So speaking of rotation centers, 765 00:27:26,850 --> 00:27:28,919 um, they also 766 00:27:28,920 --> 00:27:31,139 Microsystems builds nice, 767 00:27:31,140 --> 00:27:32,579 uh, effect sensors. 768 00:27:33,840 --> 00:27:35,759 They come in two flavors, absolute. 769 00:27:35,760 --> 00:27:36,930 And, uh. 770 00:27:38,140 --> 00:27:40,549 Relative, so a but 771 00:27:40,550 --> 00:27:42,769 absolute bit absolute revolution is quite 772 00:27:42,770 --> 00:27:44,959 nice, but not enough. 773 00:27:44,960 --> 00:27:47,149 And so they they 774 00:27:47,150 --> 00:27:49,489 build rings with 128 poles 775 00:27:49,490 --> 00:27:51,589 and you interpolate between two 776 00:27:51,590 --> 00:27:53,839 poles and loose 777 00:27:53,840 --> 00:27:54,799 the the. 778 00:27:54,800 --> 00:27:56,869 Yeah, it's not absolute anymore 779 00:27:56,870 --> 00:27:59,149 but pretty, pretty, 780 00:27:59,150 --> 00:28:01,369 uh, accurate. 781 00:28:01,370 --> 00:28:03,499 And if you combine both so on 782 00:28:03,500 --> 00:28:05,329 one axis, one absolute center to 783 00:28:05,330 --> 00:28:08,599 basically index uh um 784 00:28:08,600 --> 00:28:10,759 the relative center you 785 00:28:10,760 --> 00:28:13,069 gain. Uh yeah. 786 00:28:13,070 --> 00:28:15,319 Seven to bit seventeen bit uh 787 00:28:15,320 --> 00:28:17,629 absolute center which is 788 00:28:17,630 --> 00:28:19,879 at least in theory, I mean this 789 00:28:19,880 --> 00:28:22,339 is calculated, not measured, 790 00:28:22,340 --> 00:28:23,719 really, really accurate. 791 00:28:23,720 --> 00:28:25,789 And each center is about 792 00:28:25,790 --> 00:28:28,189 ten dollars and the magnets 793 00:28:28,190 --> 00:28:29,909 are five dollars each. 794 00:28:29,910 --> 00:28:32,779 Uh, another nice thing about 795 00:28:32,780 --> 00:28:34,819 those centers is that a half direct 796 00:28:34,820 --> 00:28:36,979 quadrature output and all the modern 797 00:28:36,980 --> 00:28:39,409 micro controllers have direct 798 00:28:39,410 --> 00:28:42,649 hardware, creditor inputs or decoders. 799 00:28:42,650 --> 00:28:44,629 And, uh, so you can just read the 800 00:28:44,630 --> 00:28:46,879 resistor and see the 801 00:28:46,880 --> 00:28:49,039 value of your SANZAR without any 802 00:28:50,690 --> 00:28:52,699 decoding protocols, whatever. 803 00:28:52,700 --> 00:28:54,919 Uh, a problem, though, is that 804 00:28:54,920 --> 00:28:57,889 we don't know how non-linearity, 805 00:28:57,890 --> 00:28:59,959 uh, will work 806 00:28:59,960 --> 00:29:02,929 or is a problem in 807 00:29:02,930 --> 00:29:05,629 high current switching 808 00:29:05,630 --> 00:29:07,609 because the magnet of the magnet fields 809 00:29:07,610 --> 00:29:08,599 antisemite. 810 00:29:08,600 --> 00:29:10,159 They will produce. 811 00:29:10,160 --> 00:29:12,769 And, um, that shouldn't 812 00:29:12,770 --> 00:29:14,869 matter too much because the and a factor. 813 00:29:14,870 --> 00:29:18,379 So the lack position won't depend 814 00:29:18,380 --> 00:29:21,199 on the um 815 00:29:21,200 --> 00:29:23,509 on the on the error 816 00:29:23,510 --> 00:29:25,639 from the rotation sensor, but on the 817 00:29:25,640 --> 00:29:27,319 mechanical areas like manufacturing 818 00:29:27,320 --> 00:29:29,779 errors, uh, bending and flexing 819 00:29:29,780 --> 00:29:32,209 because it's, it's not a rigid body, 820 00:29:32,210 --> 00:29:33,739 it's a real thing. 821 00:29:33,740 --> 00:29:35,929 And uh, another thing is that, 822 00:29:35,930 --> 00:29:38,749 uh, the sampling time 823 00:29:38,750 --> 00:29:40,579 of the last measurement isn't clear if 824 00:29:40,580 --> 00:29:42,649 you do a digital readout, which you can 825 00:29:42,650 --> 00:29:44,869 do, but, 826 00:29:44,870 --> 00:29:47,209 uh, with credit to output, 827 00:29:47,210 --> 00:29:49,399 that is OK because it's a fixed delay 828 00:29:49,400 --> 00:29:51,469 so that the credit output has 829 00:29:51,470 --> 00:29:53,809 a fixed delay from the last temporal 830 00:29:53,810 --> 00:29:54,709 time. 831 00:29:54,710 --> 00:29:56,839 But the simpler 832 00:29:56,840 --> 00:29:58,939 the output will, uh, stop 833 00:29:58,940 --> 00:30:00,859 working at higher velocities. 834 00:30:00,860 --> 00:30:03,349 So velocity 835 00:30:03,350 --> 00:30:05,539 calculation with those sensors 836 00:30:05,540 --> 00:30:06,529 is a bit of a problem. 837 00:30:06,530 --> 00:30:09,169 If anyone knows the solution for that, 838 00:30:09,170 --> 00:30:10,220 tell us after the talk. 839 00:30:12,020 --> 00:30:13,070 Now back to Geass 840 00:30:15,440 --> 00:30:15,759 Meters. 841 00:30:15,760 --> 00:30:17,929 This is really a lot 842 00:30:17,930 --> 00:30:20,029 because if you just use your 843 00:30:20,030 --> 00:30:22,099 usual screwdriver, 844 00:30:22,100 --> 00:30:24,689 they claim they can do like 50 845 00:30:24,690 --> 00:30:25,969 meters. 846 00:30:25,970 --> 00:30:28,149 You will probably never reach that. 847 00:30:28,150 --> 00:30:30,409 You need like 30 meters to 848 00:30:30,410 --> 00:30:32,659 to screw in a screw. 849 00:30:32,660 --> 00:30:33,319 And to really. 850 00:30:33,320 --> 00:30:35,569 Hartwood, our motor 851 00:30:35,570 --> 00:30:37,849 talk is around 852 00:30:37,850 --> 00:30:39,979 two meters because we 853 00:30:39,980 --> 00:30:42,679 only calculate a calculated 854 00:30:42,680 --> 00:30:44,759 the meters uh, uh, 855 00:30:44,760 --> 00:30:46,549 the motor talk right now. 856 00:30:46,550 --> 00:30:48,739 And, um, we 857 00:30:48,740 --> 00:30:50,389 need a reduction of one to fifty. 858 00:30:50,390 --> 00:30:52,459 Maybe that leaves 859 00:30:52,460 --> 00:30:54,529 us with not 860 00:30:54,530 --> 00:30:56,059 too many gering options. 861 00:30:56,060 --> 00:30:58,129 One option is 862 00:30:58,130 --> 00:31:01,129 a fancy thing called, uh, harmonic drive, 863 00:31:01,130 --> 00:31:03,529 also called strain wave gering. 864 00:31:03,530 --> 00:31:06,319 Um, it's quite a nice thing. 865 00:31:06,320 --> 00:31:08,329 It's Don Extensor expensive. 866 00:31:08,330 --> 00:31:11,329 So one is probably 867 00:31:11,330 --> 00:31:13,759 starting at a thousand K, but, 868 00:31:13,760 --> 00:31:15,889 uh, they are 869 00:31:15,890 --> 00:31:17,999 really expensive and planetary. 870 00:31:18,000 --> 00:31:20,329 These girls are cheaply available, 871 00:31:20,330 --> 00:31:22,429 uh, for example, in your 872 00:31:22,430 --> 00:31:24,739 cordless screwdriver, but 873 00:31:24,740 --> 00:31:27,019 uh have different uh 874 00:31:27,020 --> 00:31:28,020 yeah. 875 00:31:28,430 --> 00:31:30,739 They, they have a backlash 876 00:31:30,740 --> 00:31:33,019 usually. So if you 877 00:31:33,020 --> 00:31:35,149 um if you turn 878 00:31:35,150 --> 00:31:37,519 the motor in a different direction 879 00:31:37,520 --> 00:31:39,919 that will be play in, in the gears 880 00:31:39,920 --> 00:31:42,169 and that can break 881 00:31:42,170 --> 00:31:44,569 things because if if the 882 00:31:44,570 --> 00:31:46,639 gear spins freely with that 883 00:31:46,640 --> 00:31:47,659 talks. Yeah. 884 00:31:47,660 --> 00:31:49,749 Usually just tiff's 885 00:31:49,750 --> 00:31:51,609 icebreaking from the here. 886 00:31:51,610 --> 00:31:53,719 That isn't a problem at all of the I want 887 00:31:53,720 --> 00:31:56,239 to drive and drive and 888 00:31:56,240 --> 00:31:58,199 they, they are flat whites and. 889 00:31:58,200 --> 00:31:59,089 Yeah. 890 00:31:59,090 --> 00:32:01,379 But uh we try 891 00:32:01,380 --> 00:32:03,859 to get away with planetaria years 892 00:32:03,860 --> 00:32:06,169 and then there is a one 893 00:32:06,170 --> 00:32:07,579 more actuator system. 894 00:32:07,580 --> 00:32:09,649 It's a linear actuator, 895 00:32:09,650 --> 00:32:11,929 it's basically like hydraulics. 896 00:32:11,930 --> 00:32:14,359 But without hydraulics you lose, 897 00:32:14,360 --> 00:32:16,069 you use uh, screw 898 00:32:17,840 --> 00:32:20,209 most common things that ball screws. 899 00:32:20,210 --> 00:32:21,799 And then there's some fancy thing called 900 00:32:21,800 --> 00:32:24,019 planetary roller screw, which has 901 00:32:24,020 --> 00:32:26,359 a planetary gear built into 902 00:32:26,360 --> 00:32:28,369 the to the screw. 903 00:32:28,370 --> 00:32:30,439 We won't go, uh, go into 904 00:32:30,440 --> 00:32:32,899 detail, see it, because it's a task force 905 00:32:32,900 --> 00:32:35,059 on, uh, if you're 906 00:32:35,060 --> 00:32:36,529 really interested in it. 907 00:32:36,530 --> 00:32:37,739 Um. 908 00:32:37,740 --> 00:32:40,259 So to to test all this, 909 00:32:40,260 --> 00:32:42,569 we've built a motor test bet 910 00:32:42,570 --> 00:32:44,459 and the motor test bed is basically a 911 00:32:44,460 --> 00:32:45,869 giant pendulum. 912 00:32:45,870 --> 00:32:48,119 It's a one meter long pole 913 00:32:48,120 --> 00:32:50,699 where we bolt it on, uh, 914 00:32:50,700 --> 00:32:52,829 10 kilograms of, like, 915 00:32:52,830 --> 00:32:53,849 handlebar whites. 916 00:32:56,070 --> 00:32:58,259 And so 917 00:32:58,260 --> 00:33:00,239 if you do the math again, the static 918 00:33:00,240 --> 00:33:02,789 torque is up to 100 meters 919 00:33:02,790 --> 00:33:04,889 to test everything we want. 920 00:33:04,890 --> 00:33:07,769 And the dynamic torque can obviously 921 00:33:07,770 --> 00:33:09,869 be much higher because, 922 00:33:09,870 --> 00:33:12,029 yeah, it has 923 00:33:12,030 --> 00:33:13,829 two parts. 924 00:33:13,830 --> 00:33:15,929 One for actual 925 00:33:15,930 --> 00:33:18,179 axle, uh, motors like 926 00:33:18,180 --> 00:33:20,279 the one that drives into the planetary 927 00:33:20,280 --> 00:33:23,399 gears and one for Linera actuators 928 00:33:23,400 --> 00:33:25,889 like balls, screw systems. 929 00:33:25,890 --> 00:33:28,229 And, uh, yeah, as soon as 930 00:33:28,230 --> 00:33:30,329 we have the first tests, we will 931 00:33:30,330 --> 00:33:32,669 probably post a video material 932 00:33:32,670 --> 00:33:35,369 of Breaking Geass Motors 933 00:33:35,370 --> 00:33:37,559 and controllers and everything 934 00:33:37,560 --> 00:33:38,560 will burn. 935 00:33:39,930 --> 00:33:41,289 So, uh. 936 00:33:42,290 --> 00:33:44,929 Obviously, we had a look 937 00:33:44,930 --> 00:33:47,719 what exists 938 00:33:47,720 --> 00:33:50,239 in the interview in the academic field 939 00:33:50,240 --> 00:33:52,399 right now, and two simple 940 00:33:52,400 --> 00:33:55,369 projects are Tulip and Lola 941 00:33:55,370 --> 00:33:57,469 Tulip is from a university 942 00:33:57,470 --> 00:33:59,239 in the Netherlands, the University of 943 00:33:59,240 --> 00:34:01,819 Eindhoven. Dahlstrom, 20, and its 944 00:34:01,820 --> 00:34:03,889 rather small, uh, one on a 945 00:34:03,890 --> 00:34:06,539 20 centimeters 15 kg and 946 00:34:06,540 --> 00:34:08,809 uh, uses, uh, interesting concept 947 00:34:08,810 --> 00:34:11,599 named a serious elastic activation 948 00:34:11,600 --> 00:34:13,879 in the knee, which basically meant 949 00:34:13,880 --> 00:34:16,369 they couple a motor with 950 00:34:16,370 --> 00:34:19,009 a spring add to, um, 951 00:34:19,010 --> 00:34:20,928 conserve energy. 952 00:34:20,929 --> 00:34:23,269 Uh, that is uh yeah. 953 00:34:23,270 --> 00:34:25,488 During the food contact to load basically 954 00:34:25,489 --> 00:34:27,499 the spring during the foot contact. 955 00:34:27,500 --> 00:34:29,928 Uh but uh they lose 956 00:34:29,929 --> 00:34:31,549 uh, bandwidth with this. 957 00:34:31,550 --> 00:34:34,249 So they uh um 958 00:34:34,250 --> 00:34:37,369 that the control is only 959 00:34:37,370 --> 00:34:39,689 five to 10 hertz fast. 960 00:34:39,690 --> 00:34:42,439 Uh, they get away with rush motors 961 00:34:42,440 --> 00:34:44,718 because they are light enough 962 00:34:44,719 --> 00:34:46,819 and, uh, planetary gears. 963 00:34:46,820 --> 00:34:48,979 And they you have a 964 00:34:48,980 --> 00:34:51,259 predecessor named Flame for 965 00:34:51,260 --> 00:34:54,109 which I will show video shortly. 966 00:34:54,110 --> 00:34:56,839 So back to the kinematics, uh, 967 00:34:56,840 --> 00:34:59,149 later, uh, earlier showed, um, 968 00:34:59,150 --> 00:35:01,579 the kinematics for our robot project. 969 00:35:01,580 --> 00:35:03,829 Uh, it's, uh, comparable 970 00:35:03,830 --> 00:35:06,139 to this basically the same three degrees 971 00:35:06,140 --> 00:35:07,549 of freedom in the hip. 972 00:35:07,550 --> 00:35:09,829 So this this 973 00:35:09,830 --> 00:35:11,899 and you cannot show that too 974 00:35:11,900 --> 00:35:14,539 good. But you can turn your hip at 975 00:35:14,540 --> 00:35:16,909 one in the knee and 976 00:35:16,910 --> 00:35:18,469 two and ankles. 977 00:35:18,470 --> 00:35:22,129 So, uh, pitch on and 978 00:35:22,130 --> 00:35:24,469 roll and, uh, 979 00:35:24,470 --> 00:35:26,629 the ankle is, uh, the ankle roll 980 00:35:26,630 --> 00:35:28,859 is passive, so they just 981 00:35:28,860 --> 00:35:30,590 attach springs to it and no motor. 982 00:35:31,610 --> 00:35:33,739 So now no it will play the 983 00:35:33,740 --> 00:35:34,740 video 984 00:35:38,780 --> 00:35:40,040 just a second. 985 00:35:43,590 --> 00:35:44,590 This new video. 986 00:35:55,000 --> 00:35:56,770 So this is flame, 987 00:35:59,710 --> 00:36:02,049 as you can see, flame 988 00:36:02,050 --> 00:36:04,119 moves and a slight curve. 989 00:36:04,120 --> 00:36:06,599 That's because as the predecessor 990 00:36:06,600 --> 00:36:08,919 of Tulip, it's oh 991 00:36:08,920 --> 00:36:11,349 yeah, whatever, it misses 992 00:36:11,350 --> 00:36:12,819 one degree of freedom in the hip. 993 00:36:13,930 --> 00:36:16,359 So it has only two degrees 994 00:36:16,360 --> 00:36:18,549 in our freedom and the hip, and that 995 00:36:18,550 --> 00:36:20,889 means that it can 996 00:36:20,890 --> 00:36:22,059 control it. 997 00:36:22,060 --> 00:36:24,699 Movement around the Z axis. 998 00:36:24,700 --> 00:36:27,099 So the rotation of the Z axis. 999 00:36:27,100 --> 00:36:29,229 So it as a result 1000 00:36:29,230 --> 00:36:31,449 it moves in a curve because it can 1001 00:36:31,450 --> 00:36:32,450 control it. 1002 00:36:33,400 --> 00:36:35,170 Next up is. 1003 00:36:36,320 --> 00:36:39,019 Lola Lola is 1004 00:36:39,020 --> 00:36:41,719 a fully sized humanoid 1005 00:36:41,720 --> 00:36:43,429 one at one hundred and eighty 1006 00:36:43,430 --> 00:36:45,559 centimeters, 55 kilograms, 1007 00:36:45,560 --> 00:36:47,539 but it's to Munich. 1008 00:36:47,540 --> 00:36:49,609 It has really many 1009 00:36:49,610 --> 00:36:50,569 degrees of freedom. 1010 00:36:50,570 --> 00:36:51,859 Twenty five in total. 1011 00:36:51,860 --> 00:36:54,299 But the arms and 1012 00:36:54,300 --> 00:36:57,199 the that actuated as well. 1013 00:36:57,200 --> 00:36:58,200 And 1014 00:36:59,750 --> 00:37:01,579 it has seven degrees of freedom. 1015 00:37:01,580 --> 00:37:03,739 Polec the 1016 00:37:03,740 --> 00:37:06,019 nice actuation concept is borrowed 1017 00:37:06,020 --> 00:37:08,209 here, as you might 1018 00:37:08,210 --> 00:37:10,849 see on the picture. 1019 00:37:10,850 --> 00:37:12,170 Number five is 1020 00:37:13,580 --> 00:37:16,879 the ball screw and 1021 00:37:16,880 --> 00:37:18,949 they use it to bend the 1022 00:37:18,950 --> 00:37:20,659 knees and the ankles. 1023 00:37:20,660 --> 00:37:22,280 Think of it, uh, 1024 00:37:23,360 --> 00:37:26,089 at least for the knee, like on your 1025 00:37:26,090 --> 00:37:27,929 standard excavator. 1026 00:37:27,930 --> 00:37:30,349 Yeah, like you have arm 1027 00:37:30,350 --> 00:37:32,899 and to the arm by 1028 00:37:32,900 --> 00:37:35,029 reducing the piston 1029 00:37:35,030 --> 00:37:37,399 length or hear the 1030 00:37:37,400 --> 00:37:40,009 distance of the balls screw 1031 00:37:40,010 --> 00:37:42,079 and they use harmonic drives all 1032 00:37:42,080 --> 00:37:44,509 over. So everything that is not done 1033 00:37:44,510 --> 00:37:46,789 by a linear actuators 1034 00:37:46,790 --> 00:37:49,009 uses harmonic drives and 1035 00:37:49,010 --> 00:37:51,799 industrial grade brushless 1036 00:37:51,800 --> 00:37:52,800 motors. 1037 00:37:53,520 --> 00:37:55,609 Um, the activation 1038 00:37:55,610 --> 00:37:57,499 concept with all degrees of freedom is 1039 00:37:57,500 --> 00:37:59,629 here. Uh, basically 1040 00:37:59,630 --> 00:38:01,109 it's comparable. 1041 00:38:01,110 --> 00:38:03,019 So at least for the next, it's comparable 1042 00:38:03,020 --> 00:38:05,299 to Tulip and our approach, 1043 00:38:05,300 --> 00:38:07,729 uh, with the exception that 1044 00:38:07,730 --> 00:38:09,829 they have a total active 1045 00:38:09,830 --> 00:38:12,679 toe ajoint joint, uh, 1046 00:38:12,680 --> 00:38:14,899 they claim that that 1047 00:38:14,900 --> 00:38:16,999 this is useful to, uh, walk 1048 00:38:17,000 --> 00:38:19,369 faster, not an actual 1049 00:38:19,370 --> 00:38:21,439 target at the moment, and, 1050 00:38:21,440 --> 00:38:23,329 uh, climb stairs and steps, 1051 00:38:24,410 --> 00:38:26,119 which would be nice, but should be doable 1052 00:38:26,120 --> 00:38:27,739 as well without it. 1053 00:38:27,740 --> 00:38:29,899 So and, uh, as a special feature, the hip 1054 00:38:29,900 --> 00:38:32,779 that is tilted 1055 00:38:32,780 --> 00:38:34,789 against the X Y plain, you can see that 1056 00:38:34,790 --> 00:38:37,009 and the Chromatics. 1057 00:38:37,010 --> 00:38:38,659 We have a video for this as well. 1058 00:38:45,960 --> 00:38:48,119 So this is Lola, and 1059 00:38:49,290 --> 00:38:51,599 as you could see, as you can see, a 1060 00:38:51,600 --> 00:38:54,209 pushing to flame, um, 1061 00:38:54,210 --> 00:38:56,669 Lola never has straight 1062 00:38:56,670 --> 00:38:58,349 legs but 1063 00:38:59,610 --> 00:39:01,259 always bent knees. 1064 00:39:01,260 --> 00:39:03,030 And that is because a 1065 00:39:04,080 --> 00:39:06,569 bushman, the guy who 1066 00:39:06,570 --> 00:39:08,939 wrote the control of Lola, 1067 00:39:08,940 --> 00:39:11,159 uh, is 1068 00:39:11,160 --> 00:39:13,439 who we based our work on, 1069 00:39:13,440 --> 00:39:14,939 our controller work on. 1070 00:39:14,940 --> 00:39:17,099 So they it looks yeah, 1071 00:39:17,100 --> 00:39:18,029 they have arms. 1072 00:39:18,030 --> 00:39:20,099 And to conserve the angular momentum, 1073 00:39:20,100 --> 00:39:22,349 like we told you earlier, 1074 00:39:22,350 --> 00:39:24,030 looks way better, but, uh. 1075 00:39:25,740 --> 00:39:27,289 Yeah, yeah. 1076 00:39:27,290 --> 00:39:28,290 So 1077 00:39:29,910 --> 00:39:32,039 they already started this point. 1078 00:39:32,040 --> 00:39:33,719 So, um. 1079 00:39:36,540 --> 00:39:38,669 Now, we do that later on, so the 1080 00:39:38,670 --> 00:39:40,530 current status is, um, 1081 00:39:41,640 --> 00:39:43,799 yeah, some lation is on a good 1082 00:39:43,800 --> 00:39:44,800 way. 1083 00:39:45,270 --> 00:39:47,039 We studied existing designs. 1084 00:39:47,040 --> 00:39:49,619 We have built a workshop in the last year 1085 00:39:49,620 --> 00:39:51,869 with a milling machine, a small 1086 00:39:51,870 --> 00:39:53,979 lathe, a fully fledged 1087 00:39:53,980 --> 00:39:55,409 electronics workshop. 1088 00:39:55,410 --> 00:39:57,509 And the biggest challenge right now 1089 00:39:57,510 --> 00:40:00,359 is to to get 1090 00:40:00,360 --> 00:40:02,459 an activation concept that you can 1091 00:40:02,460 --> 00:40:03,699 pay for. 1092 00:40:03,700 --> 00:40:05,699 Uh, yeah. 1093 00:40:05,700 --> 00:40:07,889 So next steps next year 1094 00:40:07,890 --> 00:40:09,929 will be to burn, like I said before, to 1095 00:40:09,930 --> 00:40:12,269 burn motors, to burn drivers 1096 00:40:12,270 --> 00:40:14,249 and to test years. 1097 00:40:14,250 --> 00:40:16,469 And after the gear question 1098 00:40:16,470 --> 00:40:18,599 is solved, we will start 1099 00:40:18,600 --> 00:40:21,479 constructing our first pair of legs. 1100 00:40:21,480 --> 00:40:22,480 So. 1101 00:40:25,440 --> 00:40:26,440 Additionally, 1102 00:40:27,510 --> 00:40:29,609 in the last demo, uh, Novarro, 1103 00:40:29,610 --> 00:40:31,949 to you, the terrain was known 1104 00:40:31,950 --> 00:40:34,649 to the robot and therefore we 1105 00:40:34,650 --> 00:40:36,969 began building a camera system. 1106 00:40:36,970 --> 00:40:39,629 Um, this is the camera 1107 00:40:39,630 --> 00:40:42,479 with a command, uh, to 1108 00:40:42,480 --> 00:40:45,089 whoever knows what a seamount is. 1109 00:40:45,090 --> 00:40:46,090 And, um, 1110 00:40:47,220 --> 00:40:49,109 it's a scientific, uh, camera based on 1111 00:40:49,110 --> 00:40:51,689 that part of the project, uh, 1112 00:40:51,690 --> 00:40:53,999 build a fully open source film camera 1113 00:40:54,000 --> 00:40:56,129 and Fourcade resolution, 1114 00:40:56,130 --> 00:40:57,389 which is quite amazing. 1115 00:40:57,390 --> 00:40:59,639 And it's based on a simple 1116 00:40:59,640 --> 00:41:01,439 SANZAR with 2K resolution. 1117 00:41:01,440 --> 00:41:03,270 So full HD, um, 1118 00:41:04,380 --> 00:41:06,719 up to three hundred forty fps 1119 00:41:06,720 --> 00:41:09,149 12th with dynamic, uh, 1120 00:41:09,150 --> 00:41:10,079 color depth. 1121 00:41:10,080 --> 00:41:12,059 And it said it has a global shutter. 1122 00:41:12,060 --> 00:41:14,279 So uh, not like on 1123 00:41:14,280 --> 00:41:16,499 your favorite GoPro video where you see 1124 00:41:16,500 --> 00:41:19,379 the prop of the plane 1125 00:41:19,380 --> 00:41:21,769 flexing all over the screen. 1126 00:41:21,770 --> 00:41:24,389 It can take it takes 1127 00:41:24,390 --> 00:41:26,609 the image of all pixels at the same 1128 00:41:26,610 --> 00:41:27,539 time. 1129 00:41:27,540 --> 00:41:29,669 And uh, additionally, all of the line 1130 00:41:29,670 --> 00:41:31,759 files, uh, are available 1131 00:41:31,760 --> 00:41:32,669 on get up. 1132 00:41:32,670 --> 00:41:35,579 Just if, you know, Kickett 1133 00:41:35,580 --> 00:41:36,839 can just open it. 1134 00:41:36,840 --> 00:41:38,919 We have it with us and we'll, uh, 1135 00:41:38,920 --> 00:41:40,679 hack on the firmware for the rest of the 1136 00:41:40,680 --> 00:41:41,680 event. 1137 00:41:42,420 --> 00:41:44,989 And that's it. 1138 00:41:44,990 --> 00:41:45,990 Yeah. 1139 00:41:54,000 --> 00:41:55,679 OK, thank you very much. 1140 00:41:55,680 --> 00:41:57,809 As always, we have microphones 1141 00:41:57,810 --> 00:41:59,879 in the room if you have questions, so 1142 00:41:59,880 --> 00:42:01,529 please line up in front of the 1143 00:42:01,530 --> 00:42:02,639 microphones. 1144 00:42:02,640 --> 00:42:04,709 We also should have a signal angel in 1145 00:42:04,710 --> 00:42:06,909 the room who can answer 1146 00:42:06,910 --> 00:42:08,369 your questions if you have them on the 1147 00:42:08,370 --> 00:42:10,499 Internet. So Ulsterman I 1148 00:42:10,500 --> 00:42:12,749 on Twitter and they will be relayed here 1149 00:42:12,750 --> 00:42:13,769 into the room. 1150 00:42:13,770 --> 00:42:15,269 So our partner. 1151 00:42:15,270 --> 00:42:16,270 Any questions 1152 00:42:18,840 --> 00:42:19,840 now? 1153 00:42:20,910 --> 00:42:21,910 Any questions. 1154 00:42:23,930 --> 00:42:26,279 Well, can be a microphone 1155 00:42:26,280 --> 00:42:27,819 please. Line up behind microphones. 1156 00:42:27,820 --> 00:42:28,820 Right next. 1157 00:42:30,870 --> 00:42:32,329 OK, so yeah. Please. 1158 00:42:32,330 --> 00:42:34,379 Question about the girls actually now 1159 00:42:34,380 --> 00:42:36,209 about the I'm not sure of the language to 1160 00:42:36,210 --> 00:42:38,520 assist Malkia if they can contribute. 1161 00:42:40,000 --> 00:42:42,629 Um warm I think. 1162 00:42:42,630 --> 00:42:44,849 Yes. That's the big 1163 00:42:44,850 --> 00:42:47,129 problem about them is they have very 1164 00:42:47,130 --> 00:42:49,289 large reduction ratios that 1165 00:42:49,290 --> 00:42:51,329 they're inefficient because there is 1166 00:42:51,330 --> 00:42:53,459 friction that did the snail 1167 00:42:53,460 --> 00:42:55,709 is actually sliding against 1168 00:42:55,710 --> 00:42:57,809 the, uh, the the gear, the 1169 00:42:57,810 --> 00:42:58,979 wall there. 1170 00:42:58,980 --> 00:43:01,189 And as you saw, I mean, you have 1171 00:43:01,190 --> 00:43:03,359 a Wikipedia claims that there are no 1172 00:43:03,360 --> 00:43:04,609 50 percent effective. 1173 00:43:04,610 --> 00:43:07,409 So if you have 250 watts, 1174 00:43:07,410 --> 00:43:08,729 then this thing is going to get really 1175 00:43:08,730 --> 00:43:09,730 warm. 1176 00:43:10,830 --> 00:43:12,749 So this is the reason why they would 1177 00:43:12,750 --> 00:43:14,579 otherwise be ideal are, for example, 1178 00:43:14,580 --> 00:43:17,309 using windshield wipers for cars. 1179 00:43:17,310 --> 00:43:19,829 Um, but I think our power requirements 1180 00:43:19,830 --> 00:43:22,049 are too large and additionally, 1181 00:43:22,050 --> 00:43:23,489 they are self-locking. 1182 00:43:23,490 --> 00:43:25,679 So if 1183 00:43:25,680 --> 00:43:28,019 anything collides with your leg and 1184 00:43:28,020 --> 00:43:30,239 your leg isn't in the stance you 1185 00:43:30,240 --> 00:43:32,399 thought it was, it would break because 1186 00:43:32,400 --> 00:43:34,619 the gear won't it 1187 00:43:34,620 --> 00:43:35,620 won't move. 1188 00:43:38,250 --> 00:43:39,339 Thanks. 1189 00:43:39,340 --> 00:43:40,889 OK, from spin, 1190 00:43:41,910 --> 00:43:44,039 yeah, I just was wondering, 1191 00:43:44,040 --> 00:43:46,409 all of the robots were essentially 1192 00:43:46,410 --> 00:43:47,509 humanoid robots. 1193 00:43:47,510 --> 00:43:48,869 I was just wondering if other bipedal 1194 00:43:48,870 --> 00:43:50,459 creatures were considered like maybe an 1195 00:43:50,460 --> 00:43:52,529 ostrich, which evolutionarily 1196 00:43:52,530 --> 00:43:55,229 speaking, is actually better for bipedal 1197 00:43:55,230 --> 00:43:56,729 walking than the human being is 1198 00:43:58,350 --> 00:44:00,509 curiosity. Well, can you give me tips 1199 00:44:00,510 --> 00:44:02,159 for avoiding the robot apocalypse? 1200 00:44:05,520 --> 00:44:07,589 Well, as far as 1201 00:44:07,590 --> 00:44:09,809 the famous case idea puts it, I don't 1202 00:44:09,810 --> 00:44:11,909 think this is a problem at the moment. 1203 00:44:11,910 --> 00:44:14,489 So just climb up a tree 1204 00:44:14,490 --> 00:44:16,589 and put down some water. 1205 00:44:16,590 --> 00:44:17,590 But 1206 00:44:18,750 --> 00:44:20,159 regarding the ostrich. 1207 00:44:21,940 --> 00:44:22,940 I think 1208 00:44:24,040 --> 00:44:26,109 I think from the point 1209 00:44:26,110 --> 00:44:28,389 of view of the rather simplified physics, 1210 00:44:28,390 --> 00:44:30,939 it's much the same because, 1211 00:44:30,940 --> 00:44:33,099 you know, it also has two legs and the 1212 00:44:33,100 --> 00:44:35,289 legs similarly can 1213 00:44:35,290 --> 00:44:36,290 move its feet. 1214 00:44:37,350 --> 00:44:39,509 So I guess the physics 1215 00:44:39,510 --> 00:44:41,849 is very abstract levels 1216 00:44:41,850 --> 00:44:43,499 for me, quite similar to writing a 1217 00:44:43,500 --> 00:44:45,089 control, I would also probably be 1218 00:44:45,090 --> 00:44:46,090 similar. 1219 00:44:46,830 --> 00:44:49,319 So I'm not sure 1220 00:44:49,320 --> 00:44:51,509 if it's from a purely mechanical 1221 00:44:51,510 --> 00:44:53,729 point of view, much different from 1222 00:44:53,730 --> 00:44:54,959 a human. 1223 00:44:54,960 --> 00:44:56,739 Other than that, the human has arms and 1224 00:44:56,740 --> 00:44:58,199 it has wings. 1225 00:44:58,200 --> 00:45:00,269 And as you saw, I mean, 1226 00:45:00,270 --> 00:45:02,699 we just think of the torso as one big 1227 00:45:02,700 --> 00:45:04,709 rigid body and don't model the details. 1228 00:45:06,990 --> 00:45:08,640 Does this answer the question? 1229 00:45:10,090 --> 00:45:11,090 OK. 1230 00:45:12,300 --> 00:45:14,219 Yeah, there's a question from the IOC. 1231 00:45:14,220 --> 00:45:16,679 OK, are there any plans for strict 1232 00:45:16,680 --> 00:45:18,869 Lex robots or are they going 1233 00:45:18,870 --> 00:45:22,049 to stay with Bendix? 1234 00:45:22,050 --> 00:45:23,739 Well, this depends on the controller. 1235 00:45:23,740 --> 00:45:26,219 So the problem is if you have trade 1236 00:45:26,220 --> 00:45:28,529 legs, then you lose one degree 1237 00:45:28,530 --> 00:45:29,530 of freedom. 1238 00:45:30,680 --> 00:45:32,869 Because essentially, you can't you 1239 00:45:32,870 --> 00:45:35,749 can't independently control the 1240 00:45:35,750 --> 00:45:38,239 default position anymore, that you 1241 00:45:38,240 --> 00:45:39,829 just have one degree of freedom left, 1242 00:45:39,830 --> 00:45:40,729 which is clear. Of course. 1243 00:45:40,730 --> 00:45:43,189 I mean, if your leg is straight, then 1244 00:45:43,190 --> 00:45:44,899 the distance between the hip and the 1245 00:45:44,900 --> 00:45:46,479 ankle has to remain constant. 1246 00:45:47,510 --> 00:45:49,989 And this kind of complicates control 1247 00:45:49,990 --> 00:45:51,229 design. 1248 00:45:51,230 --> 00:45:53,419 Um, so at some point 1249 00:45:53,420 --> 00:45:55,579 we might get around this, 1250 00:45:55,580 --> 00:45:57,649 but right now it's 1251 00:45:57,650 --> 00:46:00,319 probably simpler to stay with bent legs 1252 00:46:00,320 --> 00:46:02,449 and not know this is cast in stone, 1253 00:46:02,450 --> 00:46:03,439 right on this control. 1254 00:46:03,440 --> 00:46:05,509 It's not really optimized 1255 00:46:05,510 --> 00:46:07,819 for building an actual robot 1256 00:46:07,820 --> 00:46:09,469 yet at the moment you're experimenting. 1257 00:46:09,470 --> 00:46:11,869 So this might be considered 1258 00:46:11,870 --> 00:46:13,619 in the future, but at the moment it's the 1259 00:46:13,620 --> 00:46:15,050 so-called singularity. 1260 00:46:17,170 --> 00:46:19,239 Yeah, puts us off it, even 1261 00:46:19,240 --> 00:46:21,309 though it looks non-human. 1262 00:46:23,660 --> 00:46:26,089 Again, a question here from a front line, 1263 00:46:26,090 --> 00:46:28,099 first of all, thank you for the talk, 1264 00:46:28,100 --> 00:46:29,089 then I have a question. 1265 00:46:29,090 --> 00:46:30,589 You said that you implemented the 1266 00:46:30,590 --> 00:46:32,529 algorithms from Lytro Featherstone's 1267 00:46:32,530 --> 00:46:34,789 originally dynamics algorithms. 1268 00:46:34,790 --> 00:46:36,949 And I think there is a library that 1269 00:46:36,950 --> 00:46:39,319 exists, the ideal rigid body dynamics 1270 00:46:39,320 --> 00:46:41,749 library. Do you noted or did you 1271 00:46:41,750 --> 00:46:42,349 have a look at it? 1272 00:46:42,350 --> 00:46:44,179 I know of it. 1273 00:46:44,180 --> 00:46:46,769 I had a quick look at it, 1274 00:46:46,770 --> 00:46:49,759 but it seemed to me 1275 00:46:49,760 --> 00:46:52,789 that it was quite slow. 1276 00:46:52,790 --> 00:46:54,859 And the reason 1277 00:46:54,860 --> 00:46:57,349 so it's not the reason why we implemented 1278 00:46:57,350 --> 00:46:59,329 this ourselves is because. 1279 00:47:00,730 --> 00:47:02,349 We make something we only consider 1280 00:47:02,350 --> 00:47:04,029 kinematic chanes at the moment, not 1281 00:47:04,030 --> 00:47:06,309 trees, and I think 1282 00:47:06,310 --> 00:47:08,619 this makes a low level algorithm faster 1283 00:47:08,620 --> 00:47:10,779 because you can just put your bodies 1284 00:47:10,780 --> 00:47:13,329 in a linear list. 1285 00:47:13,330 --> 00:47:15,609 And the RBD al, I think, 1286 00:47:15,610 --> 00:47:17,589 really allocates a tree structure because 1287 00:47:17,590 --> 00:47:19,389 it can deal with somewhat generic case of 1288 00:47:19,390 --> 00:47:20,530 kinematic trees. 1289 00:47:21,730 --> 00:47:23,799 I did not actually PROFILET. 1290 00:47:23,800 --> 00:47:25,869 I built it and ran it on the 1291 00:47:25,870 --> 00:47:27,489 example and it turned out to be 1292 00:47:27,490 --> 00:47:28,779 relatively slow. 1293 00:47:28,780 --> 00:47:30,009 I don't want to insult anyone. 1294 00:47:30,010 --> 00:47:31,449 Maybe that's my fault. 1295 00:47:31,450 --> 00:47:34,119 But I suppose 1296 00:47:34,120 --> 00:47:36,219 this is because in the lowest loops, 1297 00:47:36,220 --> 00:47:38,709 it actually does a lot of 1298 00:47:38,710 --> 00:47:40,779 unordered memory access, whereas if 1299 00:47:40,780 --> 00:47:43,419 you do kinematic change, 1300 00:47:43,420 --> 00:47:45,609 you just can go to the body 1301 00:47:45,610 --> 00:47:46,610 one after the other. 1302 00:47:48,490 --> 00:47:50,709 So our system is far less generic. 1303 00:47:50,710 --> 00:47:52,629 It's really just for this robot and not 1304 00:47:52,630 --> 00:47:53,630 much else. 1305 00:47:54,460 --> 00:47:56,979 No, no, thanks. 1306 00:47:56,980 --> 00:47:58,389 Okay. Do we have any other question from 1307 00:47:58,390 --> 00:47:59,649 the Internet? 1308 00:47:59,650 --> 00:48:00,969 Yes. Them to ask, 1309 00:48:02,110 --> 00:48:04,469 is there or will there be an integration? 1310 00:48:07,450 --> 00:48:09,039 Eventually, yes. 1311 00:48:09,040 --> 00:48:10,040 I guess 1312 00:48:11,800 --> 00:48:14,439 one one thing 1313 00:48:14,440 --> 00:48:16,719 about this, though, is all this motion 1314 00:48:16,720 --> 00:48:18,399 planning algorithms that we all heard 1315 00:48:18,400 --> 00:48:20,559 about, the last talk, 1316 00:48:20,560 --> 00:48:22,659 they usually focused on static 1317 00:48:22,660 --> 00:48:24,969 trajectories. So, for example, 1318 00:48:24,970 --> 00:48:27,189 like my arm, I 1319 00:48:27,190 --> 00:48:28,239 am an industrial robot. 1320 00:48:28,240 --> 00:48:31,609 My arm is here and I want to get it here. 1321 00:48:31,610 --> 00:48:33,849 This is this is a this is a typical 1322 00:48:33,850 --> 00:48:35,619 collision avoidance problem because I 1323 00:48:35,620 --> 00:48:36,789 can't just move straight. 1324 00:48:36,790 --> 00:48:39,279 I have to move like this. 1325 00:48:39,280 --> 00:48:41,379 And I think this is the kind of problem 1326 00:48:41,380 --> 00:48:42,849 that our eyes are. 1327 00:48:42,850 --> 00:48:43,929 But our eyes actually. 1328 00:48:43,930 --> 00:48:46,359 But this this satellite 1329 00:48:46,360 --> 00:48:48,369 images that were mentioned focuses on 1330 00:48:49,630 --> 00:48:51,489 the thing about this kind of trajectory 1331 00:48:51,490 --> 00:48:53,499 is that it doesn't matter how fast you 1332 00:48:53,500 --> 00:48:55,839 execute it, you can just go slow 1333 00:48:55,840 --> 00:48:57,339 or fast as long as you stay on the 1334 00:48:57,340 --> 00:48:58,779 trajectory. 1335 00:48:58,780 --> 00:49:00,849 And when 1336 00:49:00,850 --> 00:49:03,159 I looked at it, it seemed 1337 00:49:03,160 --> 00:49:05,379 that it didn't have algorithms for our 1338 00:49:05,380 --> 00:49:07,749 kind of problem that actually matters 1339 00:49:07,750 --> 00:49:10,479 how fast you execute that trajectory, 1340 00:49:10,480 --> 00:49:12,849 because just because some 1341 00:49:12,850 --> 00:49:15,189 walks like a walk works, 1342 00:49:15,190 --> 00:49:16,809 it doesn't mean that it will continue to 1343 00:49:16,810 --> 00:49:19,989 work. If you go half as fast 1344 00:49:19,990 --> 00:49:22,029 because the reaction forces change the 1345 00:49:22,030 --> 00:49:24,189 change, you actually have to consider 1346 00:49:24,190 --> 00:49:26,439 the dynamics and 1347 00:49:26,440 --> 00:49:28,389 all of the assembling based motion 1348 00:49:28,390 --> 00:49:30,759 playing I witnessed, at least, at least 1349 00:49:30,760 --> 00:49:33,069 as far as I know, don't 1350 00:49:33,070 --> 00:49:34,389 typically deal with this. 1351 00:49:36,030 --> 00:49:37,709 That being said, of course, I mean, it's 1352 00:49:37,710 --> 00:49:39,479 still a very nice option to use the rice, 1353 00:49:39,480 --> 00:49:41,729 for example, for this camera project, 1354 00:49:41,730 --> 00:49:43,799 because you can 1355 00:49:43,800 --> 00:49:45,869 feed it with raw image data. 1356 00:49:45,870 --> 00:49:47,969 And it's at 1357 00:49:47,970 --> 00:49:50,349 least that is what the last claimed. 1358 00:49:50,350 --> 00:49:52,499 Yeah. And, uh, yeah, 1359 00:49:52,500 --> 00:49:54,579 the whole image pipeline is within 1360 00:49:54,580 --> 00:49:55,589 Ross and. 1361 00:49:55,590 --> 00:49:56,549 Yeah, yeah. 1362 00:49:56,550 --> 00:49:58,199 That sounds really convenient. 1363 00:49:58,200 --> 00:49:59,729 And they're it really makes sense to 1364 00:49:59,730 --> 00:50:01,409 avoid this kind of duplication. 1365 00:50:04,410 --> 00:50:06,809 OK, are there any other questions? 1366 00:50:08,350 --> 00:50:09,089 It doesn't look like it. 1367 00:50:09,090 --> 00:50:11,069 So I ask her again for one round of 1368 00:50:11,070 --> 00:50:12,679 applause for Felix, an awkward.