WEBVTT 1 00:00:00.080 --> 00:00:02.000 You know when you look at an old school wind 2 00:00:02.080 --> 00:00:06.360 up toy, like one of those little tin cars, there's 3 00:00:06.400 --> 00:00:09.560 this illusion of intelligence. You wind the key, you set 4 00:00:09.599 --> 00:00:12.160 it down on the floor, and it just zips across 5 00:00:12.160 --> 00:00:14.880 the room. It looks, I don't know, purposeful, right. 6 00:00:14.960 --> 00:00:18.199 It has a trajectory. It's interacting with the physical world 7 00:00:18.239 --> 00:00:20.839 in a very literal sense, just moving its mass from 8 00:00:20.879 --> 00:00:21.760 point A to point B. 9 00:00:21.920 --> 00:00:26.359 But it's completely blind. Oh, it's just releasing potential energy 10 00:00:26.440 --> 00:00:29.600 from a spring on a fixed mechanical path. Yeah, I mean, 11 00:00:29.640 --> 00:00:31.399 somebody drops a shoe in front of it. It just 12 00:00:31.480 --> 00:00:35.119 crashes into the leather and spins its little wheels until 13 00:00:35.159 --> 00:00:35.840 the spring dies. 14 00:00:35.960 --> 00:00:38.200 Yeah, it has absolutely no idea the shoe is there. 15 00:00:38.280 --> 00:00:42.079 It's not making choices exactly. Well, it's more than just blind, really, 16 00:00:42.119 --> 00:00:46.200 it's completely agnostic to reality. It's a machine, sure, but 17 00:00:46.280 --> 00:00:50.000 it lacks any mechanism to perceive its environment or alter 18 00:00:50.079 --> 00:00:52.039 its behavior based on what it finds. 19 00:00:52.119 --> 00:00:55.479 And crossing that massive evolutionary gap from a blind wind 20 00:00:55.560 --> 00:00:59.719 up toy to a machine that can actually perceive that shoe, stop, 21 00:01:00.000 --> 00:01:02.880 think and navigate around it. That takes an incredible amount 22 00:01:02.880 --> 00:01:03.840 of engineering. 23 00:01:03.439 --> 00:01:04.799 An unbelievable amount yeah. 24 00:01:04.840 --> 00:01:08.319 Yeah, today we are exploring exactly how to make that leap. 25 00:01:09.040 --> 00:01:11.719 Welcome to the deep dive where we are going under 26 00:01:11.760 --> 00:01:16.599 the hood of Lent and Joseph's manual Learning Robotics using Python. 27 00:01:16.719 --> 00:01:18.519 It's such a great source to dive into. 28 00:01:18.799 --> 00:01:21.000 We're going to see what it actually takes to build 29 00:01:21.120 --> 00:01:25.959 a differential drive service robot, specifically a robotic waiter. 30 00:01:26.200 --> 00:01:28.560 And it's a brilliant journey for you to follow along 31 00:01:28.560 --> 00:01:31.920 with because it forces you to synthesize disciplines. You can't 32 00:01:31.959 --> 00:01:34.079 just be a programmer, and you can't just be a mechanic. 33 00:01:34.239 --> 00:01:37.640 You have to bridge the physical world and the digital world. 34 00:01:37.799 --> 00:01:40.599 Okay, let's unpack this because before we can even think 35 00:01:40.599 --> 00:01:44.000 about building our robotic waiter, we really need to define 36 00:01:44.319 --> 00:01:48.000 what separates a tree robot from just, you know, a 37 00:01:48.040 --> 00:01:51.159 complex machine. You really do, and honestly, we have to 38 00:01:51.239 --> 00:01:53.480 fight through a century of science fiction myths to get 39 00:01:53.480 --> 00:01:54.560 to a working definition. 40 00:01:54.640 --> 00:01:58.239 Oh absolutely. Even the origin of the word itself sets 41 00:01:58.319 --> 00:02:01.319 up this expectation that engineers have been wrestling with ever since. 42 00:02:01.359 --> 00:02:04.760 I mean, the term robot didn't originate in an MIT laboratory. 43 00:02:05.400 --> 00:02:08.280 It was coined in a theater in nineteen twenty a 44 00:02:08.400 --> 00:02:11.919 check writer named Carol Kappek wrote a play called ru Are. 45 00:02:12.159 --> 00:02:15.240 Which stands for Rossum's Universal Robots right exactly. 46 00:02:15.520 --> 00:02:17.039 He was trying to come up with a term for 47 00:02:17.240 --> 00:02:21.680 artificial human workers, and his brother Joseph actually suggested robode, 48 00:02:21.800 --> 00:02:22.560 which carries a. 49 00:02:22.560 --> 00:02:25.319 Very specific cultural weight, doesn't it very much? 50 00:02:25.360 --> 00:02:28.879 So it stems from the word robota in Czech and Slovak, 51 00:02:29.319 --> 00:02:33.919 which translates to work or more accurately surf labor or 52 00:02:34.080 --> 00:02:35.159 hard drudgery. 53 00:02:35.319 --> 00:02:35.639 Wow. 54 00:02:36.039 --> 00:02:39.280 So right from its birth, the concept implies a machine 55 00:02:39.319 --> 00:02:43.159 designed to take on the heavy, undesirable lifting for humanity. 56 00:02:43.319 --> 00:02:46.280 Though I mean spoiler alert for a play from the 57 00:02:46.319 --> 00:02:51.120 nineteen twenties, those robotic serfs eventually revolt and wipe out humanity. 58 00:02:50.759 --> 00:02:54.000 A narrative trope that has completely dominated our perception of 59 00:02:54.080 --> 00:02:57.240 robotics ever since. But you know, if we strip away 60 00:02:57.240 --> 00:03:00.439 the Hollywood dramatization and look for a functional, modern defy definition, 61 00:03:00.680 --> 00:03:04.080 roboticists like Maji Jamataric offer a much clearer lens. 62 00:03:04.159 --> 00:03:04.960 Okay, what's her tick? 63 00:03:05.120 --> 00:03:07.840 She defines a robot as an autonomous system existing in 64 00:03:07.879 --> 00:03:10.840 the physical world, able to sense its environment and act 65 00:03:10.879 --> 00:03:11.319 on it to. 66 00:03:11.319 --> 00:03:14.639 Achieve goals, which fundamentally disqualifies my washing machine. 67 00:03:14.759 --> 00:03:15.360 Yes it does. 68 00:03:15.520 --> 00:03:17.800 My washing machine doesn't sense anything. It just runs a 69 00:03:17.800 --> 00:03:21.080 pre programmed timer, much like the tin wind up toy. Yeah, 70 00:03:21.120 --> 00:03:24.599 but I was thinking about this definition, and it also 71 00:03:24.680 --> 00:03:28.960 seems to disqualify something incredibly smart, like my email spam filter. 72 00:03:29.159 --> 00:03:30.919 Ah, that's an interesting point. 73 00:03:30.800 --> 00:03:34.919 Right, because a spam filter learns, it adapts, it acts 74 00:03:35.000 --> 00:03:38.159 autonomously to keep junk out of my inbox. Yeah, but 75 00:03:38.240 --> 00:03:40.719 it doesn't live in the physical world. The data is 76 00:03:40.759 --> 00:03:43.840 just perfectly spoon fed to it in a stable digital environment. Right. 77 00:03:44.560 --> 00:03:47.960 Is the sheer chaos of a messy physical bedroom what 78 00:03:48.159 --> 00:03:51.120 makes building a true robot so uniquely difficult. 79 00:03:51.280 --> 00:03:53.919 That is the absolute core of the challenge. A spam 80 00:03:53.960 --> 00:03:56.719 filter never has to worry about a sudden gust of wind, 81 00:03:57.080 --> 00:03:59.680 or the floor being slippery, or a dog running by 82 00:04:00.000 --> 00:04:02.400 exactly or the lighting in the room changing and blinding 83 00:04:02.400 --> 00:04:06.159 its camera. The physical world is wildly unpredictable. The friction 84 00:04:06.360 --> 00:04:09.039 on a carpet is different from the friction on hardwood. 85 00:04:09.639 --> 00:04:13.000 Sensing that unpredictable chaos, making sense of it, and then 86 00:04:13.039 --> 00:04:16.360 physically exerting force upon it, that continuous loop is what 87 00:04:16.519 --> 00:04:19.959 separates true robotics from pure software engineering. 88 00:04:20.199 --> 00:04:23.800 So if a true robot must sense an act in 89 00:04:23.879 --> 00:04:27.160 this chaotic physical space, how do we build a brain 90 00:04:27.240 --> 00:04:31.199 that can process all that messy sensory information and decide 91 00:04:31.199 --> 00:04:31.920 what to do well. 92 00:04:31.920 --> 00:04:34.360 This brings us to the fundamental anatomy of a robot. 93 00:04:34.759 --> 00:04:37.560 You have the physical body. You have sensors which measure 94 00:04:37.560 --> 00:04:39.920 the environment to create what we call a digital state. 95 00:04:40.519 --> 00:04:42.879 You have effectors or the motors and arms that do 96 00:04:42.920 --> 00:04:47.160 the actual moving and sitting between the sensors and the effectors, 97 00:04:47.160 --> 00:04:48.439 you have the controllers. 98 00:04:48.639 --> 00:04:50.360 The brain, precisely the brain. 99 00:04:50.720 --> 00:04:53.839 And giving a machine a brain that could handle physical 100 00:04:53.879 --> 00:04:57.600 chaos really started around nineteen sixty six with a robot 101 00:04:57.680 --> 00:05:02.480 developed at the Stanford Research Institute famously named Shaky. Shaky, Yeah, Shaky. 102 00:05:02.680 --> 00:05:05.279 It was a milestone because it didn't just execute a 103 00:05:05.360 --> 00:05:08.199 list of hard coded commands. It could actually reason. How So, 104 00:05:08.399 --> 00:05:11.040 if you gave Shakey a high level command, it could 105 00:05:11.120 --> 00:05:15.439 break that complex goal down into smaller, solvable intermediate steps. 106 00:05:15.800 --> 00:05:18.199 I mean, trying to get Shaky to navigate around literal 107 00:05:18.199 --> 00:05:21.000 blocks in a room actually led researchers to invent the 108 00:05:21.040 --> 00:05:22.199 a star search algorithm. 109 00:05:22.240 --> 00:05:25.879 Wait, really, the same pathfinding tool used in computer science today, 110 00:05:26.040 --> 00:05:26.680 the very same. 111 00:05:26.759 --> 00:05:30.720 It's foundational. But Shaky got its name for a reason. 112 00:05:31.199 --> 00:05:33.920 It was incredibly slow and jerky. 113 00:05:34.000 --> 00:05:35.560 Oh, because it had to think so much. 114 00:05:35.800 --> 00:05:39.800 Yes, it would move a tiny bit, stop, think for 115 00:05:39.839 --> 00:05:42.040 a very long time, and then move a tiny bit more. 116 00:05:42.600 --> 00:05:46.439 Trying to plan every single movement perfectly just isn't practical. 117 00:05:46.560 --> 00:05:49.360 No, especially in a dynamic environment with people walking. 118 00:05:49.120 --> 00:05:53.720 Around exactly, And that tension led to the development of 119 00:05:53.800 --> 00:05:57.839 different control paradigms. You have the hierarchical or deliberative paradigm, 120 00:05:57.839 --> 00:05:58.800 which is what Shakey used. 121 00:05:58.839 --> 00:05:59.839 Okay, what does that look like. 122 00:06:00.120 --> 00:06:03.360 The sequence is sense the world, plan a route, then act. 123 00:06:03.519 --> 00:06:07.120 It's very intelligent, but computing that plan takes critical time. 124 00:06:07.759 --> 00:06:10.519 On the opposite end, you have the reactive paradigm. This 125 00:06:10.600 --> 00:06:13.839 is simply sense then act. There is no planning, just 126 00:06:13.920 --> 00:06:14.879 immediate response. 127 00:06:15.199 --> 00:06:16.759 Let me see if I have this right, because I 128 00:06:16.759 --> 00:06:19.480 was trying to map this onto human biology all reading. Sure, 129 00:06:19.560 --> 00:06:22.120 if I accidentally brush my hand against a hont stove, 130 00:06:22.720 --> 00:06:26.959 I don't stop sense the temperature, formulate a spatial plan 131 00:06:27.000 --> 00:06:29.720 to move my arm, and then execute the movement. 132 00:06:29.879 --> 00:06:31.079 No, you'd burn your hand. 133 00:06:31.079 --> 00:06:35.399 Right, My spinal cord just bypasses my brain entirely and 134 00:06:35.480 --> 00:06:37.639 yanks my hand back in a fraction of a second. 135 00:06:38.240 --> 00:06:40.800 Is reactive control. Basically a digital reflex. 136 00:06:41.040 --> 00:06:44.160 A spinal reflex is a phenomenal way to picture it, actually, 137 00:06:44.519 --> 00:06:49.720 but with one major caveat A robot's reflex is completely programmable. 138 00:06:50.000 --> 00:06:52.360 And if we connect this to the bigger picture of 139 00:06:52.439 --> 00:06:54.560 the robotic waiter we are trying to build from the 140 00:06:54.560 --> 00:06:58.519 source material, you quickly realize you can't rely purely on 141 00:06:58.519 --> 00:06:59.279 one paradigm. 142 00:06:59.279 --> 00:06:59.959 You need accommodate. 143 00:07:00.240 --> 00:07:01.199 You need a hybrid model. 144 00:07:01.279 --> 00:07:03.120 Yes, because it has to be smart enough to find 145 00:07:03.160 --> 00:07:06.000 the table, but fast enough not to run over a customer. 146 00:07:06.120 --> 00:07:11.240 Exactly that. The robot needs a hierarchical deliberative plan to 147 00:07:11.319 --> 00:07:13.959 note that payble four is across the dining room, to 148 00:07:14.000 --> 00:07:16.639 map an efficient path around the stationary booths, and to 149 00:07:16.720 --> 00:07:20.360 calculate an arrival time. But if a patron suddenly steps 150 00:07:20.360 --> 00:07:22.639 backward out of their chair holding a tray of drinks, 151 00:07:23.040 --> 00:07:25.399 the robot does not have three seconds to sit there 152 00:07:25.439 --> 00:07:27.199 and recalculate a new global map. 153 00:07:27.240 --> 00:07:27.920 It would crash. 154 00:07:28.160 --> 00:07:30.720 It needs that reactive reflex to slam on the brakes 155 00:07:30.720 --> 00:07:33.839 of the millisecond it's light ar detects a sudden obstacle. 156 00:07:34.639 --> 00:07:38.360 The hybrid model layers these systems, a slow smart planner 157 00:07:38.480 --> 00:07:41.560 running in the background and a fast reactive safety system 158 00:07:41.639 --> 00:07:42.600 running in the foreground. 159 00:07:42.600 --> 00:07:45.360 All right, so we understand this hybrid brain. But a 160 00:07:45.399 --> 00:07:49.680 brain needs a physical vessel to carry the soup. If 161 00:07:49.680 --> 00:07:52.839 we are actually engineering this robotic waiter, how do we 162 00:07:52.920 --> 00:07:54.839 design the physical machine from scratch? 163 00:07:55.079 --> 00:07:58.920 Well, you start by defining your hard constraints. Engineering is 164 00:07:58.959 --> 00:08:02.839 all about solving specific problems. For this project, the robot 165 00:08:02.879 --> 00:08:05.639 needs to carry food, so the text specifies a payload 166 00:08:05.680 --> 00:08:07.839 capacity of up to five kilograms. 167 00:08:07.920 --> 00:08:08.240 Okay. 168 00:08:08.360 --> 00:08:10.759 It needs to travel at roughly a human walking base 169 00:08:10.839 --> 00:08:13.839 to not be disruptive, which means a target speed between 170 00:08:13.879 --> 00:08:15.680 er point twenty five and one meter per second. 171 00:08:15.759 --> 00:08:16.399 That makes sense. 172 00:08:16.519 --> 00:08:19.279 It also needs more than three centimeters of ground clearance 173 00:08:19.319 --> 00:08:23.000 to get over doorway thresholds without getting stuck. And crucially, 174 00:08:23.120 --> 00:08:25.040 it needs to be relatively low cost. 175 00:08:25.279 --> 00:08:27.639 And the mechanical solution the book walks us through is 176 00:08:28.040 --> 00:08:31.959 a differential drive system. Yes, it's modeled after the turtlebot architecture. 177 00:08:32.440 --> 00:08:34.200 If you picture it, it looks kind of like a 178 00:08:34.240 --> 00:08:38.000 three tiered wedding cake made of metal plates, a base plate, 179 00:08:38.320 --> 00:08:40.919 a middle plate, and a top plate. That's a good visual, 180 00:08:41.399 --> 00:08:44.080 But the drive system is what caught my eye. It 181 00:08:44.120 --> 00:08:47.120 only has two powered wheels on the left and right sides, 182 00:08:47.720 --> 00:08:51.080 and then these unpowered castor wheels like you'd find on 183 00:08:51.159 --> 00:08:53.200 the bottom of an office chair on the front and back, 184 00:08:53.559 --> 00:08:54.840 just to keep it from tipping over. 185 00:08:55.200 --> 00:08:59.440 Differential drive is brilliant in its simplicity. By independently controlling 186 00:08:59.559 --> 00:09:02.080 just the yeat and direction of those two side wheels, 187 00:09:02.240 --> 00:09:03.840 you can steer the robot. 188 00:09:03.480 --> 00:09:06.879 Effortlessly without needing a heavy, complex steering rack like a 189 00:09:06.960 --> 00:09:07.600 car uses. 190 00:09:07.799 --> 00:09:10.559 Exactly, well, you can't just slap any motors onto those 191 00:09:10.559 --> 00:09:12.519 wheels and call it a day. You have to calculate 192 00:09:12.559 --> 00:09:13.759 the physics. 193 00:09:13.279 --> 00:09:16.519 Right, because if you guess wrong, the robot either moves 194 00:09:16.559 --> 00:09:19.399 at its nail's pace or it completely stalls out when 195 00:09:19.440 --> 00:09:20.559 you put a bowl of soup on it. 196 00:09:20.679 --> 00:09:24.159 Exactly, you are managing the tension between speed and torque. 197 00:09:24.240 --> 00:09:26.960 The text walks through the calculations. If you want this 198 00:09:27.080 --> 00:09:29.200 robot to travel at a modest point three to five 199 00:09:29.320 --> 00:09:31.879 meters per second, and you are using wheels with a 200 00:09:31.960 --> 00:09:34.919 nine centimeter diameter, to maintain that ground clearance. 201 00:09:35.159 --> 00:09:35.639 Okay, right. 202 00:09:35.639 --> 00:09:38.279 In the math, the geometry dictates the wheels must spin 203 00:09:38.320 --> 00:09:42.279 at roughly seventy four revelations per minute. The author standardizes 204 00:09:42.320 --> 00:09:45.519 this by selecting an off the shelf eighty rpm motor. 205 00:09:45.639 --> 00:09:49.000 But speed is only half the battle. Torque is the muscle, 206 00:09:49.240 --> 00:09:50.000 right right. 207 00:09:50.320 --> 00:09:54.279 Torque is the twisting force required to overcome inertia and friction. 208 00:09:54.960 --> 00:09:57.720 Think about pushing a heavy box across a room. The 209 00:09:57.799 --> 00:10:00.600 hardest part is always that initial show to get it 210 00:10:00.600 --> 00:10:01.759 to budge from a dead stop. 211 00:10:01.840 --> 00:10:03.440 Yeah, once it's sliding, it's easier. 212 00:10:03.799 --> 00:10:07.320 Our robotic waiter. The chassis plus that five kilogram payload 213 00:10:07.360 --> 00:10:10.960 weighs about fifteen kilograms total. That weight is pressing down on. 214 00:10:10.919 --> 00:10:13.759 The floor, and the floor has friction, a lot of it. 215 00:10:14.039 --> 00:10:16.080 If you factor in a friction coefficient of zero point 216 00:10:16.159 --> 00:10:19.039 six for a standard indoor surface, the math reveals that 217 00:10:19.080 --> 00:10:21.480 the motors need to generate ten point three to two 218 00:10:21.600 --> 00:10:25.399 kilogram centimeters of torque just to break that static friction 219 00:10:25.519 --> 00:10:26.639 and get the robot moving. 220 00:10:26.759 --> 00:10:27.039 Wow. 221 00:10:27.480 --> 00:10:30.120 If you buy a motor with only five kilogram centimeters 222 00:10:30.120 --> 00:10:32.159 of tork, it won't matter how fast it can spin. 223 00:10:32.519 --> 00:10:35.279 The wheels will just hum, heat up, and stall. 224 00:10:35.559 --> 00:10:39.559 That transition from abstract code to high school physics is wild. 225 00:10:40.039 --> 00:10:42.679 You have to literally calculate the friction of the floor, 226 00:10:43.000 --> 00:10:45.360 and once that math is locked in, you have to 227 00:10:45.399 --> 00:10:46.279 design the parts. 228 00:10:46.440 --> 00:10:47.639 Yes, the actual model. 229 00:10:47.679 --> 00:10:51.200 He also uses libricad for the two D bluefrints and 230 00:10:51.360 --> 00:10:54.600 Blender for the three D models. But here's where I 231 00:10:54.639 --> 00:10:58.080 got really confused reading the source. Oh, when it's time 232 00:10:58.080 --> 00:11:00.679 to build the three D model in Blender, the author 233 00:11:00.720 --> 00:11:03.679 doesn't use the mouse. They don't drag and drop shapes. 234 00:11:04.000 --> 00:11:07.960 They open Blenders, Python API, the boopy module and write 235 00:11:08.039 --> 00:11:11.559 lines of Python code just to generate a three D cylinder. 236 00:11:11.679 --> 00:11:12.320 Ah. 237 00:11:12.399 --> 00:11:15.000 Yes, Why would someone write a script to draw a 238 00:11:15.080 --> 00:11:17.840 shape when they could literally just click and drag the 239 00:11:17.879 --> 00:11:19.240 mounts and be done in three seconds. 240 00:11:19.320 --> 00:11:22.080 I know it feels entirely counterintuitive until you consider the 241 00:11:22.120 --> 00:11:25.399 reality of iterative engineering. When you drag a mouse to 242 00:11:25.480 --> 00:11:28.919 draw a cylinder, you are introducing human imperfection. You might 243 00:11:28.960 --> 00:11:31.320 be off by a fraction of a millimeter, right, But 244 00:11:31.440 --> 00:11:35.360 more importantly, a hand drawn shape is static. Programmatic modeling 245 00:11:35.399 --> 00:11:38.600 allows you to completely parameterize your dimensions. 246 00:11:38.159 --> 00:11:39.759 Meaning you link the shape to the. 247 00:11:39.720 --> 00:11:43.159 Math exactly Imagine you build the robot and you realize 248 00:11:43.159 --> 00:11:45.960 your waiter actually needs to carry ten kilograms of food 249 00:11:46.000 --> 00:11:48.159 instead of five. The physics change. 250 00:11:48.200 --> 00:11:49.840 You need bigger motors. 251 00:11:49.639 --> 00:11:52.159 Which require bigger mounts, which means the base plate needs 252 00:11:52.200 --> 00:11:54.840 to be wider. If you drew it by hand, you 253 00:11:54.919 --> 00:11:58.519 have to manually resize the chassis, reposition the wheel axes, 254 00:11:58.799 --> 00:12:00.320 and check every clearance by I. 255 00:12:01.080 --> 00:12:02.240 That sounds like a nightmare. 256 00:12:02.320 --> 00:12:05.080 It is, But if you used Python, you simply open 257 00:12:05.080 --> 00:12:07.480 your script, change the variable payload weight to. 258 00:12:07.480 --> 00:12:10.000 Ten, and run the code and it does it all 259 00:12:10.039 --> 00:12:10.320 for you. 260 00:12:10.600 --> 00:12:15.399 The math automatically recalculates, resizes the cylinder, shifts the wheel mounts, 261 00:12:15.440 --> 00:12:19.039 and spits out a flawless, updated three D model. Plus 262 00:12:19.159 --> 00:12:22.840 the script can automatically export the STL files needed for 263 00:12:22.919 --> 00:12:27.200 simulation without any graphical artifacts. You aren't drawing a picture, 264 00:12:27.279 --> 00:12:29.399 you are engineering a responsive system. 265 00:12:29.480 --> 00:12:32.120 Okay. I love that the code itself becomes the ultimate 266 00:12:32.159 --> 00:12:34.559 precision tool. So now we have our three D model, 267 00:12:34.759 --> 00:12:38.440 perfectly generated by Python, sitting on as differential drive wheels, right. 268 00:12:38.600 --> 00:12:41.120 But to make it actually navigate a virtual restaurant, we 269 00:12:41.240 --> 00:12:44.440 run into the physics of driving, and this introduces kinematics. 270 00:12:44.799 --> 00:12:49.600 Yes. Kinematics is the study of motion, the mathematics of 271 00:12:49.600 --> 00:12:53.200 how things move without worrying about the underlying forces like 272 00:12:53.320 --> 00:12:54.559 mass or friction that we. 273 00:12:54.639 --> 00:12:56.720 Just discussed, so just the geometry of it. 274 00:12:56.799 --> 00:12:59.440 Basically, for our robot, we have to look at its 275 00:12:59.480 --> 00:13:03.440 degrees of freedom or its pose on a flat restaurant floor. 276 00:13:03.639 --> 00:13:06.600 The robot operates in a standard X and y coordinate 277 00:13:06.639 --> 00:13:10.240 system like a graph, but it also has a heading 278 00:13:10.279 --> 00:13:13.240 the direction it's facing, which is represented by the Greek 279 00:13:13.279 --> 00:13:16.759 letter theta, So its pose is always defined by x, 280 00:13:16.919 --> 00:13:17.799 y and theta. 281 00:13:18.200 --> 00:13:21.720 But because it uses that two wheel differential drive, it 282 00:13:21.759 --> 00:13:24.960 has a major movement limitation. The source calls it a 283 00:13:25.000 --> 00:13:28.639 non holonomic constraint, a very intimidating term which sounds like 284 00:13:28.679 --> 00:13:31.120 a terrifying math term, but it just basically just what 285 00:13:31.240 --> 00:13:33.360 I deal with when I try to parallel park my car. 286 00:13:33.480 --> 00:13:35.039 Actually, yes, because my. 287 00:13:35.000 --> 00:13:37.639 Car can't just slide sideways into a spot. I have 288 00:13:37.720 --> 00:13:40.480 to roll forward or backward based on where the wheels 289 00:13:40.480 --> 00:13:42.879 are pointing. I have to do this whole geometric dance 290 00:13:42.919 --> 00:13:46.679 of turning, reversing, and straightening out just to move a 291 00:13:46.720 --> 00:13:49.080 few feet to the left. Face does our robotic waiter 292 00:13:49.120 --> 00:13:51.600 have the same problem, like, if table four is directly 293 00:13:51.639 --> 00:13:54.080 to its left, can it just strafe sideways? 294 00:13:54.200 --> 00:13:57.879 It absolutely cannot, and your parallel parking frustration is the 295 00:13:58.039 --> 00:14:02.159 exact manifestation of a non Holow constraint. The robot cannot 296 00:14:02.240 --> 00:14:04.759 change its position on the x or y axis without 297 00:14:04.759 --> 00:14:07.639 first changing its data it's heading wow. To reach of 298 00:14:07.679 --> 00:14:10.360 that table to its left, it must execute a specific 299 00:14:10.440 --> 00:14:16.200 foundational algorithm for inverse kinematics vrot vahead v rot. 300 00:14:16.240 --> 00:14:18.279 Rotate, drive ahead, rotate again correct. 301 00:14:18.360 --> 00:14:21.200 It rotates in place to face the target coordinates. It 302 00:14:21.279 --> 00:14:23.679 drives ahead in a straight line to reach them, and 303 00:14:23.720 --> 00:14:26.039 then it rotates a second time to face the final 304 00:14:26.120 --> 00:14:29.879 desired orientation, say, facing the customer to deliver the plate. 305 00:14:30.000 --> 00:14:30.320 Got it. 306 00:14:30.679 --> 00:14:33.440 What's fascinating here is the geometry of how it turns. 307 00:14:34.120 --> 00:14:37.159 Because the two wheels are fixed on a single horizontal axis, 308 00:14:37.360 --> 00:14:40.159 anytime the left wheel and right wheels spin at different speeds, 309 00:14:40.360 --> 00:14:42.279 the robot naturally sweeps through an arc. 310 00:14:42.399 --> 00:14:43.559 Okay, I can picture that it. 311 00:14:43.639 --> 00:14:47.200 Rotates around a specific invisible pivot point located somewhere along 312 00:14:47.279 --> 00:14:50.639 that extended axis line. This is called the instantaneous center 313 00:14:50.679 --> 00:14:52.159 of curvature, or ICC. 314 00:14:52.240 --> 00:14:55.080 And the math is constantly crunching the wheel speeds to 315 00:14:55.080 --> 00:14:57.120 figure out where that invisible pivot. 316 00:14:56.799 --> 00:15:01.399 Point is continually forward. Kinematics is the mes asking, given 317 00:15:01.440 --> 00:15:03.720 the current speed of my left wheel and right wheel, 318 00:15:04.080 --> 00:15:07.320 where will my X y and theta be in five seconds? 319 00:15:08.399 --> 00:15:12.360 In Verse, kinematics asks the much harder question, I need 320 00:15:12.399 --> 00:15:16.559 to be at this specific X y and theta Exactly 321 00:15:16.600 --> 00:15:18.879 how fast should I spin my left wheel versus my 322 00:15:18.960 --> 00:15:21.799 right wheel to make my ICC carve the perfect arc 323 00:15:21.879 --> 00:15:22.360 to get there? 324 00:15:22.440 --> 00:15:25.440 But wait to calculate any of that, the robot needs 325 00:15:25.480 --> 00:15:28.000 to know exactly how far its wheels have actually turned 326 00:15:28.000 --> 00:15:30.480 in the real world. It doesn't have GPS indoors, how 327 00:15:30.480 --> 00:15:33.240 does it know it drove two meters and not one ah. 328 00:15:33.360 --> 00:15:36.600 It relies on wheel adometry. Attached to the motors are 329 00:15:36.639 --> 00:15:40.000 sensors called wheel encoders encoders Okay. The text explains that 330 00:15:40.039 --> 00:15:44.320 these encoders output binary signals microscopic digital clicks or steps 331 00:15:44.360 --> 00:15:47.519 as the physical wheel rotates. If you know exactly how 332 00:15:47.559 --> 00:15:49.960 far the wheel travels in one tiny step, you just 333 00:15:50.000 --> 00:15:50.919 count the steps. 334 00:15:50.600 --> 00:15:53.200 And multiply, so it's basically counting its own footsteps in 335 00:15:53.240 --> 00:15:53.600 the dark. 336 00:15:53.919 --> 00:15:56.600 Yes, if you think of the cameras and light oars 337 00:15:56.679 --> 00:16:00.240 as the robot's eyes. The wheel encoders are its inner ear. 338 00:16:00.720 --> 00:16:05.919 They provide proprioception. They give the robot a constant mathematical 339 00:16:05.919 --> 00:16:09.399 awareness of its own body moving through space, feeding real 340 00:16:09.480 --> 00:16:11.759 numbers back into those kinematics equations. 341 00:16:11.840 --> 00:16:13.879 Oh yeah, so we've got the Python three D model. 342 00:16:13.919 --> 00:16:16.200 We have the torque calculations that we have the complex 343 00:16:16.279 --> 00:16:18.200 kinematics and encoders all. 344 00:16:18.039 --> 00:16:19.559 Figured out everything we need. 345 00:16:19.679 --> 00:16:22.600 But before we spend a single dollar ordering real motors 346 00:16:22.679 --> 00:16:26.279 or cutting metal plates, the book has us take all 347 00:16:26.279 --> 00:16:30.600 this logic and plug it into the matrix the simulation. 348 00:16:30.279 --> 00:16:33.519 Which is the most crucial step in modern robotics. Simulation 349 00:16:33.639 --> 00:16:36.480 gives you a sandbox to test your real production ready 350 00:16:36.519 --> 00:16:40.080 coming on virtual hardware. It's low cost and more importantly, 351 00:16:40.240 --> 00:16:41.399 zero physical. 352 00:16:41.039 --> 00:16:42.279 Risk, no broken parts. 353 00:16:42.360 --> 00:16:45.759 Exactly. If your inverse kinematics math is inverted and your 354 00:16:46.000 --> 00:16:48.960 virtual robot accelerates to maximum speed and drive straight into 355 00:16:48.960 --> 00:16:51.320 a virtual wall, you don't have a pile of broken 356 00:16:51.320 --> 00:16:53.559 metal and a fired engineer. You just hit reset on 357 00:16:53.600 --> 00:16:54.120 the simulation. 358 00:16:54.480 --> 00:16:57.480 Here's where it gets really interesting for me. The tools 359 00:16:57.600 --> 00:17:01.399 used for this are gazebo and ros because zebo makes sense. 360 00:17:01.399 --> 00:17:04.119 It's the three D physics simulator. It renders the restaurant, 361 00:17:04.160 --> 00:17:07.559 the tables, and calculates the virtual gravity. But ROS, the 362 00:17:07.640 --> 00:17:11.079 robot operating system, is what actually runs the brain, although 363 00:17:11.319 --> 00:17:13.720 the text makes a point to say it isn't actually 364 00:17:13.759 --> 00:17:17.799 an operating system like Windows or Linux. It's a meta 365 00:17:17.880 --> 00:17:20.079 operating system and a distributed framework. 366 00:17:20.160 --> 00:17:22.960 That's a vital distinction ROS. It's on top of a 367 00:17:22.960 --> 00:17:27.920 traditional operating system. At its core, ROS is a communication framework. 368 00:17:28.640 --> 00:17:32.960 A modern robot runs dozens of separate executable programs simultaneously, 369 00:17:33.000 --> 00:17:36.359 one for vision, one for driving, one for mapping. ROS 370 00:17:36.440 --> 00:17:40.359 calls these individual programs nodes nodes. Yes, you have a 371 00:17:40.359 --> 00:17:43.119 central directory called the ROS master that keeps track of 372 00:17:43.119 --> 00:17:45.960 what nodes are running. But the actual data sharing happens 373 00:17:45.960 --> 00:17:49.079 through a brilliant published and subscribe model using data streams 374 00:17:49.079 --> 00:17:49.880 called topics. 375 00:17:50.079 --> 00:17:52.200 So this publish and subscribe thing, I'm trying to wrap 376 00:17:52.200 --> 00:17:54.480 my head around it. If a wheel encoder has new 377 00:17:54.519 --> 00:17:57.519 odometry data, does it just shout it out? Is it 378 00:17:57.559 --> 00:17:59.839 sort of like a social media feed where a node 379 00:18:00.440 --> 00:18:03.400 tweets its speed to a topic and hope someone else 380 00:18:03.440 --> 00:18:03.960 is reading it. 381 00:18:04.039 --> 00:18:07.720 That is an incredibly useful way to conceptualize it. The 382 00:18:07.720 --> 00:18:11.759 wheel encoder node publishes its data to a topic named, 383 00:18:12.000 --> 00:18:16.079 for example, slash odometry. It has absolutely no idea who 384 00:18:16.160 --> 00:18:17.960 is reading it, or if anyone who is reading it 385 00:18:18.000 --> 00:18:18.279 at all. 386 00:18:18.400 --> 00:18:18.880 Oh wow. 387 00:18:19.079 --> 00:18:22.839 Conversely, your motor control node needs to know how fast 388 00:18:22.839 --> 00:18:26.000 the robot is moving, so it subscribes to the slash 389 00:18:26.000 --> 00:18:28.440 o doomitory topic. It essentially follows. 390 00:18:28.039 --> 00:18:29.880 That feed, just waiting for updates. Yeah. 391 00:18:30.240 --> 00:18:32.880 Whenever new data appears on the topic, the motor node 392 00:18:32.880 --> 00:18:36.000 reads it and adjusts the power. The two nodes never 393 00:18:36.079 --> 00:18:38.400 speak directly to each other. They just interact with the feed. 394 00:18:38.480 --> 00:18:40.799 They don't even need to know the other one exists exactly. 395 00:18:40.920 --> 00:18:44.519 And this decoupled architecture is what makes ros so powerful. 396 00:18:44.839 --> 00:18:47.640 Because the nodes are completely independent, they don't even need 397 00:18:47.680 --> 00:18:51.440 to be written in the same programming language. Wait really, Yeah, 398 00:18:51.839 --> 00:18:54.640 your wheel encoder node could be a simple Python script 399 00:18:54.720 --> 00:18:58.960 running on a tiny Raspberry Pie strapped to the robot's base. Meanwhile, 400 00:18:59.000 --> 00:19:02.200 your complex path planning node could be a heavy performance 401 00:19:02.200 --> 00:19:05.880