So far, you’ve seen how you can integrate acceleration data from an accelerometer to get change in velocity, and you’ve seen how you can integrate velocity to get change in position or displacement. And displacement and velocity are important quantities to a self driving car, so it’s really fortunate that we can calculate them from … Read more
In the next notebook, you’re going to learn a technique that will let you integrate any function of a single variable and all it’s going to take is a loop. Before you jump into this code, let me briefly explain the theory behind what you’re going to be doing. So, let’s say you want to … Read more
When you calculate the area under a curve, what you’re actually doing is taking an integral. And the mathematical symbol for the integral is this stretched out “S” looking shape. And often it’ll have what are called bounds of integration at the bottom and the top. So, in this case, t1 is the lower bound … Read more
We’re going to come back to the elevator example in a little bit. First, I want to remind you of something you saw a few of courses back. Earlier in this category, when you were learning about matrices in motion models, you may remember seeing a graph that looks something like this. And this was … Read more
You just made a plot of acceleration versus time for an elevator as it goes upwards from the ground floor and then stops two floors above. And that data looks something like this. Now, I want to call your attention to five regions of this data. The first section is from when I started collecting … Read more
Position, velocity, and acceleration are all related. And you’ve seen the velocity is the derivative of position, and acceleration is the derivative of velocity. Before we jump into calculus, it’s important to get a feel for what acceleration really means. And one way to do that is to look at the units associate with each … Read more
In this typical problem, the vehicles position is given to you in terms of this nice algebraic expression, and the corresponding graph. And when you know the algebraic description of a function, like position, then there are all sorts of clever things you can do to calculate the derivative exactly. And by exact, I mean … Read more
Data often tells a story. And often, a good plot can really help reveal what that story is. Now I’d like to show you how I think about these position versus time graphs to figure out the story the data tells. Here, we have two axes. In this case, time is the horizontal X axis … Read more
Congratulations. In this lesson, you’ve seen how you can use trigonometry to deconstruct motion into x and y components. You’ll use this ability along with your knowledge of derivatives and integrals, in the final project for this course. In this project, you will be reconstructing the x, y trajectory of a vehicle using the raw … Read more
So let me demonstrate how to solve a problem like this. Here we have a vehicle with a heading of 65 degrees and the displacement of 17 meters. I’m going to show you how I would find out the “x” systematically and the first thing I’m going to do is draw the triangle. Here we … Read more
Remember our initial problem? Given the vehicles heading angle and the displacement, calculate delta x and delta y. Well, you can now solve that problem. But now, instead of thinking about a vehicle and a displacement, we can just think about a right triangle. And this let’s us change our problem statement to this. Given … Read more
At this point, you’ve calculated integrals of velocity data, acceleration data and angular velocity data. And hopefully, you’re building a good intuitive sense for what it means to take an integral. Now, I have a confession to make. Some of the real data I’ve been showing you has actually not been real. In fact, occasionally, … Read more
Welcome back students. It’s great to see you again. Today, we’re going to talk about odometry. Odometry sounds crazy, is the robot’s ability to integrate internal measurements, like it’s wheel rotation, other stuff, to figure out how far it’s gone. Before we do this, I want to make a human odometry experiment with you. Okay, … Read more
Let me do the same quiz again. Now we have two landmarks and the picture I’m giving you is a robot with three total positions. There’s a landmark here, and a landmark here, and say this landmark is being seen in these two positions, in these landmark, two poses, but landmark L_1 is not seen … Read more
The answer is, our initial constraint would touch this guy over here. The van to the second motion touches these things over here. The second to third, these guys, and then the landmark observation over here. Put something between x0 and the landmark, that sits here, here, here, here again and here. This observation over … Read more
I’m going to add one last thing here the initial robot location. If we define x_0 to be zero, which is the origin of the map then what this means is we add one over here and zero over here and the reason why is this constraint is that x_0 is zero. So let’s take … Read more
And here’s the answer. Obviously, X1 minus L0 is minus nine because L0 minus X1 is a measurement of plus nine. So let’s add this in. We had one over here on the main diagonal, one. We subtract one off the main diagonal just like before, simple pattern, and then the nine over here goes … Read more
Let me do another quiz. Supposing x_1, we see landmark L_0 at a distance of nine, this gives me a relative constraint between x_1 over here and landmark zero, which is over here. So just like before, these link two things together relatively, the x_1 and the L_0. Now this doesn’t look like a sub … Read more
So, here’s the answer. Let me just re-transform this as it’s done over here. X1 minus x2 is now plus four, and x2 minus x1 is minus four. So, I have to add plus one over here, minus one over there, plus one in this diagonal element over here, and minus one over here. Let … Read more
What we do is we make a matrix and also a vector. And we label the matrix, which is quadratic with all the poses and all the landmarks. Here we assume the landmarks are distinguishable and every time we make an observation, say between two poses, they become little additions locally in the four elements … Read more
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