4-8. Optional: Vehicle Motion and Calculus

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