4-7. Simultaneous Localization and Mapping

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

Let me take you about my favorite methods of all called Graph SLAM. This is one of many methods for SLAM, and this abundance by far the easiest to explain. Let’s assume we have a robot, and it’s called arbitrarily the initial location, x equals zero and y equals zero. For this example, we just … Read more

So now we’ll learn all about Linear Graph Slam, and that’s quite a bit. And it’s really simple. Every time there’s a constraint, initial position, motion or measurement, we take this constraint and add something to omega and C. What we add is the constraint itself, but it’s up multiplied by a strength factor, there … Read more

I’m going to give you a glimpse as to why it works. Suppose we have two roller positions x0 and x1 and we know that 10-apart with some Gaussian noise, we know that the Gaussian noise and exploitation moves thr rightward position 10-off the leftward position, but there is some uncertainty. When we talked about … Read more

So, I’m trying it out and see what happens. So, before it was minus 3, 2, 5, 7. Now, the first position is completely unchanged, and I’ll explain to you in a second why. The third one, went from five to 5.5, and the landmark went down from seven to 6.8. So graphically, this guy … Read more

He has a really tricky quiz. Let’s look at the forward motion again. Say I changed the last measurement from two down to one. You might remember the robot poses, we minus three, two and five. Before their modification, then my position was seven. But if one doesn’t really add up, a one suggests I … Read more

The last thing I can tell you before we go into programming is, why this makes any sense. Suppose you fill the matrix, which I call omega, and the vector, which will give the Greek name of xi. Then I can find the best solution for all the landmark position or the work position, by … Read more

And the correct answer is six for the following missing links. This guy here gives me two values in the matrix, this guy here another two and this link here is also missing. So it’s another two. So it’s six values missing. Let’s prove it to ourselves. Moving from x_0 to x_1 filter this area, … Read more

Hi students. I am back to teach you a bit about SLAM. There was a request, a popular request actually in email and discussion forum. So SLAM is a method for mapping. It’s short for simultaneous localization and mapping. And some of this might show up and the final exam, so do pay attention. Mapping … Read more