Grid Cell

Each cell of this grid, each box in this grid, would represent an outcome.

Otherwise, if our grid cell is navigable at all,

To do so, let's give the grid cell names.

Let's make this grid cell red over here as well.

As you can see, each grid cell now has a label.

Suppose x is my grid cell and Z is my measurement.

Instead of assigning this just to the grid cell, in the algorithm called hybrid A , it memorizes the exact x prime, y prime, and theta prime and associates it with this grid cell over here the first time the grid cell is expanded.

I first check if the grid cell I'm considering is the goal.

And it has to be an action that action navigable grid cell.

I'm going to ask you given that you traversing from grid cell to grid cell costs you 1, or 1 using the definition of the MDP lecture before.

So suppose we had a grid cell, and we attempt to go north.

That product gave us the non normalized posterior distribution for the grid cell.

No matter what grid cell we consider, the p(Z) is the same.

And place cells also get this kind of path integration input from a kind of cell called a grid cell.

In the inner loop, I now iterate over all elements in my grid cell.

If I change this, for example, by opening up this grid cell over here.

Now I go through each grid cell and for each cell, I collect possible cells that the robot might have come from.

I would expect at the ith grid cell over here from this list over there.

The answer as it turns out will be just 0.2 everywhere, and the reason is with every grid cell being equally likely, applying this motion model will still make each grid cell equally likely.

If there was our grid cells over here and we asked one time step later about a specific grid cell over here, we would combine 0.8 from over here, 0.1 from over here, and 0.1 from over here into the probability of this grid cell.

Scrolling down further, if we arrived at a valid grid cell in that it's still inside the grid and it's not an obstacle, then like before we add to the value the value of this new grid cell plus the cost of the corresponding action.

The easiest way to understand what's going on is to realize that this is a function here that assigns to each grid cell a number, and the p(Z) doesn't have the grid cell as an index.

Grid

Grid

Grid

Grid

A value function associates to each grid cell the length of the shortest path to the goal.

One is move in which the car just goes 1 grid cell forward in its present orientation.

But nevertheless, our paths that come out are nice, smooth, and curved paths, and every time we expand a grid cell we memorize explicitly the continuous values of x prime, y prime, and theta with this grid cell.

Suppose we have 5 grid cells as before with an initial distribution that assigns 1 to the first grid cell and 0 to all the other ones.

In my software, this means the robot has to stay inside the grid, and the grid cell has to be unoccupied, which is this test over here.

So, the probability of seeing red at the red grid cell is 0.8, and the probability of seeing green at the green cell is also 0.8.

I write it superscript so there is no confusion with the index i, which is the grid cell.

Ʃp(xi)log p(xi) as the expected log (logarithmic) likelihood of the probability of each grid cell.

If x2 falls into the grid and y2 falls into the grid and x2, y2 is not yet checked, which is tested by this field called closed, and the grid cell is navigable there is no obstacle here.

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