Suppose there is a grid like in the image.
##The robot can't cross the red nodes.

At start the robot will be placed on "A". Then it should solve the grid and reach to "B"
##The robot can't cross the red nodes.

Then the robot will be placed again on "A" and it should navigate to "B" using the shortest path.

(I drew "red" nodes just to be seen clearly that does not matter which color the node is)

What are the methods and algorithms that can be used for an application like this.
I did a little research and a lot of results came up for grid solving but not all of them can be implemented on arduino.
Thanks in advance.

I can't see your picture. When I view page source on your post, and find the link to your picture, I get a 403 error.

Did you watch the you tube video? Did you see what the robot did at every intersection?

When it had found a path to the target, it was able to replay the path, because it kept track of the intersections, and which way it needed to go at the intersection. Think about how you give people directions to your house. "At the third light, turn right. Make the 4th left..."

PaulS:
I can't see your picture. When I view page source on your post, and find the link to your picture, I get a 403 error.

Did you watch the you tube video? Did you see what the robot did at every intersection?

When it had found a path to the target, it was able to replay the path, because it kept track of the intersections, and which way it needed to go at the intersection. Think about how you give people directions to your house. "At the third light, turn right. Make the 4th left..."

Oh don't you see the image? Anyway it is just as the grid in the video.
Yeah I saw the robot in the video.

But what I need is more information.
There is the Left hand method and the right hand method for solving the grid. That is the only two methods I know. What I need to know is if there is more methods to solve the grid.
And algorithms for calculating the shortest path.