Using an Android phone to get the shortest path to a robot

Hi guys.
So my project in a nutshell is a robot that goes to an area by travelling a shortest path. Of cause there's more than that. But not ready to give out cause I'm building this as a new invention for science fair in school.
Think of a imaginary uneven shape. This is marked on a map. What my robot needs to do is find the point in the border of the shape and navigate itself to it. Land is a bare land. So the path should be a straight line.
So I'm here to ask you professionals how can I get the approch to this? Where should I start? What is the best way to do this? How can I do this with an Android phone?

If the robot is outdoors, use GPS to locate it, and these algorithms to navigate.

How will the robot know about the map with the "uneven shape" marked on it?

Hello sir,
For starters lets forget about the uneven shape.
Let's think of one point.

OK, how will the robot know about the map with the point marked on it?

Have you gone through the material in the link posted in reply #1?