# How can I calculate the shortest path between two 2d vector points in an environment with obstacles?

I have a 2D plane, with a fixed height and width of 10M. The plane has an agent (or robot) in the point $$(1, 2.2)$$, and an electric outlet in the point $$(8.2, 9.1)$$. The plane has a series of obstacles.

Is there an algorithm to find the shortest path between the agent and the goal?

And if the point has a fixed wingspan? For example, that the space between O and N is smaller than the agent, and then the agent cannot cross?

## 1 Answer

The usual way to solve this kind of problem is to construct a configuration space: extruding all the polygonal obstacles by sliding the polygon corresponding to the robot around them (some slides).

The exterior vertices of the configuration space can then be used as input to a path-planning algorithm, such as A*.