The basic RRT explores the space by sampling and if the goal is connected to the tree, the solution is returned. Can you define retrieving the path as a graph search?
I would argue, that it is not graph search.
In the implementation, you keep all the nodes in a flat list and check which of the nodes is closest to the sampled point. As all nodes are checked, this might be seen as a brute-force graph search, but in the implementation is just for loop iterating though all the points in a list.
The goal check is done for the newly added points to the tree. It is checked if it is in the vicinity of the goal point. If yes, then the path is defined by going up the tree to the root. This is also not search, since the list is available in the form of pointers from the child nodes to the parent nodes.
Assuming RRT is done in two steps:
- Grow your tree from start state until one node is near enough to the goal state
- Output path from start state to goal state along tree
I'm assuming based on your question that you're asking if part 2 is a graph search?
Usually in RRT, each node has exactly one parent (since it's a tree) and you can just walk back from the end node to the start node by following the parents of each node. I guess that kind of qualifies as a graph search?
If each node has more than one parent (like in PRM) then you need to use a shortest path graph search algorithm to find the shortest path in your graph from the start state to end state