# Rapid Exploring Random Trees

* Add start node to tree 
* Repeat n times
  * Generate a random configuration, x
  * If x is in freespace using the CollisionCheck function
    * Find y, the closest node in the tree to the random configuration 
    * If \(Dist \(x, y\) > delta\) – Check if x is too far from y 
      * Find a configuration, z, that is along the path from x to y such that Dist\(z,y\) <= delta 
      * x = z; 
    * If \(LocalPlanner \(x,y\)\) – Check if you can get from x to y Add x to the tree with y as its parent

![Alt text](../../../../.gitbook/assets/1546201707049.png)

* While not done
  * Extend Tree A by adding a new node, x 
  * Find the closest node in Tree B to x, y 
  * If \(LocalPlanner\(x,y\)\) – Check if you can bridge the 2 trees
    * Add edge between x and y. 
    * This completes a route between the root of Tree A and the root of Tree B. Return this route - --
  * Else 
    * Swap Tree A and Tree B
    * ![Alt text](../../../../.gitbook/assets/1546201717793.png)