1. Rapidly Expanding Random Trees
David Johnson

2. RRT’s Promoted by Steve Lavalle and James Kuffner
Alternative to other randomized approaches
Probabilistic roadmap planner

3. Why another? Need to extend to PRM depends on connecting points
Non-holonomic (car)
Differential constraints (velocity, etc)
Actuator constraints
PRM depends on connecting points
May require a generalized nonlinear controller
slow
Solved over thousands of connections

4. RRT Components X = Configuration Space or more general
X = C-space + Velocity + Acceleration + ….

5. RRT Components

6. Basic RRT algorithm

7. Basic Extend

8. Example in holonomic empty space

9. Why “Rapidly Exploring”?
What is the probability that a vertex will be extended?
Proportional to the area of its Voronoi region
If just choose a vertex at random and extend, then it would act like random walk instead
Biased towards start vertex

10. Refinement vs. Expansion
If the random sample falls in …… These two modes of behavior are controlled by Voronoi bias only. We want to learn to control it.
refinement
expansion
Where will the random sample fall? How to control the behavior of RRT?

11. Determining the Boundary
in general, changing the boundary of the domain controls the two modes in some way
Expansion dominates
Balanced refinement and expansion
The tradeoff depends on the size of the bounding box

12. Extension to Non-holonomic
The new_state computation handles all the complicated part
Given a state x and inputs u
Integrate numerically to get new position
What input u do we use?
All
One
Heuristic

13. Problem Non-biased RRT explores in all directions
Not aimed at the goal
Use a small percentage of targets to be the goal or its neighborhood

14. How Far to Extend? Use distance measures from collision detection
Big steps when far away

15. Bi-directional Grow from start and goal Extend a tree
Try to connect nearest vertex of other tree to new vertex
Swap roles
Connecting trees can be difficult
Controls problem

16. Examples