1. Probabilistic Roadmap
Hadi Moradi

2. Overview What is PRM? What are previous approaches?
What’s the algorithm?
Examples

3. What is it?
A planning method which computes collision-free paths for robots of virtually any type moving among stationary obstacles

4. Problems before PRMs Hard to plan for many dof robots
Computation complexity for high-dimensional configuration spaces would grow exponentially
Potential fields run into local minima
Complete, general purpose algorithms are at best exponential and have not been implemented

5. Weaker Completeness Complete planner  Heuristic planner 
Probabilistic completeness:

6. Motivation
Geometric complexity
Space dimensionality

7. Example a a x x PR manipulator Cylinder 360 270 180 90 0.25 0.5 0.75x
0.25
0.5
0.75
1.0
PR manipulator
Cylinder

8. Example: Random points
360
270
180 a 90 a x x
0.25
0.5
0.75
1.0
PR manipulator
Cylinder

9. Random points in collision
360
270
180 a 90 a x x
0.25
0.5
0.75
1.0
PR manipulator
Cylinder

10. Connecting Collision-free Random points
360
270
180 a 90 a x x
0.25
0.5
0.75
1.0
PR manipulator
Cylinder

11. Probabilistic Roadmap (PRM)
local path
free space
milestone mb mg
[Kavraki, Svetska, Latombe,Overmars, 95]

12. The Principles of PRM Planning
Checking sampled configurations and connections between samples for collision can be done efficiently.
A relatively small number of milestones and local paths are sufficient to capture the connectivity of the free space.

13. The Learning Phase
Construct a probabilistic roadmap

14. The Query Phase
Find a path from the start and goal configurations to two nodes of the roadmap

20. The Query Phase
Need to find a path between an arbitrary start and goal configuration, using the roadmap constructed in the learning phase.

24. What if we fail? Maybe the roadmap was not adequate.
Could spend more time in the Learning Phase
Could do another Learning Phase and reuse R constructed in the first Learning Phase.

25. Example – Results
This is a fixed-based articulated robot with 7 revolute degrees of freedom.
Each configuration is tested with a set of 30 goals with different learning times.

26. Results
With expansion
Without expansion

27. Issues Why random sampling? Smart sampling strategies
Final path smoothing

28. Issues: Connectivity
Bad
Good

29. Disadvantages
Spends a lot of time planning paths that will never get used
Heavily reliant on fast collision checking
An attempt to solve these is made with Lazy PRMs
Tries to minimize collision checks
Tries to reuse information gathered by queries

30. References
Kavraki, Svestka, Latombe, Overmars, IEEE Transactions on Robotics and Automation, Vol. 12, No. 4, Aug. 1996