2. Probabilistic Roadmaps for Path Planning in High-Dimensional Configuration Spaces Kavraki, Svestka, Latombe, Overmars 1996 Presented by Dongkyu, Choi On the day of 16 th April 2003 CS326a: Motion Planning, Spring 2002-03Prof. Jean-Claude Latombe

3. Background Path Planning for Robots in known and static workspaces Fast heuristic planners for few-dof case Efficient heuristic planners for many-dof case?

4. Background (cont’d) Complete path planning in high-dimensional C-spaces is too complex Boost performance by sacrificing the completeness

5. Probabilistic Roadmaps: Introduction Efficiency-driven Robots with many dofs (high-dim C-spaces) Static environments Probabilistic techniques to incrementally build a roadmap in C f space of holonomic robot s g s ~ g ~

6. Probabilistic Roadmaps: General Method Learning Phase –Construction Step –Expansion Step Query Phase

7. Learning Phase: Procedure Construction Step –Start with empty R=(N,E) –Generate a random free config c and add to N –Choose a subset N c of candidate neighbors around c from N –Try to connect c to each of selected nodes* in N c in the order of increasing distance from c (w/ local planner) * Select only the nodes not graph-connected to c –Add the edge found to E –Repeat the above until satisfied

8. Learning Phase: Procedure (cont’d) Local Planner –Need to be both ‘deterministic’ and very ‘fast’ for best results Deterministic LP: eliminates the need to store local paths Fast LP: ensures quasi-instantaneous planning queries

9. Learning Phase: Procedure (cont’d) Expansion Step –Find the nodes in ‘difficult’ regions using heuristic weight function w(c) –Expand c using random-bounce walks –Repeat as necessary

10. Learning Phase: Procedure (cont’d) Heuristic Weight Function –Several options to define w(c) Inversely proportional to the ‘number of nodes within some predefined distance from c’ Inversely proportional to the ‘distance from c to the nearest connected component not containing c’ Proportional to the ‘failure ratio of the local planner’

11. Learning Phase: Procedure (cont’d) Random-Bounce Walks –Pick a random direction of motion in C-space –Move in the direction until an obstacle is hit –Choose a new random direction when hit –Repeat until the path can be connected to another node –Store the final config n and the edge (c,n) in R –Store the computed path (non-deterministic) –Record that n belongs to the same connected component as c

12. Learning Phase: Illustrated Example Construction Step Efficiency-driven Robots with many dofs (high-dim C-spaces) Static environments Collision !

13. Learning Phase: Illustrated Example (cont’d) Expansion Step Efficiency-driven Robots with many dofs (high-dim C-spaces) Static environments 0.33 1.00 0.25 0.50 0.33 0.50 0.25 0.33 0.50 1.00 0.50 1.00 0.50 1.00 0.33 0.50 Efficiency-driven Robots with many dofs (high-dim C-spaces) Static environments

14. Query Phase: Procedure Given the start and goal config s and g, calculate feasible paths P s and P g to the nodes s and g on the roadmap (w/ LP) Recalculate the path P from s to g using the roadmap Return the total path: P s – P – P g -1 ~~ ~~

15. Probabilistic Roadmaps: Implementation General or Customized Implementations Experiments with 7-dof fixed- and free-based robots 100% success when given enough learning time Reasonable results when given shorter learning time Queries faster than Randomized Path Planner Learning+Query slower than RPP in many cases

16. Probabilistic Roadmaps: Challenges Obstacles added/removed Obstacles moving along known trajectories