1. Roland Geraerts and Mark Overmars ICRA 2007 The Corridor Map Method: Real-Time High-Quality Path Planning

2. Previous work Potential field planners –Flexible –Slow / local minima Probabilistic Roadmap Methods –Fast –Ugly paths –Output: fixed paths in response to a query Predictable motions Lacks flexibility when environment changes

3. Our planner Requirements –High-quality paths –Flexible –Extremely fast Current limitations –The robot is modeled by a disc –Experiments with only 2D problems

4. The Corridor Map Method Construction phase (off-line) –Create a system of collision-free corridors for the static obstacles GraphCorridor map: graph + clearance

5. The Corridor Map Method Query phase (on-line) –Extract corridor for given start and goal –Extract path by following attraction point Corridor: backbone path + clearance QueryPath

6. The Corridor Map Method Attraction point α(x) –Robot’s location: x –Robot’s goal: g –Radius circle: r –Euclidean distance: d Path is obtained by integration over time while updating the velocity, position, and attraction point of the robot For other behavior: locally adjust robot’s path by adding forces α(x) x g r d

7. Avoiding obstacles Adding forces –For each obstacle, add repulsive force to the robot Creating a sub-corridor –For each obstacle, move backbone path locally and recompute clearance info

8. Creating shorter paths Attraction point α(x) corresponds to point B[t] on the backbone path Add additional valid attraction point α(x, Δt), corresponding to point B[t + Δt] Valid means: x can see point B[t + Δt] α(x, 0.00)α(x, 0.05)α(x, 0.10)α(x, 0.25)

9. Experimental setup Single path planning system Created in Visual C++, Windows XP 2.66 GHz P4 processor, 1 GB memory Each experiment was run 100 times Statistics: running time of query phase, CPU load Input graphs created using –“ Creating High-quality Roadmaps for Motion Planning in Virtual Environments “- IROS 2006 –Environments were discretized: 100x100 cells

10. Experimental setup MazeField 1.6 seconds20 seconds

11. Experiments – Smooth paths Maze Query time:2.41 ms CPU load: 0.026% Field Query time:0.84 ms CPU load: 0.029%

12. Experiments – Obstacles Maze: adding forces Query time:7.0—9.0 ms CPU load: 0.05—0.06% Maze: sub-corridor Query time:3.0—13.6 ms CPU load:0.025—0.10%

13. Experiments – Obstacles Maze

14. Experiments – Obstacles Field: adding forces Query time:2.0—2.3 ms CPU load: 0.05—0.05% Field: sub-corridor Query time:1.0—7.0 ms CPU load:0.03—0.16%

15. Experiments – Obstacles Field

16. Experiments – Short paths Maze: Δt = 0 Query time:2.41 ms CPU load: 0.026% Maze: Δt = 0.2 Query time:9.64 ms CPU load: 0.104%

17. Experiments – Short paths Maze

18. Experiments – Short paths Field: Δt = 0 Query time:0.84 ms CPU load: 0.029% Field: Δt = 0.2 Query time:3.36 ms CPU load: 0.116%

19. Experiments – Short paths Field

20. Conclusions The CMM produces high-quality paths –Natural paths: smooth, short / large clearance The CMM is flexible –Paths are locally adjustable The CMM is fast –CPU load < 0.1%

21. Future work Extend experiments with 2½D / 3D problems Study applications –Planning of a group –Steering a camera –Alternative routes –Tactical planning