1. Planning Among Movable Obstacles with Artificial Constraints Presented by: Deborah Meduna and Michael Vitus by: Mike Stilman and James Kuffner

2. Motivation http://www.cs.cmu.edu/~mstilman/mov/WAFR06-Planning.avi

3. Outline Problem Definition Main Topics –TRANSIT –TRANSFER Algorithm Overview –Artificial Constraints –Obstacle Identification –Constraint Resolution Results

4. Problem Definition Separate configuration spaces for different obstacle locations Obstacle movement restricted to robot motion Motion planning restricted to the robot subspace

5. TRANSIT Moves the robot along a path while obstacles remain fixed Valid if and only if path is in the robot’s collision-free space

6. Moves the robot and ONE obstacle along a path to a new state Valid if and only if: –The robot and obstacle paths are in collision- free space –The robot and obstacle do not collide along the path TRANSFER

7. Problem Scope Monotone vs. Non-monotone –Monotone: each movable obstacle only needs to be moved once –Non-monotone: can be broken into multiple monotone plans Presented Planner is Linear-Monotone

8. Algorithm Overview (1) Plan a path through the cluttered environment –Allow translation through movable obstacles Determine the last obstacle that has to be moved

9. Algorithm Overview (2) Plan a path to Transfer the last obstacle and Transit the robot to the goal –Adds artificial constraints for earlier timesteps Resolve conflicts between movable obstacles and artificial constraints

10. Artificial Constraints Robot Transit operations create constraints on all obstacle configurations: –Robot motion along path sweeps volume V

11. Artificial Constraints Robot Transfer operations create constraints on non-moving obstacle configurations

12. Reverse Search - Motivation Assembly planning: –Much smaller branching factor due to actual constraints Movable obstacles: –Final configuration not pre-determined Must use forward search –Use reverse search for the ordering of which obstacles to move –Transfer of the last obstacle is performed first Adds artificial constraints

13. Obstacle Identification Identifies last obstacle to be manipulated prior to reaching the goal or sub-goal Utilize relaxed planner, P last, allowing paths through movable obstacles Select O L, last obstacle in collision with path

14. Constraint Resolution Plans a Transfer path for O L and the following Transit path to the goal The two paths form artificial constraints –No obstacles scheduled earlier in time than O L can be within the two swept volumes

16. Example Show movie from CMU http://www.cs.cmu.edu/~mstilman/mov/WAFR06-Execution.avi

17. Results Figures 1, 2 and 4 not solve- able by existing planners 1 2 4 3

18. Conclusions Future Work: –Include accessibility constraints –Incorporate heuristics for generating Transfer paths