1. PRM and Multi-Space Planning Problems : How to handle many motion planning queries? Jean-Claude Latombe Computer Science Department Stanford University 1 (based on discussions with Tim Bretl and Kris Hauser)

2. PRM Planning in Single Space  Applicable to robots with many dofs  In expansive configuration spaces: Probabilistically complete + fast convergence  But unable to detect that no solution exists  Cutoff on running time 2

3. 3 Convergence of a PRM Planner ??? What should be the cutoff time?

4. Planning in Multiple Spaces Example 1: Climbing Robot 4 4-contact move 3-contact move

5. 5 Climbing Robot Dilemma [Bretl, 2005]  Thousands of spaces  many PRM queries  Most queries have no solution  Running times for feasible queries are highly variable  Large time cutoff  Prohibitive time is wasted on infeasible queries  Small time cutoff  Critical queries might not be solved difficult queries or bad luck?

6. Other Examples  Navigation on irregular terrain [Hauser, 2008] 6

7. Other Examples  Dexterous manipulation 7

8. Other Examples  Mechanical assembly 8

9. Other Examples  Spatial re-arrangements of movable objects 9 [Stillman and Kuffner, 2007]

10.  Modular reconfigurable robots Other Examples [Yim]

11. Other Examples  Integration of task and motion planning 11 Change battery Go to toolbox Grasp screwdriver Go to old battery Unscrew screws Grasp old battery Ungrasp screwdriver Remove old battery

12. Basic Architecture High-level Planner (graph searching) Motion Planner (PRM) queryresult Many queries are infeasible  “climbing-robot” dilemma 12 Each query involves a distinct configuration space, with its own dimensionality, parameterization, and/or constraints.  queries cannot be processed using one single precomputed roadmap

13. Possible Approaches  Estimating query feasibility  Lazy PRM planning 13 High-level Planner (graph searching) Motion Planner (PRM) queryresult

14. Learning Transition Feasibility [Hauser, 2008]  Create a large dataset of labeled transitions  Train a classifier  : transition  {feasible, non-feasible}  Use classifier to select sequences of spaces with likely feasible transitions between them  But no work yet on learning feasibility of entire queries (that require connecting two transitions) 14 4 contacts 3 contacts Non-feasible if empty

15. Possible Approaches  Estimating query feasibility  Lazy PRM planning 15 High-level Planner (graph searching) Motion Planner (PRM) queryresult

16. Lazy PRM Planning [Bohlin & Kavraki, 2000; Sanchez-Ante, 2001]  Observation: PRM planning wastes much time testing that sampled configurations and connections are valid (e.g., free of collision).  Idea: Perform a computation only when there is enough evidence that it may be useful. 16

17. Lazy Collision Checking of Connections [Sanchez-Ante, 2001] 17 s g X

18. Lazy Collision Checking of Connections [Sanchez-Ante, 2001] 18 s g

19. Rationale  Configuration spaces are rarely chaotic: so, the connection between close valid configurations has high probability of being valid  Most of the time spent by a PRM planner is in testing connections  Most valid connections will not be part of the final solution  Testing connections is more expensive for valid connections than for invalid ones  Postpone testing a connection until the test is likely to be useful 19

20. Extending Lazy PRM Planning 20 Create a bag of fine-grain computational probes: Node sampling Node Connection

21. Extending Lazy PRM Planning 21  Sample a node and partially test if it is valid p1p1 p8p8 p7p7 p6p6 p5p5 p4p4 p3p3 p2p2 rd d > r+r’  p 1 = 1 d ≤ r+r’  p 1 ~ d/r+r’ r’

22. Extending Lazy PRM Planning 22  Create connection and partially test if it is valid p1p1 p8p8 p7p7 p6p6 p5p5 p4p4 p3p3 p2p2 p 12 p 23 p 24 p 45 p 38 p 46 p 47

23. Extending Lazy PRM Planning 23  Test further that a node is valid p1p1 p 12 p 23 p 24 p 45 p 38 p 46 p 47 p8p8 p7p7 p6p6 p5p5 p4’p4’ p3p3 p2p2

24. Extending Lazy PRM Planning 24  Test further that a connection is valid p1p1 p8p8 p7p7 p6p6 p5p5 p4’p4’ p3p3 p2p2 p 12 p 23 p 24 p 45 p 38 p 46 p 47 ’

25. Potential Advantages  More choices  opportunity for much smarter, more efficient strategies  More flexibility in distributing computation over several spaces, e.g., focus on queries that have the highest probability of being feasible  Compatibility with probabilistic modeling of uncertainty, e.g., probabilistic distribution of obstacles 25

26. Conclusion  We will have to live with imperfect motion planners like PRM planners  Important problems require handling many motion planning queries in distinct spaces  “climbing-robot” dilemma  Possible approaches to address this dilemma: —Fast and reliable evaluation of query feasibility (e.g., using trained classifiers) —Extended lazy PRM planning 26

27. 27

28. Narrow Passages  I don’t think they are the main issue in PRM planning.  They are unlikely to occur by chance.  Intentionally creating complex narrow passages is not easy. 28 Alpha puzzle