1

PRM and Multi-Space Planning Problems:

How to handle many motion planning queries?

Jean-Claude LatombeComputer Science Department

Stanford University

(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

3

Convergence of a PRM Planner

???What should be the cutoff time?

4

Planning in Multiple Spaces

Example 1: Climbing Robot

4-contact move

3-contact move

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 queriesor bad luck?

6

Other Examples Navigation on irregular terrain [Hauser,

2008]

7

Other Examples Dexterous manipulation

8

Other Examples Mechanical assembly

9

Other Examples Spatial re-arrangements of movable

objects

[Stillman and Kuffner, 2007]

Modular reconfigurable robotsOther Examples

[Yim]

11

Other Examples Integration of task and motion planning

Change battery

Go to toolboxGrasp screwdriver

Go to old batteryUnscrew screws

Grasp old batteryUngrasp screwdriver

Remove old battery

12

Basic Architecture

High-level Planner

(graph searching)

Motion Planner(PRM)

query resultMany queries are infeasible “climbing-robot” dilemma

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

High-level Planner

(graph searching)

Motion Planner(PRM)

query result

Learning Transition Feasibility[Hauser, 2008] Create a large dataset of labeled transitions

Train a classifier Q : 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

High-level Planner

(graph searching)

Motion Planner(PRM)

query result

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.

17

Lazy Collision Checking of Connections [Sanchez-Ante, 2001]

sg

X

18

Lazy Collision Checking of Connections [Sanchez-Ante, 2001]

sg

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

Create a bag of fine-grain computational probes:

Nodesampling

NodeConnection

21

Extending Lazy PRM Planning

Sample a node and partially test if it is valid

p1 p8

p7p6p5

p4

p3p2

r d d > r+r’ p1 = 1d ≤ r+r’ p1 ~ d/r+r’

r’

22

Extending Lazy PRM Planning

Create connection and partially test if it is valid

p1 p8

p7p6p5

p4

p3p2

p12

p23

p24

p45

p38

p46

p47

23

Extending Lazy PRM Planning

Test further that a node is valid

p1 p12

p23

p24

p45

p38

p46

p47

p8

p7p6p5

p4’

p3p2

24

Extending Lazy PRM Planning

Test further that a connection is valid

p1 p8

p7p6p5

p4’

p3p2

p12

p23

p24

p45

p38

p46

p47’

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

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

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.

Alpha puzzle