Creating Small Roadmaps for Solving Motion Planning Problems

Roland Geraerts and Mark Overmars

MMAR 2005

Introduction

• Related work

• Reachability roadmap

• Experiments

• Conclusions & current work

Related Work – Probabilistic Roadmap Method

• Construction phaseForbidden spaceFree space

Sample

c

Colliding path

c

c’

c

Local path

c’c’c

c

Related Work – Probabilistic Roadmap Method

• Query phaseForbidden spaceFree space

Sample

Start / goalLocal path

Shortest path

Related Work – Visibility Based Roadmap

Forbidden spaceFree space

Connector sampleGuard sample

Local pathStart / goalShortest path

Related Work – Shortcomings

• PRM– Path not always found

– Large roadmap

• Visibility PRM– Path not always found

– Slower

239 nodes, 0.3 seconds 51 nodes, 17 seconds39 nodes, 0.15 seconds 39 nodes, 0.15 seconds

Reachability

• Coverage– Each free sample can be

connected to a vertex in the graph

• Maximal connectivity– For each two vertices v’,v’’:

• If there exists a path between v’ and v’’ in the free space, then there exists a path between v’ and v’’ in the graph

Reachability Roadmap

• Coverage

• Maximal connectivity

• Roadmap pruning

RR – Coverage

• Art gallery problem is NP-hard

• Calculate set of candidate guards

• Computation of reachability regionsdiscretize space medial axis transf. distance transform overlay candidate guards

RR – Maximal Connectivity

• Calculate connector for each pair of nodes whose reachability areas overlap

RR – Pruning

• Steiner problem is NP-complete– Input: set of guards, set of connectors,

all feasible connections between them

– Output: shortest roadmap that spans the guards

• Graph operations

initial roadmap Steiner tree all connections MST

Experimental Setup

• Test environments

Grid Rotated grid Manipulator

Village

Experimental Results

• Gridresolution technique time (s) |N| |E| |G|

80 x 80

RR

PRM

vis-PRM

0.33

0.74

20.49

13

158

31

12

157

30

88

638

381

Experimental Results

• Rotated gridresolution technique time (s) |N| |E| |G|

200 x 200

RR

PRM

vis-PRM

7

16

>3600

249

5889

n.a.

248

5887

n.a.

388

2328

n.a.

Experimental Results

• Manipulatorresolution technique time (s) |N| |E| |G|

60 x 60 x 60

RR

PRM

vis-PRM

11

86

>3600

313

11095

n.a.

306

11091

n.a.

388

2306

n.a.

Experimental Results

• Villageresolution technique time (s) |N| |E| |G|

180x22x60

RR

PRM

vis-PRM

556

>3600

>3600

176

n.a.

n.a.

142

n.a.

n.a.

1268

n.a.

n.a.

Conclusions

• New algorithm for creating roadmaps– Roadmap is small– Roadmap is resolution complete– Efficient for 2D and 3D problems

• Roadmap of RR is much smaller than the roadmap created by the PRM

• Vis-PRM creates small roadmaps, but takes much time to terminate

Current Work

• Roadmap with high clearance

Reachability roadmap Retracted roadmap

Current Work

• Roadmap with high clearance

Reachability roadmap Retracted roadmap

Current Work

• Roadmap with high clearance– Technique for adding clearance also works for

articulated robots

Start and goal Initial path High-clearance path