Creating High-quality Roadmaps for Motion Planning in Virtual Environments

Roland Geraerts and Mark OvermarsIROS 2006

Requirements• The roadmap

– is resolution complete– is small– contains useful cycles– provides high-clearance paths

res. complete, small useful cycles high-clearance paths

Outline• Reachability Roadmap Method (RRM)

– Resolution complete roadmap– Small roadmap

• Adding useful cycles• Adding clearance to the roadmap• Experiments• Conclusions & current work

RRM – Criteria• 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 Method• Paper

– R. Geraerts and M.H. Overmars. Creating small roadmaps for solving motion planning problems. MMAR 2005, pp. 531-536

• Outline of algorithm– Discretizes the free space– Computes small set of guards – Guards are connected via connector– Resulting roadmap is pruned

Adding Useful Cycles• Paper

– D. Nieuwenhuisen and M.H. Overmars. Useful cycles in probabilistic roadmap graphs. ICRA 2004, pp. 446-452

• Useful edge– Edge (v,v’) is K-useful if K * d(v,v’) < G(v,v’)

v’ v

Adding Useful Cycles• Useful node

– Node v is useful if there is an obstacle inside the cycle being formed

v’

v’’

v

Adding Useful Cycles• Algorithm

– Create RRM roadmap– Add useful nodes– Create a queue with all collision-free edges

• Queue is sorted on increasing edge length

– Add edge from the queue to the graph if edge is K-useful

RRM useful nodes final roadmap

Providing High-clearance Paths

• Paper– R. Geraerts and M.H. Overmars. Clearance based path

optimization for motion planning. ICRA 2004, pp. 531-536

• Retract edges to the medial axis– Retraction of a sample

d

d

Providing High-clearance Paths

• Paper– R. Geraerts and M.H. Overmars. Clearance based path

optimization for motion planning. ICRA 2004, pp. 531-536

• Retract edges to the medial axis– Retraction of an edge

Experimental Setup• Field

• House

• Office

• Quake

Experimental Results• Field

Graph statistics Path statisticsresolution technique time (s) |V| |E| SPF avg query

(ms) 94 x 94 RRM

RRM*0.750.91

2943

1847

1.5701.137

4.32.3

RRM RRM* RRRM

Experimental Results• Field

Clearance timemin avg max s

RRM*RRRM

0.030.34

2.713.08

6.446.46 24

RRM RRM* RRRM

Experimental Results• Office

Graph statistics Path statisticsresolution technique time (s) |V| |E| SPF avg query

(ms)130x80 RRM

RRM*1.102.70

154167

147180

1.8121.181

3.83.6

RRM RRM* RRRM

Experimental Results• Office

Clearance timemin avg max s

RRM*RRRM

0.000.01

1.601.77

6.827.53 320

RRM RRM* RRRM

Experimental Results• House

Graph statistics Path statisticsresolution technique time (s) |V| |E| SPF avg query

(ms)57 x 20 x40 RRM

RRM*11.6718.68

3434

3334

1.2251.224

8.28.2

RRM RRM* RRRM

Experimental Results• House

Clearance timemin avg max s

RRM*RRRM

0.000.13

2.173.33

5.6410.41 49

RRM RRM* RRRM

Experimental Results• Quake

Graph statistics Path statisticsresolution technique time (s) |V| |E| SPF avg query

(ms)57 x 20 x40 RRM

RRM*306.44384.90

71132

65216

2.0681.194

27.141.5

RRM RRM* RRRM

Experimental Results• Quake

Clearance timemin avg max s

RRM*RRRM

0.000.05

2.903.28

9.459.75 343

RRM RRM* RRRM

Conclusions• High-quality roadmap

– resolution complete– small– short and alternative paths– high-clearance paths– fast query times

Future Work• Corridor Map Method

– Creating high-quality paths within 1 ms• Paths are smooth, short or have large clearance

– Method is flexible• Paths avoid dynamic obstacles

Future Work• Corridor Map Method

– Creating high-quality paths within 1 ms• Paths are smooth, short or have large clearance

– Method is flexible• Paths avoid dynamic obstacles

Smooth path Short path Path avoiding obstacles