creating high-quality roadmaps for motion planning in virtual environments roland geraerts and mark...
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Creating High-quality Roadmaps for Motion Planning in Virtual Environments
Roland Geraerts and Mark Overmars
IROS 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 statistics
resolution technique time (s) |V| |E| SPF avg query (ms)
94 x 94 RRMRRM*
0.750.91
2943
1847
1.5701.137
4.32.3
RRM RRM* RRRM
Experimental Results
• Field
Clearance time
min avg max s
RRM*RRRM
0.030.34
2.713.08
6.446.46 24
RRM RRM* RRRM
Experimental Results
• Office
Graph statistics Path statistics
resolution technique time (s) |V| |E| SPF avg query (ms)
130x80 RRMRRM*
1.102.70
154167
147180
1.8121.181
3.83.6
RRM RRM* RRRM
Experimental Results
• Office
Clearance time
min avg max s
RRM*RRRM
0.000.01
1.601.77
6.827.53 320
RRM RRM* RRRM
Experimental Results
• House
Graph statistics Path statistics
resolution technique time (s) |V| |E| SPF avg query (ms)
57 x 20 x40 RRMRRM*
11.6718.68
3434
3334
1.2251.224
8.28.2
RRM RRM* RRRM
Experimental Results
• House
Clearance time
min avg max s
RRM*RRRM
0.000.13
2.173.33
5.6410.41 49
RRM RRM* RRRM
Experimental Results
• Quake
Graph statistics Path statistics
resolution technique time (s) |V| |E| SPF avg query (ms)
57 x 20 x40 RRMRRM*
306.44384.90
71132
65216
2.0681.194
27.141.5
RRM RRM* RRRM
Experimental Results
• Quake
Clearance time
min 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