Creating High-quality Roadmaps for Motion Planning in Virtual

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 • Office • House • Quake

Experimental Results • Field Graph statistics resolution technique 94 x 94 RRM* RRM Path statistics time (s) |V| |E| SPF avg query (ms) 0. 75 0. 91 29 43 18 47 1. 570 1. 137 4. 3 2. 3 RRM* RRRM

Experimental Results • Field Clearance time min RRM* RRRM avg max s 0. 03 0. 34 2. 71 3. 08 6. 44 6. 46 24 RRM* RRRM

Experimental Results • Office Graph statistics resolution technique 130 x 80 RRM* RRM Path statistics time (s) |V| |E| SPF avg query (ms) 1. 10 2. 70 154 167 147 180 1. 812 1. 181 3. 8 3. 6 RRM* RRRM

Experimental Results • Office Clearance time min RRM* RRRM avg max s 0. 00 0. 01 1. 60 1. 77 6. 82 7. 53 320 RRM* RRRM

Experimental Results • House Graph statistics resolution technique 57 x 20 x 40 RRM* RRM Path statistics time (s) |V| |E| SPF avg query (ms) 11. 67 18. 68 34 34 33 34 1. 225 1. 224 8. 2 RRM* RRRM

Experimental Results • House Clearance time min RRM* RRRM avg max s 0. 00 0. 13 2. 17 3. 33 5. 64 10. 41 49 RRM* RRRM

Experimental Results • Quake Graph statistics resolution technique 57 x 20 x 40 RRM* RRM Path statistics time (s) |V| |E| SPF avg query (ms) 306. 44 384. 90 71 132 65 216 2. 068 1. 194 27. 1 41. 5 RRM* RRRM

Experimental Results • Quake Clearance time min RRM* RRRM avg max s 0. 00 0. 05 2. 90 3. 28 9. 45 9. 75 343 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