1. CG-UFRGS Real-Time Multi-Agent Path Planning on Arbitrary Surfaces Rafael P. Torchelsen 1, Luiz F. Scheidegger 1, Guilherme N. Oliveira 1, Rui Bastos 2, João L. D. Comba 1 1 Instituto de Informática - PPGC, UFRGS - Brazil 2 NVIDIA Corporation

2. CG-UFRGS Obstacle Real-Time Multi-Agent Path Planning on Arbitrary Surfaces 2 Goal Agent Obstacle Shortest free path

3. CG-UFRGS Related Work 3 Planar Surfaces 123 1)Avneesh Sud, Erik Andersen, Sean Curtis, Ming Lin, and Dinesh Manocha. Real-time Path Planning in Dynamic Virtual Environments Using Multi-agent Navigation Graphs. IEEE TVCG 2008 2)S. J. Guy, J. Chhugani, C. Kim, N. Satish, M. Lin, D. Manocha, and P. Dubey. ClearPath: Highly Parallel Collision Avoidance for Multi-Agent Simulation. ACM SIGGRAPH/Eurographics Symposium on Computer Animation 2009 3)Avneesh Sud, Russell Gayle, Erik Andersen, Stephen Guy, Ming Lin, and Dinesh Manocha Real-time Navigation of Independent Agents Using Adaptive Roadmaps. ACM Symposium on Virtual Reality Software and Technology 2007

4. CG-UFRGS Related Work 4 Again: Planar Surfaces Command and Conquer™ Distance computation is cheap Euclidian Distance: The mesh isn't considered on the distance computation

5. CG-UFRGS Contributions Multi-agent navigation on non-planar surfaces Multi-resolution distance computation GPU-based approach for collision avoidance CPU/GPU path planning pipeline 5

6. CG-UFRGS Outline Related Work Background Global Navigation – Hierarchical Computation of Distances Local Navigation – Collision Grid – Finding an Unobstructed Direction Results Discussion Conclusion 6

7. CG-UFRGS Background Global Navigation Local Navigation 7 Obstacle Goal Agent Obstacle

8. CG-UFRGS Global Navigation 8 Several fields are need per frame Constant FPS Incremental Computation Fast Initial Movement Incremental Resolution Performance Parallel Computation Rafael P. Torchelsen, Francisco Pinto, Rui Bastos and João L. D. Comba. Approximate on-Surface Distance Computation using Quasi-Developable Charts. Computer Graphics Forum v. 28 (Pacific Graphics 2009)

9. CG-UFRGS Hierarchical Computation of Distances 9 Rendering Distance Field Computation Distance Field Computation Distance Field Computation Distance Field Computation Distance Field Computation Distance Field Computation N Threads f4r3f4r3 f1r1f1r1 A1A1 AmAm M Agents A2A2 A3A3 A4A4... Path Planning... f4r2f4r2 f3r3f3r3 f2r1f2r1 f2r2f2r2 f3r2f3r2 f3r1f3r1 M Threads CPU GPU Available f4r3f4r3 f1r1f1r1 f4r2f4r2 f3r3f3r3 f2r1f2r1 f2r2f2r2 f3r2f3r2 f3r1f3r1 Distance Fields Destination Resolution To be Processed FdrrFdrrr Not Ready fdrrfdrrr Ready fdrrfdrrr First... FdrrFdrrr Last Collision Grid Distance Fields Destination Resolution Distance Field Slot

10. CG-UFRGS Outline Related Work Background Global Navigation – Hierarchical Computation of Distances Local Navigation – Collision Grid – Finding an Unobstructed Direction Results Discussion Conclusion 10

11. CG-UFRGS Collision Grid 11 A1A1 AmAm M Agents A2A2 A3A3 A4A4... Collision Grid Advantage 1 Agent 1 Cell Minimal Concurrent Access Static Data Structure Regular GPU-Friendly Advantage 1 Agent 1 Cell Minimal Concurrent Access Static Data Structure Regular GPU-Friendly

12. CG-UFRGS 3-D Collision Grid: Advantage 12 A2A2 A2A2 A1A1 A1A1 A3A3 A3A3 Obstacle

13. CG-UFRGS Collision Test 13 A1A1 A1A1 ? p1p1 ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? r CP 1 CP 2 ? CP 3 CP 4 CP 5 CP 6 CP 0 CP 7 ? Cell checked for collision r Distance between collision check points AnAn Agent pnpn Agent destination Path taken Collision test radius around CP CP n Collision check point along the path

14. CG-UFRGS Collision Avoidance 14 A1A1 A1A1 p1p1 A3A3 A3A3 A2A2 A2A2 +α+α -α-α +2α -2α +β+β -β-β

15. CG-UFRGS Rotating the Gradient 15 0º 15º 45º 80º 90º 120º Rotation A1A1 A1A1 Goal A1A1 A1A1

16. CG-UFRGS Finding a Free Route ????? ????? ??????? ??????? ??????? ????? ????? p1p1 A2A2 A2A2 A1A1 A1A1 ????? ????? ?????? ?????? ?????? ????? ????? A2A2 A2A2 p1p1 A1A1 A1A1 ????? ????? ????? ????? ????? ?????? ?????? ????? ????? ????? A2A2 A2A2 p1p1 A1A1 A1A1 ????? ???????? ???????? ???????? ???????? ????? A2A2 A2A2 A1A1 A1A1 p1p1

17. CG-UFRGS Outline Related Work Background Global Navigation – Hierarchical Computation of Distances Local Navigation – Collision Grid – Finding an Unobstructed Direction Results Discussion Conclusion 17

18. CG-UFRGS Results 18 Tris: 20 000 Verts: 10 000 FPS: 30 Agents: 512 Grid Res: 128 3 Tris: 20 000 Verts: 10 000 FPS: 30 Agents: 512 Grid Res: 128 3 The agent color indicates the goal it is after After the agent reaches a goal it moves to another The agent color indicates the goal it is after After the agent reaches a goal it moves to another

19. CG-UFRGS 19 Tris: 10 000 Verts: 5 000 FPS: 30 Agents: 512 Grid Res: 128 3 Tris: 10 000 Verts: 5 000 FPS: 30 Agents: 512 Grid Res: 128 3 The agent color indicates the goal it is after After the agent reaches a goal it moves to another The agent color indicates the goal it is after After the agent reaches a goal it moves to another Results

20. CG-UFRGS Performance 20

21. CG-UFRGS Outline Related Work Background Global Navigation – Hierarchical Computation of Distances Local Navigation – Collision Grid – Finding an Unobstructed Direction Results Discussion Conclusion 21

22. CG-UFRGS Discussion Non Collision Free – First step towards the solution Only collision avoidance Collision Grid – Non smooth response – False positive 22 A2A2 A2A2 A1A1 A1A1

23. CG-UFRGS Conclusion 23 Multi-agent navigation on non-planar surfaces Multi-resolution distance computation GPU-based approach for collision avoidance CPU/GPU path planning pipeline

24. CG-UFRGS Questions? 24

25. CG-UFRGS 25

26. CG-UFRGS Performance 26