1. REAL-TIME NAVIGATION OF INDEPENDENT AGENTS USING ADAPTIVE ROADMAPS Avneesh Sud 1, Russell Gayle 2, Erik Andersen 2, Stephen Guy 2, Ming Lin 2, Dinesh Manocha 2 1: Microsoft Corp 2: UNC Chapel Hill http://gamma.cs.unc.edu/crowd/aero

2. Motivation  Navigating to goal - important behavior in virtual agent simulation  Navigation requires path planning  Compute collision-free paths  Satisfy constraints on the path  Exhibit crowd dynamics

3. Motivation Simulation of Virtual Humans ViCrowd [ Musse & Thalmann01; EPFL ] ABS [ Tecchia et al.01; UCL ] Virtual Iraq [ICT/USC 06]

4. Motivation Interactive simulation of crowds/virtual agents in games Assassin’s Creed Second Life Spore

5. Challenges  Path planning for multiple (thousands of) independent agents simultaneously  Each agent is a dynamic obstacle  Exact path planning for each agent in dynamic environments is P-space complete

6. Goal  Real-time navigation for multiple virtual agents  Independent behavior  Global path planning  Dynamic environments  Thousands of agents

7. Applications  Crowd simulation  Multi-robot planning  Social engineering  Training and simulation  Exploration  Entertainment

8. Main Results  Adaptive-Elastic ROadmaps (AERO): Graph structure for global navigation that adpats to dynamic environments  Augment global path planning with local dynamics model

9. Results: Tradeshow Demo Simulation of 100 agents in an urban environment, 10fps

10. Outline  Related Work  Our Approach  Results  Discussion and Conclusion

11. Outline  Related Work  Our Approach  Results  Discussion and Conclusion

12. Related Work  Multiple agent planning  Crowd dynamics

13. Related Work  Multiple agent planning  Global path planning [ Bayazit et al.02, Li & Chou03, Pettre et al.05 ]  Local methods [ Khatib86 ]  Hybrid [ Lamarche & Donikian04 ]  Dynamic environments [ Quinlan & Kthaib93, Yang & Brock06, Gayle et al. 07, Li & Gupta07, Sud et al. 2007 ]  Crowd Simulation

14. Related Work  Multiple agent planning  Crowd Simulation  Agent-based methods [ Reynolds87, Musse & Thalmann97, Sung et al.04, Pelechano et al.07 ]  Cellular Automata [ Hoogendoorn et al00, Loscos et al.03, Tu & Terzopoulos 93]  Particle Dynamics [ Helbing03, Sugiyama et al. 01 ]  Continuous Methods [ Helbing05, Treuille et al.06 ]

15. Outline  Related Work  Our Approach  Overview  Adaptive Elastic Roadmaps (AERO)  Navigation using AERO  Results  Discussion and Conclusion

16. Overview At each time step Environment (Static Obstacles, Dynamic Obstacles, and Agents) Local Dynamics Adaptive Elastic Roadmap Scripted Behaviors Collision Detection

17. Overview At each time step Environment (Static Obstacles, Dynamic Obstacles, and Agents) Local Dynamics Adaptive Elastic Roadmap Scripted Behaviors Collision Detection

18. Outline  Related Work  Our Approach  Overview  Adaptive Elastic Roadmaps (AERO)  Navigation using AERO  Results  Discussion and Conclusion

19. Adaptive Elastic Roadmaps (AERO)  Global connectivity graph  Continuously adapts to dynamic obstacles  Physically-based updates  Localized roadmap deformations and maintenance  Advantage: Efficient to deform roadmap than recompute & replan

20. AERO: Representation  Representation  Graph G = { M, L }  M = set of dynamic milestones  L = set of reactive links l j (t) = [ p 0 (t) p 1 (t) p 2 (t) … p n (t) ] Where p k (t) is a dynamic particle

21. AERO: Representation  Representation  Graph G = { M, L }  M = set of dynamic milestones  L = set of reactive links l j (t) = [ p 0 (t) p 1 (t) p 2 (t) … p n (t) ] Where p k (t) is a dynamic particle

22. AERO: Force Model  Applied forces influence roadmap behavior  Force on particle/milestone i:  Internal Forces  Prevent unnecessary link expansion  Prevent roadmap drift  External Forces  Respond to obstacle motion

23. AERO: Force Model  Quasi-Static simulation  Considers particles at rest  Prevents undesirable link oscillations  Verlet integrator

24. AERO: Maintenance  Roadmap maintenance  Link removal Deformation energy Prevent overly stretched links Proximity to obstacles  Link insertion Repair removed links Explore for new path options

25. AERO: Maintenance  Link insertion 1. Check removed links 2. Check disconnected components 3. Biased exploration toward the “wake” of moving obstacles

26. AERO: Demo

27. AERO: Link Bands  Region of free space closer to a link  Collision free zone in neighborhood of a link  Identify nearest link for each agent for path search

28. AERO: Link Bands Link 1 Link 2 Band 1

29. AERO: Link Bands Link 2

30. AERO: Link Bands Link 1 Band 1

31. Outline  Related Work  Our Approach  Overview  Adaptive Elastic Roadmaps (AERO)  Navigation using AERO  Results  Discussion and Conclusion

32. Navigation: Path Planning  Source link  link band containing agent  Goal link  link band containing goal  Link weights  Path length  Link band width  Agent density

33. Navigation: Local Dynamics  Generalized force model of pedestrian dynamics [Helbing 2003]  Emergent crowd behavior at varying densities

34. Navigation: Local Dynamics  F soc : Social repulsive force among agents  F att : Attractive force among agents  F obs : Repulsive force from obstacles  F r : Roadmap force

35. Navigation: Local Dynamics  F soc : Social repulsive force among agents  F att : Attractive force among agents  F obs : Repulsive force from obstacles  F r : Roadmap force

36. Overview At each time step Environment (Static Obstacles, Dynamic Obstacles, and Agents) Local Dynamics Adaptive Elastic Roadmap Scripted Behaviors Collision Detection

37. Outline  Related Work  Our Approach  Results  Discussion and Conclusion

38. Implementation  3Ghz Pentium D CPU, 2GB RAM  NVIDIA GeForce 7900 GPU, 512MB  OpenGL

39. Demos  Maze  Tradeshow  City

40. Demos: Maze

41. Demos: City

42. Demos: Tradeshow

43. Timings

44. Outline  Related Work  Our Approach  Results  Discussion and Conclusion

45. Conclusions  Physically-based, adapting roadmap AERO  Adapts to motion of obstacles  Handle changes in free space connectivity  Combine with a local dynamics model using link bands  Efficient localized updates  No assumptions on motion

46. Limitations  Unrealistic high-DoF human motion  Computed paths may not be optimal  Lacks convergence guarantees

47. Future Work  Develop multi-resolution techniques  Exploit natural grouping behavior  Higher DoF articulated models for more realistic motions  Example / Learning based methods to guide simulation [Lerner2007]

48. Acknowledgements  UNC GAMMA Group  Anonymous reviewers  Funding organizations  ARO  ONR  NSF  DARPA / RDECOM  Intel Corp  Microsoft Corp

49. Questions?  http://gamma.cs.unc.edu/crowd/aero http://gamma.cs.unc.edu/crowd/aero  avneesh.sud@microsoft.com avneesh.sud@microsoft.com