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

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

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

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

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

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

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

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

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

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

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

Related Work  Multiple agent planning  Crowd dynamics

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 ]  Crowd Simulation

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 ]

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

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

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

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

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

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

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

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

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

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

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

AERO: Demo

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

AERO: Link Bands Link 1 Link 2 Band 1

AERO: Link Bands Link 2

AERO: Link Bands Link 1 Band 1

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

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

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

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

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

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

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

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

Demos  Maze  Tradeshow  City

Demos: Maze

Demos: City

Demos: Tradeshow

Timings

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

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

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

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]

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

Questions?  