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REAL-TIME NAVIGATION OF INDEPENDENT AGENTS USING ADAPTIVE ROADMAPS
Avneesh Sud1, Russell Gayle2, Erik Andersen2, Stephen Guy2, Ming Lin2, Dinesh Manocha2
1: Microsoft Corp 2: UNC Chapel Hill
http://gamma.cs.unc.edu/crowd/aero
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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
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Motivation
Simulation of Virtual Humans
ViCrowd [Musse & Thalmann01; EPFL] ABS [Tecchia et al.01; UCL]
Virtual Iraq [ICT/USC 06]
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Motivation
Interactive simulation of crowds/virtual agents in games
Assassin’s Creed
Second Life
Spore
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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
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Goal
Real-time navigation for multiple virtual agents Independent behavior Global path planning Dynamic environments Thousands of agents
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Applications
Crowd simulation Multi-robot planning Social engineering Training and simulation Exploration Entertainment
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Main Results
Adaptive-Elastic ROadmaps (AERO): Graph structure for global navigation that adpats to dynamic environments
Augment global path planning with local dynamics model
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Results: Tradeshow Demo
Simulation of 100 agents in an urban environment, 10fps
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Outline
Related Work Our Approach Results Discussion and Conclusion
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Outline
Related Work Our Approach Results Discussion and Conclusion
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Related Work
Multiple agent planning Crowd dynamics
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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
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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]
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Outline
Related Work Our Approach
Overview Adaptive Elastic Roadmaps (AERO) Navigation using AERO
Results Discussion and Conclusion
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OverviewAt each time step
Environment(Static Obstacles,
Dynamic Obstacles,and Agents)
Local Dynamics
AdaptiveElastic Roadmap
Scripted Behaviors
Collision Detection
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OverviewAt each time step
Environment(Static Obstacles,
Dynamic Obstacles,and Agents)
Local Dynamics
AdaptiveElastic Roadmap
Scripted Behaviors
Collision Detection
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Outline
Related Work Our Approach
Overview Adaptive Elastic Roadmaps (AERO) Navigation using AERO
Results Discussion and Conclusion
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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
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AERO: Representation
Representation Graph G = { M, L } M = set of dynamic milestones L = set of reactive links
lj(t) = [ p0(t) p1(t) p2(t) … pn(t) ]
Where pk(t) is a dynamic particle
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AERO: Representation
Representation Graph G = { M, L } M = set of dynamic milestones L = set of reactive links
lj(t) = [ p0(t) p1(t) p2(t) … pn(t) ]
Where pk(t) is a dynamic particle
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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
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AERO: Force Model
Quasi-Static simulation Considers particles at rest Prevents undesirable link oscillations
Verlet integrator
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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
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AERO: Maintenance Link insertion
1. Check removed links2. Check disconnected components3. Biased exploration toward the “wake”
of moving obstacles
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AERO: Demo
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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
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AERO: Link Bands
Link 1
Link 2
Band 1
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AERO: Link Bands
Link 2
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AERO: Link Bands
Link 1
Band 1
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Outline
Related Work Our Approach
Overview Adaptive Elastic Roadmaps (AERO) Navigation using AERO
Results Discussion and Conclusion
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Navigation: Path Planning
Source link link band containing agent Goal link link band containing goal Link weights
Path length Link band width Agent density
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Navigation: Local Dynamics
Generalized force model of pedestrian dynamics [Helbing 2003]
Emergent crowd behavior at varying densities
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Navigation: Local Dynamics
Fsoc : Social repulsive force among agents
Fatt : Attractive force among agents Fobs : Repulsive force from obstacles Fr : Roadmap force
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Navigation: Local Dynamics
Fsoc : Social repulsive force among agents
Fatt : Attractive force among agents Fobs : Repulsive force from obstacles Fr : Roadmap force
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OverviewAt each time step
Environment(Static Obstacles,
Dynamic Obstacles,and Agents)
Local Dynamics
AdaptiveElastic Roadmap
Scripted Behaviors
Collision Detection
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Outline
Related Work Our Approach Results Discussion and Conclusion
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Demos
Maze Tradeshow City
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Demos: Maze
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Demos: City
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Demos: Tradeshow
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Timings
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Outline
Related Work Our Approach Results Discussion and Conclusion
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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
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Limitations
Unrealistic high-DoF human motion Computed paths may not be optimal Lacks convergence guarantees
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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]
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Acknowledgements
UNC GAMMA Group Anonymous reviewers Funding organizations
ARO ONR NSF DARPA / RDECOM Intel Corp Microsoft Corp