Real-time Navigation of Independent Agents Using Adaptive Roadmaps

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

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

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. 2007]

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

OverviewAt each time step

Environment(Static Obstacles,

Dynamic Obstacles,and Agents)

Local Dynamics

AdaptiveElastic Roadmap

Scripted Behaviors

Collision Detection




Local Dynamics


Scripted Behaviors

Collision Detection

Outline




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

lj(t) = [ p0(t) p1(t) p2(t) … pn(t) ]

Where pk(t) is a dynamic particle

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

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 links2. Check disconnected components3. 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




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


Fsoc : Social repulsive force among agents

Fatt : Attractive force among agents Fobs : Repulsive force from obstacles Fr : Roadmap force


Fsoc : Social repulsive force among agents

Fatt : Attractive force among agents Fobs : Repulsive force from obstacles Fr : Roadmap force




Local Dynamics


Scripted Behaviors

Collision Detection

Outline


Demos

Maze Tradeshow City

Demos: Maze

Demos: City

Demos: Tradeshow

Timings

Outline


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?

http://gamma.cs.unc.edu/crowd/aero [email protected]

http://gamma.cs.unc.edu/crowd/aero

mailto:[email protected]

Documents

Real-time Navigation of Independent Agents Using Adaptive Roadmaps