Real-time Navigation of Independent Agents

Using Adaptive Roadmaps

Presenter: Robin van Olst

The Authors

Avneesh Sud Russell Gayle Erik Andersen

Stephen Guy Ming Lin Dinesh Manocha

Elastic Bands – Quinlan and Khatib, 1993 Elastic Roadmaps – Yang and Brock, 2006

Real-time path planning for virtual agents in dynamics environments – Sud et al., 2006◦ Voronoi diagram generation using a GPU

Planning algorithms – LaValle, 2006◦ Random sampling

Self-organized pedestrian crowd dynamics and design solutions – Helbing, 2003◦ Local dynamics model (social forces)

Related work

Adaptive Elastic Roadmaps (AERO)◦ Global path planning method◦ Graph structure adapts to dynamic environments

Link bands◦ Local dynamics model◦ Augmented to AERO

Simulates a thousand of heterogeneous agents individually in real-time

Movie time!

Introduction

Adaptive Elastic Roadmaps (AERO)◦ Model description

Navigation with AERO◦ Link bands◦ Local dynamics model◦ Behaviour model

Implementation and results

Assessment

Outline

Based on a Generalized Voronoi diagram◦ Provides good initial clearance◦ Computes proximity information

Adaptive Elastic Roadmaps (AERO)

The Adaptive Elastic Roadmap◦ Consists of:

Milestones Links

Particles

◦ Is a guiding path for agents Find with graph search algorithms (A*)

Obstacles may block a path◦ Forces are applied to AERO

AERO Representation

Force on particles and milestones:

Internal forces:◦ Prevent unnecessary link deformation◦ Prevent roadmap drifting

External forces:◦ Respond to obstacle motion

AERO Force Computation

Necessary when a link is blocked Removal criteria

◦ Physics-based A link exceeds its stretching threshold

◦ Geometric-based The short distance to all obstacle is less than the

largest radius assign to an agent

AERO Link Removal

Repair removed links1. Check removed links2. Check disconnected milestones3. Repair is biased towards the area in the wake of

moving obstacles Lazy and incremental

Explore for new paths◦ Uses random sampling

Movie!

AERO Link Addition

Adaptive Elastic Roadmaps (AERO)◦ Model description

Navigation with AERO◦ Link bands◦ Local dynamics model◦ Behaviour model

Implementation and results

Assessment

Outline

Region of free space close to the nearest link◦ Space provides a collision-free path

Path planning◦ Starts at the nearest link◦ Each link is assigned a weight:

◦ Function of: link length, band width and the number of actors present on the band Each is weighted

High α: choose shortest paths (used for slow agents) High β: avoids narrow paths High γ: choose less crowded paths (used for aggressive agents)

AERO Link Bands

Local dynamics simulation◦ Helbing’s social forces model:

◦ Modified to add discomfort zones in front of moving obstacles Repulsive forces are biased along the motion of

obstacles

AERO Navigation: Link Bands

Agents can stand still, walk or jog◦ Depends on velocity◦ Uses non-parallel thresholds

Prevents oscillations◦ Aggressive agents prefer to jog

Higher maximum velocity

AERO Behaviour Modeling

Adaptive Elastic Roadmaps (AERO)◦ Model description

Navigation with AERO◦ Link bands◦ Local dynamics model◦ Behaviour model

Implementation and results

Assessment

Outline

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

Optimizations◦ Spatial hash table of all entities and links

Efficient lookups and proximity computation◦ Voronoi diagram of all obstacles is computed

Scan a window to get all the obstacles within a certain range

AERO Implementation

Performance (in ms)

Cited in ‘Abnormal crowd behavior detection using social force model’ by Mehran et al.

Results

Adaptive Elastic Roadmaps (AERO)◦ Model description

Navigation with AERO◦ Link bands◦ Local dynamics model◦ Behaviour model

Implementation and results

Assessment

Outline

Adapts to dynamic obstacles◦ Handles changes in free space connectivity

Relates to real humans?

Able to simulate a thousand independently moving heterogeneous agents in real-time◦ Efficient

No assumptions on motion

Positive Points

Unrealistic high-DoF human motion◦ Only 3-DoF motion supported

Computed paths may not be optimal

Convergence is not guaranteed◦ Agents may get stuck in local minima

Limitations

Agents require a goal◦ No wandering

No grouping◦ Does not relate to real humans

Video shows rapid changes in orientation

Probably not able to simulate denser crowds

Negative Points

More efficient local dynamics model?

Complement method with:◦ Continuum Crowds’ discomfort fields◦ Navigational Fields’ directional preference

Suggestions