1. Presenter: Robin van Olst

2. Avneesh SudRussell Gayle Erik Andersen Stephen GuyMing Lin Dinesh Manocha

3.  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)

4.  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!

5.  Adaptive Elastic Roadmaps (AERO) ◦ Model description  Navigation with AERO ◦ Link bands ◦ Local dynamics model ◦ Behaviour model  Implementation and results  Assessment

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

7.  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

8.  Force on particles and milestones:  Internal forces: ◦ Prevent unnecessary link deformation ◦ Prevent roadmap drifting  External forces: ◦ Respond to obstacle motion

9.  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

10.  Repair removed links 1.Check removed links 2.Check disconnected milestones 3.Repair is biased towards the area in the wake of moving obstacles  Lazy and incremental  Explore for new paths ◦ Uses random sampling  Movie!

11.  Adaptive Elastic Roadmaps (AERO) ◦ Model description  Navigation with AERO ◦ Link bands ◦ Local dynamics model ◦ Behaviour model  Implementation and results  Assessment

12.  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)

13.  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

14.  Agents can stand still, walk or jog ◦ Depends on velocity ◦ Uses non-parallel thresholds  Prevents oscillations ◦ Aggressive agents prefer to jog  Higher maximum velocity

15.  Adaptive Elastic Roadmaps (AERO) ◦ Model description  Navigation with AERO ◦ Link bands ◦ Local dynamics model ◦ Behaviour model  Implementation and results  Assessment

16.  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

17.  Performance (in ms)  Cited in ‘Abnormal crowd behavior detection using social force model’ by Mehran et al.

18.  Adaptive Elastic Roadmaps (AERO) ◦ Model description  Navigation with AERO ◦ Link bands ◦ Local dynamics model ◦ Behaviour model  Implementation and results  Assessment

19.  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

20.  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

21.  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

22.  More efficient local dynamics model?  Complement method with: ◦ Continuum Crowds’ discomfort fields ◦ Navigational Fields’ directional preference