1. Motion Graph for Crowd
Tao Yu

2. Problem Description
Given a set of characters and a set of constraints.
The constraints could be:
Character pose.
Position (p) and Orientation (θ).
Time interval [ta, tb] in which the configuratoin should be obtained (possibly ta=tb).

3. Problem Description Goal: Synthesize motion which: Realistic
Satisfying all constraints
Collision free (already solved by navigation algorithm?)

4. Motion Graph Each node contains a specific pose.
Each edge corresponds to a motion clip.
Any sequence of connected edges yields a seamless motion

5. Motion Graph Traditional MG based methods are limited in that:
The constraints on continuous properties (position, orientation and duration) are hard to exactly satisfy.
Search is expensive.

6. Solution (M.Sung, L.Kovar & M. Gleicher)
The basic idea is:
Search in Motion Graph for motions satisfying constraints approximately
Refine rough motions thru a randomized search algorithm so that it exactly conforms to constraints

7. Process Overview Construct Motion Graph [GSKJ03, Snap-together motion]
Sequential processing for each character
Using PRM as path planner to create constraints sequence (way point sequence)
Search for seed motions that satisfying constraints roughly
Adjusting and merging seed motions

8. The following contents are copied from authors’ presentation slides

9. Algorithm Example Rough planning Fine planning PRM query Greedy search
Create seed motions
If distance > ε
Randomly select and replace a clip
Joining with adjustment
Target
Obstacle
Initial
waypoints

10. Algorithm Example Rough planning Fine planning PRM query Greedy search
Create seed motions
If distance > ε
Randomly select and replace a clip
Joining with adjustment
Target
Obstacle
Initial 1 2 3
waypoints

11. Algorithm Rough planning Fine planning Example PRM query Greedy search
Create seed motions
If distance > ε
Randomly select and replace a clip
Joining with adjustment
Example
Target
Obstacle
Forward
Motion(Mf)
Initial 1
Backward
Motion(Mb) 2 3
Initial’

12. Algorithm Rough planning Fine planning > ε PRM query Greedy search
Cost function : How close are they?
C(Mf, Mb)
Rough planning
PRM query
Fine planning
Greedy search
Create seed motions
If distance > ε
Randomly select and replace a clip
Joining with adjustment
> ε
Forward motions
Backward motions
Compare all pair of motions and
returns minimum cost

13. Algorithm Rough planning Fine planning < ε PRM query Greedy search
Create seed motions
If distance > ε
Randomly select and replace a clip
Joining with adjustment
< ε
New motions
Old Motions
Old Motionsc
Random select and
Replace a clip

14. Algorithm Rough planning Fine planning Example PRM query Greedy search
Create seed paths
If distance > ε
Randomly select and replace a clip
Joining with adjustment
Example
Target
Obstacle
Initial
Joining
waypoints

15. Motion adjustment Old Motions New motions New motions Old Motions ε
The error is distributed to the both paths

16. Comments
This method combines path planning, collision avoidance and motion synthesis together.
Suitable for high-level behavior planner.
Not directly applicable to our existing navigation/path planning methods for crowd.

17. Potential adaptation Dense constraints
Motion prediction (Search motion in advance)
To be added…