Date post: | 22-Dec-2015 |
Category: |
Documents |
View: | 215 times |
Download: | 2 times |
Composition of complex optimal multi-character motions
C. Karen Liu
Aaron Hertzmann
Zoran Popović
Goal
Synthesize complex and realistic interactions
among multiple characters
Monster house by Sony Pictures Madden NFL by Electronic Arts
Approach
Motion sequences of
single character
User-specified
composition
Motion with interaction
among multiple
characters
Approach
QuickTime™ and aCinepak decompressor
are needed to see this picture.
QuickTime™ and aCinepak decompressor
are needed to see this picture.
• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization
Related work
Motion wapringWitkin and Popović
SIGGRAPH 95
• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization
Related work
Keyframe motion optimizationLiu and Cohen
Animation and Simulation 95
Related work
Kovar et. al. SIGGRAPH 02
Li et. al. SIGGRAPH 02
Arikan et. al. SIGGRAPH 03
• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization
• Motion wapring
• Motion composition
• Multi-character motion
• Motion optimization
Related work
Interactive motion generation from examples
Arikan and Forsyth SIGGRAPH 02
• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization
Related work
Dynamic response for motion capture animation
Zordan et. al.SIGGRAPH 05
• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization
Related work
Physically based motion transformation
Popović and Witkin SIGGRAPH 99
• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization
Related work
Learning physics-based motion style
Liu et. al. SIGGRAPH 05
Spacetime optimization
Single character
Multiple characters
Spacetime optimization
Single character
Multiple characters
Pre-defined constraints
High-level control
Spacetime optimization
Single character
Multiple characters
Pre-defined constraints
High-level control
Optimization over entire
motion
Realistic anticipation and follow-through
Spacetime optimization
Single character
Multiple characters
Pre-defined constraints
High-level controlDifficult to predict
constraints for interactive motion
Optimization over entire
motion
Realistic anticipation and follow-through
Expensive for solving large
problems
Overview
2. Compose complex interaction of multiple characters from
simple motion building blocks
1. Optimize motion,environment constraints, and timing
Overview
1. Optimize motion,environment constraints, and timing
Environment constraints User-specified
constraint
Overview
2. Compose complex interaction of multiple characters from
simple motion building blocks
• Motion optimization
• Motion composition
• Results
Optimal constraints
C(q;tc,p) =
d(q;tc)-p
c
cc
Motion representation
45.8
50
Constraint representation
Environment constraints
• Enforce the spatial relation
between a character and its
environment
• Represented as a function of joint
angles (hq) and spatial coefficient
(p)
• Activated at a particular warped
time instance
Dynamic constraints
• Ensure physical realism by
satisfying Lagrangian
dynamics at each joint DOF
• Represented as a function of
joint angles, hq
• Activated at a particular
warped time instance, gravity
ground contact
internal forces
Dynamic constraints
• Move along with environment constraints in
actual time domain
Optimization
• DOFs:
– joint angles (hq), timing (ht), environment
constraints (p), contact forces()
• Constraints:
– environment constraints, dynamic constraints,
user-specified constraints
• Objective function:
– minimizing muscle forces usage
• Motion optimization
• Motion composition
• Results
Block coordinate descent
• Optimize one block of unknowns at a time
• Interaction constraints are specified based on
the result of the previous optimization
• Blocks are selected by spatial or temporal
relations
Continuations
• Solve a sequence of problems that smoothly
approach the constraints
• Apply in concert with block coordinate descent
• Motion optimization
• Motion composition
• Results
Input dataset
• Only three motion clips: a walk cycle, a run
cycle, and a child walk cycle
• Less than 6 seconds long
• All the results are created from these three
motion sequences
QuickTime™ and aCinepak decompressor
are needed to see this picture.
Time-layered schedule
• Synthesis of a sequence of actions:
– specify common transition constraints for two problems
– solve each problem separately to reach the transition
constraint
– remove transition constraints and solve the overlap
motion
A B
C
QuickTime™ and aCinepak decompressor
are needed to see this picture.
Constrained multi-character schedule
• Synthesis of mutually constrained motion with
multiple characters:
– Specify constraints connecting two characters
– Solve one character’s motion at a time
– Increase the “strength” of the constraints to guide the
characters towards optimal solution
QuickTime™ and aCinepak decompressor
are needed to see this picture.
Decreasing-horizon optimizations
• Synthesis of reaction to unexpected events
– Specify interaction constraints for each character
– Solve for each character’s motion based on the
opponent’s latest movement
– Reduce the horizon after each run of optimizations
QuickTime™ and aCinepak decompressor
are needed to see this picture.
Acknowledgements
• Brett Allen
• UW Animation Research Lab
• NSF grants, NSERC Discovery grant, Alfred
P. Sloan Fellowship
• Electronic Arts, Sony, and Microsoft
Research