Composition of complex optimal multicharacter motions

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Composition of complex optimal multi-character
motions

• C. Karen Liu
• Aaron Hertzmann
• Zoran Popovic

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Goal
Monster house by Sony Pictures
Madden NFL by Electronic Arts

• Synthesize complex and realistic interactions
  among multiple characters

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Approach
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Approach
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Related work

• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization

Motion wapring Witkin and Popovic SIGGRAPH 95
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Related work

• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization

Keyframe motion optimization Liu and Cohen
Animation and Simulation 95
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Related work

• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization

Kovar et. al. SIGGRAPH 02
Li et. al. SIGGRAPH 02
Arikan et. al. SIGGRAPH 03
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Related work

• Motion wapring
• Motion composition
• Multi-character motion
• Motion optimization

Interactive motion generation from
examples Arikan and Forsyth SIGGRAPH 02
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Related work

• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization

Dynamic response for motion capture
animation Zordan et. al. SIGGRAPH 05
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Related work

• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization

Physically based motion transformation Popovic
and Witkin SIGGRAPH 99
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Related work

• Motion warping
• Motion composition
• Multi-character motion
• Motion optimization

Learning physics-based motion style Liu et. al.
SIGGRAPH 05
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Spacetime optimization
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Spacetime optimization
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Spacetime optimization
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Spacetime optimization
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Overview
1. Optimize motion,environment constraints, and
timing
2. Compose complex interaction of multiple
characters from simple motion building blocks
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Overview
1. Optimize motion,environment constraints, and
timing
Environment constraints
User-specified constraint
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Overview
2. Compose complex interaction of multiple
characters from simple motion building blocks
?
?
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• Motion optimization
• Motion composition
• Results

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Optimal constraints
C(qtc,p) d(qtc)-p
c
c
c
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Motion representation
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Constraint representation
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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

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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,

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Dynamic constraints

• Move along with environment constraints in actual
  time domain

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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

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• Motion optimization
• Motion composition
• Results

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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

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Continuations

• Solve a sequence of problems that smoothly
  approach the constraints
• Apply in concert with block coordinate descent

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• Motion optimization
• Motion composition
• Results

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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

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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
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Constrained multi-character schedule

• Synthesis of mutually constrained motion with
  multiple characters
• Specify constraints connecting two characters
• Solve one characters motion at a time
• Increase the strength of the constraints to
  guide the characters towards optimal solution

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Decreasing-horizon optimizations

• Synthesis of reaction to unexpected events
• Specify interaction constraints for each
  character
• Solve for each characters motion based on the
  opponents latest movement
• Reduce the horizon after each run of optimizations

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Acknowledgements
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• Brett Allen
• UW Animation Research Lab
• NSF grants, NSERC Discovery grant, Alfred P.
  Sloan Fellowship
• Electronic Arts, Sony, and Microsoft Research