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