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 PicturesMadden NFL by Electronic Arts

Approach Motion sequences of single character User-specified composition Motion with interaction among multiple characters

Approach

Motion warping Motion composition Multi-character motion Motion optimization Related work Motion wapring Witkin and Popović SIGGRAPH 95

Motion warping Motion composition Multi-character motion Motion optimization Related work Keyframe motion optimization Liu 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 control Difficult 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;t c,p) = d(q;t c )-p c c c

Motion representation

Constraint representation

Environment constraints Enforce the spatial relation between a character and its environment Represented as a function of joint angles ( h q ) 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, h q 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 ( h q ), timing ( h t ), 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

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

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

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

Acknowledgements

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