Composition of complex optimal multi-character motions C Karen

Composition of complex optimal multi-character motions C. Karen Liu Aaron Hertzmann Zoran Popović

Goal Monster house by Sony Pictures Madden NFL by Electronic Arts Synthesize complex and realistic interactions among multiple characters

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

Approach

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Spacetime optimization Single character Multiple characters

Spacetime optimization Single character Pre-defined constraints High-level control Multiple characters

Spacetime optimization Single character Pre-defined constraints High-level control Optimization over entire motion Realistic anticipation and follow-through Multiple characters

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 1. Optimize motion, environment constraints, and timing 2. Compose complex interaction of multiple characters from simple motion building blocks

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 c c

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 internal forces • Represented as a function of joint angles, hq • Activated at a particular ground contact warped time instance, gravity

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

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