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

2. Goal Synthesize complex and realistic interactions among multiple characters Monster house by Sony PicturesMadden NFL by Electronic Arts

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

4. Approach

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

6. Motion warping Motion composition Multi-character motion Motion optimization Related work Keyframe motion optimization Liu and Cohen Animation and Simulation 95

7. 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

8. Motion wapring Motion composition Multi-character motion Motion optimization Related work Interactive motion generation from examples Arikan and Forsyth SIGGRAPH 02

9. Motion warping Motion composition Multi-character motion Motion optimization Related work Dynamic response for motion capture animation Zordan et. al. SIGGRAPH 05

10. Motion warping Motion composition Multi-character motion Motion optimization Related work Physically based motion transformation Popović and Witkin SIGGRAPH 99

11. Motion warping Motion composition Multi-character motion Motion optimization Related work Learning physics-based motion style Liu et. al. SIGGRAPH 05

12. Spacetime optimization Single character Multiple characters

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

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

15. 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

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

17. Overview 1. Optimize motion,environment constraints, and timing Environment constraints User-specified constraint

18. Overview 2. Compose complex interaction of multiple characters from simple motion building blocks  

19. Motion optimization Motion composition Results

20. Optimal constraints C(q;t c,p) = d(q;t c )-p c c c

21. Motion representation 45.8 50

22. Constraint representation

23. 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

24. 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

25. Dynamic constraints Move along with environment constraints in actual time domain

26. 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

27. Motion optimization Motion composition Results

28. 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

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

30. Motion optimization Motion composition Results

31. 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

33. 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

35. 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

37. 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

39. Acknowledgements

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