Animation With Momentum

1. Interactive performances with style and substance. Animation With Momentum David Wu Microsoft Game Studios GDC 2009

2. Takeaway • Survey of recent research in the field of interactive animation from the point of view of a game developer. • Assessments of the effectiveness and overall applicability of proposed techniques • A pragmatic distillation of subsets of ideas from the large, fully designed systems presented. • Emphasis on techniques and insights applicable now.

3. Straw Man Motivation:“Animation in Games is not perfect”Da Silva et al, Siggraph 08 • [Video] • Geometric blending used to adapt existing character animations to novel situations (i.e. walk cycle on steps) does not look physically sound. • Characters do not react to external stimulation that has not been planned for (i.e. throwing boxes at people you are talking to) • They remain kinematic, which – from the point of view of physical interactions – is equivalent to having infinite inertia

4. What does an Interactive Animation System provide? • Characters that preserve the personality and style of their animations, seamlessly interact with a physically simulated world and take orders from the gamepad of abusive players and confused AIs. Figure 1: Physical feasibility is one of many challenges faced by otherwise content virtual people.

5. Will Compelling Characters and Physics make my game Sell? * figures beyond 2009 are estimates

6. SIMBICON: Simple Biped Locomotion ControlSIGGRAPH ‘07Kang Kang Yin, Kevin Loken, Michiel van de Panne • Goal is to create a robust control system for bipeds that can: • Balance • Walk with various gaits • Handle external perturbations such as varying terrain and being pushed • Transition between animations • Approximate animations from motion capture • Last goal seems to be treated as an afterthought • Quality and results are not mentioned • Not quantifiable? • This is a first order concern for games. • Robustness as measured by physical simulation results is treated as the highest priority result.

7. Van de Panne’s Animation Pipeline In addition to feeding the Mixer, closed loop feedback is required to determine FSM transitions. (i.e. Heel Strike) • Each animation is a stored as the gains and parameters of one physical controller. • Various controllers exist, each defined by a finite state machine with various parameters and gains. • Each animation corresponds to one controller that has been trained to emulate the animation using physical actuation. • In the absence of external disturbances, the resulting motion mimics the source animation. Mixer linearly blends control parameters rather than poses. Similar controllers are synchronized such that they are in the same state. A Balance post process is applied. (see next slide for details) Integrator receives forces and torques, forward dynamics equations are solved and the world state accordingly Walk Finite State Machine

8. SIMBICON: Simple Biped Locomotion ControlSIGGRAPH ’07 (continued)Kang Kang Yin, Kevin Loken, Michiel van de Panne • System is based on PD controllers acting at joints • Each animation has its own individual control system that operates the PD gains and targets with values specified by a simple finite state machine. • While this is not treated as a first order concern, the resulting controllers require very little memory. • Compression ratios of 100:1 are typical.

9. SIMBICON: Simple Biped Locomotion ControlSIGGRAPH ’07 (continued)Kang Kang Yin, Kevin Loken, Michiel van de Panne • Balance control system is an adaption of the original hopper control system developed by Raibert in the ’80s. • Main considerations are foot placement upon landing and inertial forces due to acceleration of legs in flight

10. Raiberts Hopper is Simple and effective. Unfortunately it cannot balance when stationary.

11. SIMBICON: Simple Biped Locomotion ControlSIGGRAPH ’07 (continued)Kang Kang Yin, Kevin Loken, Michiel van de Panne • [Video]

12. Continuation Methods forAdapting Simulated SkillsKangkang Yin, StelianCoros Philippe Beadoin, Michiel van de Panne SIGGRAPH’08 “Simulated characters in simulated worlds require simulated skills.” • An extension of SIMBICON • Machine learning is used to create new animation controllers based on • Existing controllers • New challenges such as variations in terrain, new goals, etc • Learning framework based on numerical optimization employing continuation methods • i.e. Creating an animation controller for pushing a table from a walking motion capture.

13. Continuation Methods forAdapting Simulated SkillsKangkang Yin, StelianCoros Philippe Beadoin, Michiel van de Panne SIGGRAPH’08 • Continuation Methods:

14. Continuation Methods forAdapting Simulated SkillsKangkang Yin, StelianCoros Philippe Beadoin, Michiel van de Panne SIGGRAPH’08 • [Video]

15. Ad Hoc Meta-analysis of perceived error in physically simulated charactersDavid Wu, GDC 09 • A number of studies have looked at the relative sensitivity of viewers towards various types of error in physical simulation of humans: • Anna Majkowska, PetrosFaloutsos, Flipping with physics: motion editing for acrobatics, Eurographics animation 2007 • Yeuhi Abe , C. Karen Liu , ZoranPopovic, Momentum-based parameterization of dynamic character motion, Graphical Models 2006 • Carol O'Sullivan , John Dingliana , ThanhGiang , Mary K. Kaiser, Evaluating the visual fidelity of physically based animations, SIGGRAPH 2003 • Paul S. A. Reitsma , Nancy S. Pollard, Perceptual metrics for character animation: sensitivity to errors in ballistic motion, SIGGRAPH 2003

16. Ad Hoc Meta-analysis of perceived error in physically simulated characters • Meta findings regarding sensitivity to error: • Linear Momentum: High • Linear Velocity: Moderate • Angular Momentum: Moderate • Angular Velocity: Low • Conservation of Energy: Low • Gravity Magnitude: Inconclusive • Static Balance: High • Dynamic Balance: High • These findings have been cited in various papers, they are considered valid despite the relatively low sample sizes and relatively poor control procedures of the studies.

17. Synthesis of Constrained Walking SkillsStelianCoros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne Siggraph Asia 08 • Given a source walk cycle and model, offline optimization is used to generate many single step walk cycle variations • Each variation is generated to with the optimization goal of a random foot placement offset.

18. Synthesis of Constrained Walking SkillsStelianCoros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne Siggraph Asia 08 • Variations are assembled to create what the authors call a “Step-to-Step Dynamics Model” or an “SSDM”. The step-to-step dynamics model (SSDM). The nonparametric (example-based) model makes predictions using the results of the offline synthesis. The given dimensions for the state and actions spaces are for the 2D bipeds.

19. Synthesis of Constrained Walking SkillsStelianCoros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne Siggraph Asia 08 • At run time, the controller uses the SSDM with its reference walk cycle to generate a continuous walk cycle that satisfies constraints discovered in real time. • The SSDM itself stores its data as samples compressed via principle component analysis on the differences between learned steps and the reference walk cycle. • Given the strong correlation between variations the authors discover the only 2-4 principle components are required. • Sampling consists of applying an N dimension blend on reference samples and then combining the result with the reference walk cycle.

20. Synthesis of Constrained Walking SkillsStelianCoros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne Siggraph Asia 08 Takeaways • The overall framework provides: • A potential alternative to traditional foot placement IK. • Higher quality results • A potential alternative to animator provided walk cycle transitions or variations • Saves animator time

21. Synthesis of Constrained Walking SkillsStelianCoros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne Siggraph Asia 08 Take-Away: PCA Hypothesis • Principle Component Analysis (PCA) is a technique used for the lossy compression of vector data sets. • A 3 DOF analogy might be DXT1 compression of a single quad of pixels. In this case only the first Principle component is maintained and this 3D vector is the is the difference between the two end point colors. • The early PCA vectors resulting from all poses of a character are strongly correlated with the signature style and physical characteristics of that character.

22. Synthesis of Constrained Walking SkillsStelianCoros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne Siggraph Asia 08 Not Mickey Mouse Take-Away: PCA Hypothesis • When performing inverse kinematics, using PCA vectors as the degrees of freedom and weighting each in a manner inversely proportional to it’s Eigenvalue, a least squares IK solution is likely to represent a pose variation that correlates highly with the preferred poses of that character. Figure 3: 1st Principle component vector consists of DOF values that produce a characteristic pose.

23. Synthesis of Constrained Walking SkillsStelianCoros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne Siggraph Asia 08 Not Mickey Mouse Take-Away: PCA Hypothesis (cont) • There are a few conditions that the dataset used to generate the Principle Component Vectors must meet for this hypothesis to hold: • Should be representative of the entire range of motions preferred poses • Should be representative in a quantitative, statistical sense • Appropriate DOF should form the initial basis • Forces or Poses? • May require doctoring of the input i.e. weighting the std deviation of underrepresented poses. Figure 4: Animation set has been over-trained. The 1st Principle Component vector is not ideal.

24. Flexible Registration of Human Motion Data with Parameterized Motion ModelsYen-Lin Chen, Jian Yuan Miny, JinxiangChaiz • An initial set of animations is collected • Animations are time-warped such that each “cycle” takes 2 seconds • PCA is performed on these animations and the 20 top Eigenmodes are maintained • These are run through a “physics filter”, which iteratively modified them until they are physically valid Figure 9: First Principle Component

25. Flexible Registration of Human … (cont) • All animations are projected onto the resulting Principle Components • The authors claim that 20 Eigen modes is enough for mostly lossless representation • New animations are “registered” into the motion database and stored as linear combinations of the components • The authors state the following applications: • Effective motion retargeting • Kinematics, dynamics and style • Physics improves believability of motions • Implicitly enforced by the Components • Consistent, realistic motion generation from sparse data. • Registration enforces the constraints implied by the sparse data and fills in the blanks with motion from existing motions.

26. Animating responsive characters with dynamic constraints in near-unactuated coordinatesYuting Ye, C. Karen Liu • Combines kinematic motion with dynamic reactions that are constrained to minimize interference with muscles essential to the base motion. • To accomplish this, the system does the following: • Projects motions

27. Animating responsive characters… (cont) • Specifically, the system does the following: • For each frame of animation, the actuator torques required to drive the motion are computed • Principle Component Analysis (PCA) is performed on all frames of all animations. • Eigenvectors with the lowest 8 Eigenvalues are collected, these form the basis for dynamic reactions. • The biped’s dynamics are represented using 8 DOF, each being a scalar multiple of one of these vectors. • For each frame of animation the forward dynamics of the system are projected onto this basis (J) • f = Mx’’ +… • Jf = (JMJt)(Jx’’) • Jtq’’ = x’’

28. Animating responsive characters… (cont) • Due to the orthogonality guarantees of PCA, these Components act in the null space of the most significant Components. • They correspond to motions requiring little or no muscle action • Hence the term “unactuated” • Furthermore the composite effect of these components tend to cancel each other out with respect to side effects at the primary, well actuated DOF.

29. Animating responsive characters… (cont) • [video]

30. Animating responsive characters… (cont) • Extremely efficient • Fairly convincing • Characters display motion consistent with their style • Primary issues is that for relatively strong perturbations the response is not convincing – you would expect perturbation to effect the walk cycle as a whole, unfortunately the problem statement forbids this. • Changing the problem statement would invalidate this technique.

31. Simulating Biped Behaviors from Human Motion DataKwang Won, SokManmyung Kim, Jehee Lee ACM Transactions on Graphics, July 2007. • Uses machine learning to construct physical controllers that can emulate motion capture data while maintaining balance • Controllers operate on an animator specified biped. • The system behaves best when the virtual biped is similar to captured subject.

32. Simulating Biped Behaviors … (cont) • Animators construct a finite state machine that describes potential transitions between animations. • Further controllers are generated and trained for each transition • All animations can transition to the balance/ recovery states.

33. Simulating Biped Behaviors … (cont) • Controllers consist of parameterized PD servos. • Training consists of finding feedback/time varying parameterization for the servos using a numerical optimization technique with the objective function of minimizing error between the motion capture and the simulated character. • The optimization problem is highly nonlinear

34. Simulating Biped Behaviors … (cont) • Optimization strategy: • Initialize solution to {0} • Scatter random points about the current solution • Optimize each point using a gradient descent technique • Select best point(s) and repeat • Slow, brute force method. • Given optimization landscape, faster search methods such as Conjugate Gradients and Quasi Newton fail to converge, so the others use a downhill simplex descent • In the second phase of learning (transitions) the optimization parameterizations consist of a linear combination of existing controllers • Speeds up the optimization considerably • Maintains style of source animations • Key takeaway.

35. Simulating Biped Behaviors … (cont) • Key Takeaways • PD servo based physical controllers with very few biped/locomotion specific heuristics are feasible • Blending controllers trained on animation with a specific style seems yield new controllers that maintain this style. • Effectiveness demonstrated for transitions, will blending work with more general extrapolations?

36. Interactive Simulation of Stylized Human LocomotionMarco da Silva, Yeuhi Abe, Jovan Popović - SIGGRAPH 08 • Animating natural human motion in dynamic environments is difficult for various reasons, including complex geometric and physical interactions. • Simulation combined with physical controllers has been demonstrated to provide an automatic solution to parts of this problem by the robotics community. • In the field of video game animation, we require style and personality in addition to competent locomotion.

37. Simulation of Stylized … (cont) • Describes the systematic synthesis of controllers that can reproduce a range of locomotion styles in interactive simulations. • Given a reference motion that describes the desired style, a control system is derived that can reproduce that style in simulation and in new environments. • Figure 1 • Numerical optimization provides a framework for computing a solution that is optimal in the context of any number of prioritized goals. • In this case the goals are balance and style, the optimization technique is quadratic programming.

38. Simulation of Stylized … (cont) • A balance strategy is pre-computed for the given style using automated analysis of linear time varying approximations. • By tailoring the balance strategy in this manner, a controller preserves the style better than a more cautious strategy

39. Simulation of Stylized … (cont) • The Style feedback loop tracks individual joint angles to compute the accelerations needed to preserve the given style. • Reference motions guide both the style and balance feedback. • The style feedback aims to preserve the nuances of the motion • The balance feedback seeks to adapt the motion of three balance critical segments • The control algorithm computes a final set of forces by maintaining a desired tradeoff between the balance and style feedback.

40. Simulation of Stylized … (cont) • Dynamic balance is a hard problem • Many dof -> infinite solutions • Numerically unstable -> most states invalid • Valid states may be balanced, but awkward • i.e. if you have a tendency to lean to the left, cranking your head to the right may help you to balance but it is not the most natural way to address the issue.

41. Simulation of Stylized … (cont) • To mitigate these problems, the authors: • Project the higher detail (60 DOF) biped onto a low detail (9 DOF, 6 Actuator DOF) model • Use a piecewise linear model to approximate the non-linear dynamics of the reduced detail model. • i.e F=MA, where M is a constant matrix. • Use a Linear Quadratic Regulator (LQR) that tracks the animation data • Assumes that poses are dynamically stable • Eliminates the need to explicitly search for any dynamically stable state.

42. Simulation of Stylized … (cont) • The 3 link model’s root is the contact foot and it has two 3 DOF actuators acting at the hips • One for the torso • One for the swing leg • The linearalized dynamic equations are precomputed, rolled together with the equations necessary for the LQR, factored and stored for each time step. • This amounts to about 20k per second of animation • The full character would require about 2 meg per second. • Aside: Is 60hz necessary?

43. Interactive Simulation of Stylized Human LocomotionMarco da Silva, Yeuhi Abe, Jovan Popović - SIGGRAPH 08 • [Video]

44. Simulation of Stylized … (cont) The results are promising: • Maintains lifelike human motion in dynamic environments, which is difficult to accomplish with kinematics or dynamics alone • Transforms a single recorded motion, valid for one environment only, into a general purpose action that can be used in many other settings or even composed with other actions to create versatile characters. • Performance reasonable in worst case, plenty of room for optimizations in normal situations.

45. Dynamo: dynamic, data-driven character control with adjustable balanceACM Siggraph Video Game Symposium PawelWrotek, OdestChadwicke Jenkins, Morgan McGuire • Combines blended animation with the results of a physical simulation • 6 DOF springs are attached to the root of the dynamic model to keep it from falling over.

46. Dynamo: dynamic, data-driven character control with adjustable balanceACM Siggraph Video Game Symposium PawelWrotek, OdestChadwicke Jenkins, Morgan McGuire While not mentioned explicitly by the authors, blending in world space helps preserve the momentum characteristics of the source animations, thus making the result more physically plausible (if the source animations is physically plausible)

47. Dynamo: dynamic, data-driven character control with adjustable balanceACM Siggraph Video Game Symposium PawelWrotek, OdestChadwicke Jenkins, Morgan McGuire • The reason for the improved preservation of momentum in world space is the fact that the Hessian describing the system dynamics in world space coordinates varies less across poses than the corresponding Hessian describing the system dynamics in joint space. • This insight is arguably the primary take-away from the paper. • A natural corollary is that physical controllers will usually be more robust when operating in world space. • The authors point out this observation in the diagram below.

48. Animating reactive motion using Momentum-based Inverse KinematicsTaku Komura, Edmond S. L. Ho and Rynson W. H. LauVirtual Worlds 2005

49. Animating reactive motion … (cont) • System designed for dynamic reactions that allow for recovery. • Intended to bridge the gap between Ragdolls and layered hit reactions for mild impacts that do not affect the characters momentum or trajectory • Animations with different stepping strategies form the basis for reactions • Foot placement of animations is modified counteract the characters momentum. • This balance strategy is basis for Asimo’s control system • The ideal foot placement point is called the Zero Moment Point

50. Animating reactive motion … (cont) • Momentum Based IK consists of: • Constraining a kinematic motion to conserve momentum each frame • This is achieved by running a physical simulation in which only the non-essential DOF have finite inertia. • Initial DOF accelerations are computed using backwards differencing between the prior state and the animation sample. • Playing back the new, modified animation. • System must be able to maintain velocity/momentum, along with state across frames