animation with momentum

ANIMATION WITH MOMENTUMInteractive performances with style and substance.

David WuMicrosoft Game StudiosGDC 2009

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.

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

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.

Will Compelling Characters and Physics make my game Sell?

2010 2011 2012 20130

102030405060708090

100

Trends of Best Selling Games

Mean Physics and Animation Quality*

* figures beyond 2009 are estimates

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.

Van de Panne’s Animation PipelineAnimation Data

Controller

MixerIntegrator

WorldState Render

• 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.

In addition to feeding the Mixer,

closed loop feedback is required to

determine FSM transitions.

(i.e. Heel Strike)

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

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.

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

SIMBICON: Simple Biped Locomotion ControlSIGGRAPH ’07 (continued)Kang Kang Yin, Kevin Loken, Michiel van de Panne

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

[Video]

SIMBICON: Simple Biped Locomotion ControlSIGGRAPH ’07 (continued)Kang Kang Yin, Kevin Loken, Michiel van de Panne

Continuation Methods forAdapting Simulated SkillsKangkang Yin, Stelian Coros 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.

Continuation Methods forAdapting Simulated SkillsKangkang Yin, Stelian Coros Philippe Beadoin, Michiel van de Panne SIGGRAPH’08 Continuation Methods:

Continuation Methods forAdapting Simulated SkillsKangkang Yin, Stelian Coros Philippe Beadoin, Michiel van de Panne SIGGRAPH’08 [Video]

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, Petros Faloutsos, Flipping with physics:

motion editing for acrobatics, Eurographics animation 2007 Yeuhi Abe , C. Karen Liu , Zoran Popovic, Momentum-based

parameterization of dynamic character motion, Graphical Models 2006

Carol O'Sullivan , John Dingliana , Thanh Giang , 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

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.

Synthesis of Constrained Walking SkillsStelian Coros, 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.

Synthesis of Constrained Walking SkillsStelian Coros, 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.

Synthesis of Constrained Walking SkillsStelian Coros, 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.

Synthesis of Constrained Walking SkillsStelian Coros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne Siggraph Asia 08Takeaways 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

Synthesis of Constrained Walking SkillsStelian Coros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne Siggraph Asia 08Take-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.

Not Mickey Mouse

Synthesis of Constrained Walking SkillsStelian Coros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne Siggraph Asia 08Take-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.

Synthesis of Constrained Walking SkillsStelian Coros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne Siggraph Asia 08

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.

Not Mickey Mouse

Flexible Registration of Human Motion Data with Parameterized Motion ModelsYen-Lin Chen, Jian Yuan Miny, Jinxiang Chaiz

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

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.

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

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’’

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.

Animating responsive characters… (cont) [video]

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.

Simulating Biped Behaviors from Human Motion DataKwang Won, Sok Manmyung 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.

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.

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

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.


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?


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.

• 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.

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


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.


Dynamic balance is a hard problem

Many dof -> infinite solutionsNumerically 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.


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.


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?


[Video]

Interactive Simulation of Stylized Human LocomotionMarco da Silva, Yeuhi Abe, Jovan Popović - SIGGRAPH 08

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.


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.

Dynamo: dynamic, data-driven character control with adjustable balanceACM Siggraph Video Game Symposium Pawel Wrotek, Odest Chadwicke 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)


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.


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

ImpactFind animation

for balance recovery

Modify Animation to match

momentum

“Momentum Based IK” blends

Simulation+Reaction

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

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

Animating reactive motion … (cont)

Seems quite effective in theory Unfortunately I was unable to find a video

Fits in nicely with existing systems Performance cost is low Not too far from what some people do

currently

Interactive Dynamic Response for GamesVictor B. Zordan, Adriano Macchietto, Jose Medina, Maarc Soriano, Chun-Chih Wu, I3D 07

Motion

Impact

Simulation

Blend Simulation -> Reaction Animation

Reaction Animation

Time

q(t)Impact

Reaction Animation

BlendFind Reaction

Simulation

Assumes many hit reactions (paper cited 500 in their tests)

Finding the appropriate reaction becomes a bottleneck Uses an optimized search tree based on a Support Vector

Machine (SVM) Quality of SVM is highly dependent on the DOF used in

classification Tried many combinations Optimal set of DOF was 20 in total:

Momentum (linear and angular) at various time steps surrounding the impact

Center of mass at same time steps Orientation at time of impact

Once a good SVM is constructed, real time search is feasible for a large number of motions Time to find animation was cited as ~2 ms vs 2 seconds prior

to the SVM.

Interactive Dynamic Response … (cont)

[video]

Interactive Dynamic Response … (cont)

Anticipation from ExampleVictor Zordan, Chun-Chih Wu, et al.

Defensive Motion

Impact

Simulation

Blend Simulation -> Reaction Animation

Reaction Animation

Time

q(t)

Impact

Reaction Animation

BlendFind Reaction

Simulation

Detect Impact

Defensive Motion

Simple Steps for Simply SteppingVictor Zordan, Chun-Chih Wu, et al.Visual Computing 2008

Predict Momentum

Find suitable step motion

Adjust for situation based on Balance

Kinematic Playback

“Inspired” by the paper Animating reactive motion using Momentum-based Inverse Kinematics

Uses Momentum based IK to drop animation

Uses principles of Dynamic Balance/Zero moment point to synthesize steps from example

Wrap: Research, Animation and Physics

Figure 3: When shipping a game, elegance and simplicity occasionally slip.When publishing a paper, elegance and simplicity occasionally slip.

There is a lot of great research and many ideas with strong potential.

When evaluating ideas, it is important to remember that the whole is not always greater than the sum of its parts.

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.

Just about every successful entertainment medium features compelling characters – personality and style are essential.

Animators are often better at creating compelling characters than random algorithms/equations.

In games we have Animators (hopefully) and many algorithms/equations. Presenting optimal relevant algorithms that

preserve the personality and style of characters/animators is the focus of this lecture.

Interactivity defines a video game. A non-interactive game is a movie.

Physics is a powerful tool that can enable Interactivity through simulation. There are other ways but they suck They are:

BEYOND THE SCOPE

OF THIS LECTURE

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.

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. I found two papers addressing this

concern Ideas and or results are depressing Not worth mentioning They are:

BEYOND THE SCOPE

OF THIS LECTURE

Questions & Answers

Figure 1: Physical feasibility is one of many challenges faced by otherwise content virtual people.

Past End of File.You should not be here. Please shut down current application. Reboot if necessary.

Problem: Game is Interactive.Animation Database is not. Modeling the large space of animations that may

be required at any moment due to open ended nature of player actions is non-trivial

Rule based controllers handle this via animation selection guided by heuristics. i.e. pre-authored decision tree populated with animation

clips. Many problems and failure cases Still the basis for many animation systems

Apparently academia sees this as a problem - over the last five years, the amount of research dedicated to this problem has grown exponentially.

The Arsenal Meta techniques

Generalizing from examples Interpolate and/or extrapolate from source animations Weighted blend of source (convex interpolation) Transform source to a new basis using direct techniques (i.e. PCA) Use source to train/derive more complex models. Splice to micro motion snippets and transition rapidly

Synthesis Physical Simulation

Rag dolls Secondary dynamics

Kinematic and/or Dynamic Constraints Inverse Kinematics “Physics Filter”

Physically based controllers General Human biometric data

The best solutions tend to be hybrid implementations of these techniques, as each has its limitations and strengths.

Hence the term “Arsenal”: Use, understand, build, augment, combine, patent

Generation and Visualization of Emotional States in Virtual Characters

Diana Arellano , Javier Varona , Francisco Perales CASA 08

The aim of this paper is to model characters that have PERSONALITY, feel EMOTIONS and can MANIFEST EMOTIONAL STATES

The motive is to create unique, real, distinguishable individuals depending on their personalities and emotional states

animation with momentum

Documents

momentum animation

jointseach animation

source animation

interactive animation

field of interactive

world state

physical controller

simple finite state