Interactive performances with style and substance.
ANIMATION WITH MOMENTUM
David Wu
Microsoft Game Studios
GDC 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?
Trends of Best Selling Games
100
80
60
Mean Physics and
Animation
Quality*
40
20
0
2010
2011
2012
2013
* figures beyond
2009 are estimates
SIMBICON: Simple Biped Locomotion Control
SIGGRAPH ‘07
Kang Kang Yin, Kevin Loken, Michiel van de Panne
 Goal is to create a robust  Last goal seems to be
control system for
bipeds that can:
treated as an
afterthought
 Balance
 Walk with various gaits
 Handle external
 Quality and results are not
mentioned
 Not quantifiable?
 This is a first order
concern for games.
perturbations such as
varying terrain and being
pushed
 Robustness as measured
 Transition between
by physical simulation
animations
results is treated as the
 Approximate animations
highest priority result.
from motion capture
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.
Integrator receives
forces and torques,
forward dynamics
equations are solved
and the world state
accordingly
Walk Finite State Machine
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)
SIMBICON: Simple Biped Locomotion Control
SIGGRAPH ’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.
SIMBICON: Simple Biped Locomotion Control
SIGGRAPH ’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
Raiberts Hopper is Simple and
effective. Unfortunately it cannot
balance when stationary.
SIMBICON: Simple Biped Locomotion Control
SIGGRAPH ’07 (continued)
Kang Kang Yin, Kevin Loken, Michiel van de Panne
 [Video]
Continuation Methods for
Adapting Simulated Skills
KangkangYin, StelianCorosPhilippe Beadoin, Michielvan 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 for
Adapting Simulated Skills
KangkangYin, StelianCorosPhilippe Beadoin, Michielvan de Panne SIGGRAPH’08
 Continuation Methods:
Continuation Methods for
Adapting Simulated Skills
KangkangYin, StelianCorosPhilippe Beadoin, Michielvan de Panne SIGGRAPH’08
 [Video]
Ad Hoc Meta-analysis of perceived error
in physically simulated characters
David 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 Skills
Stelian 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 Skills
Stelian 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 Skills
Stelian 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 Skills
Stelian Coros, 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
Synthesis of Constrained Walking Skills
Stelian Coros, 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.
Synthesis of Constrained Walking Skills
Stelian Coros, Philippe Beaudoin, Kang Kang Yin, Michiel van de Panne
Siggraph Asia 08
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.
Synthesis of Constrained Walking Skills
Stelian 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.
Flexible Registration of Human Motion
Data with Parameterized Motion Models
Yen-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 coordinates
Yuting 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 Data
Kwang 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.
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
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.
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?
Interactive Simulation of Stylized
Human Locomotion
Marco 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.
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.
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
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.
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.
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.
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?
Interactive Simulation of Stylized
Human Locomotion
Marco da Silva, Yeuhi Abe, Jovan Popović - SIGGRAPH 08
 [Video]
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.
Dynamo: dynamic, data-driven character
control with adjustable balance
ACM Siggraph Video Game Symposium
Pawel Wrotek, Odest Chadwicke 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.
Dynamo: dynamic, data-driven character
control with adjustable balance
ACM 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)
Dynamo: dynamic, data-driven character
control with adjustable balance
ACM Siggraph Video Game Symposium
Pawel Wrotek, Odest Chadwicke 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.
Animating reactive motion using Momentumbased Inverse Kinematics
Taku Komura, Edmond S. L. Ho and Rynson W. H. Lau
Virtual Worlds 2005
Impact
Find 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 Games
Victor B. Zordan, Adriano Macchietto, Jose Medina, Maarc
Soriano, Chun-Chih Wu, I3D 07
Motion
Reaction Animation
Impact
Impact
q(t)
Find Reaction
Simulation
Simulation
Time
Blend Simulation ->
Reaction Animation
Reaction Animation
Blend
Interactive Dynamic Response … (cont)
 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]
Anticipation from Example
Victor Zordan, Chun-Chih Wu, et al.
Defensive Motion
Reaction Animation
Impact
Detect Impact
q(t)
Simulation
Impact
Defensive Motion
Find Reaction
Simulation
Time
Blend Simulation ->
Reaction Animation
Reaction Animation
Blend
Simple Steps for Simply Stepping
Victor Zordan, Chun-Chih Wu, et al.
Visual Computing 2008
 “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
Predict Momentum
Find suitable step
motion
Adjust for situation
based on Balance
Combine with dynamic
constraints and existing
motion
Kinematic Playback
Wrap: Research, Animation and Physics
 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.
Figure 3: When shipping a game, elegance and simplicity occasionally slip.
When publishing a paper, elegance and simplicity occasionally slip.
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.
Characters that preserve the personality and style of their
seamlessly interact with a
physically simulated world and take orders
animations,
the gamepad of abusive players and confused AIs.
 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:
from
Characters that preserve the personality and style of their
animations, seamlessly interact with a physically simulated
take orders from the gamepad of
abusive players and confused AIs.
world and
 I found two papers addressing this concern
 Ideas and or results are depressing
 Not worth mentioning
 They are:
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