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CS 231

Inverse KinematicsIntro to Motion Capture

CS 231CS 231

Inverse KinematicsInverse KinematicsIntro to Motion CaptureIntro to Motion Capture

3D characters3D characters

RepresentationRepresentation

1)1) SkeletonSkeletonOrigin (root)Origin (root)Joint centers/Joint centers/bones lengthsbones lengths

2) 2) KeyframesKeyframesPos/Rot Root (x)Pos/Rot Root (x)Joint Angles (q)Joint Angles (q)

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Kinematics Kinematics –– study of static movementstudy of static movement

easy to computeeasy to compute intuitive to controlintuitive to controlpositioning hand/feetpositioning hand/feethigherhigher--level goalslevel goals

Forward: Forward: xx = = f(f()) Inverse: Inverse: = f= f--11((xx))

xx

)sin()sin()sin(

)cos()cos()cos(

332211

332211

llly

lllx

?

Base

1

2End Effector

3

1l2l

3l

Forward Kinematics

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What is it?What is it?

BaseBase

12 3

End End EffectorEffector

Inverse Kinematics (IK)Inverse Kinematics (IK)

Solving IK Solving IK

KinematicKinematic equations equations

)sin()sin()sin(

)cos()cos()cos(

332211

332211

llly

lllx

Number of equation : 2Number of equation : 2Unknown variables : 3Unknown variables : 3

Infinite number of solutions !Infinite number of solutions !

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RedundancyRedundancy

System DOF > End System DOF > End EffectorEffector DOFDOF

)sin()sin()sin(

)cos()cos()cos(

332211

332211

llly

lllx

System DOF = 3System DOF = 3End End EffectorEffector DOF = 2DOF = 2

Redundancy in humans?Redundancy in humans?

A redundant system has infinite number of A redundant system has infinite number of solutionssolutions

Human skeleton has 70 DOFHuman skeleton has 70 DOFSuper redundantSuper redundant

How to solve highly redundant system?How to solve highly redundant system?

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Some intuition: NaturalnessSome intuition: Naturalness

Based on observation of natural human Based on observation of natural human posture posture

NeurophysiologicalNeurophysiological/ / biomechbiomech experimentsexperiments

ExampleExampleHybrid/analytical solution for human armHybrid/analytical solution for human armComfort poseComfort posePlanningPlanning

Inverse Kinematics SolversInverse Kinematics Solvers

Analytical Analytical -- only for simplest systems only for simplest systems Optimization Optimization -- requires performance criteriarequires performance criteriaHybrid Hybrid -- combine heuristic and optimizationcombine heuristic and optimization

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Nonlinear OptimizationNonlinear Optimization

Optimization ProblemOptimization Problem

)( minimize θGoal

Available Optimization PackagesAvailable Optimization PackagesMATLAB, MATLAB, Numerical RecipesNumerical RecipesEtc...Etc...

BaseBase

12 3

End End EffectorEffector

GoalGoal

distancedistance

2

eg pp Position GoalPosition Goal

Goal Potential FunctionGoal Potential Function

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JacobianJacobian

JacobianJacobian MatrixMatrixLinearly relates endLinearly relates end--effectoreffector change to joint change to joint

angle changeangle change

)(θx f θJx

xJθ 1 θ

J

f

Differential KinematicsDifferential Kinematics

33--link arm examplelink arm example

332211

332211

2

1

sinsinsin

coscoscos

)(

)(

lll

lll

f

f

y

x

θ

θ

3

2

1

J

y

x

3

2

2

2

1

2

3

1

2

1

1

1

)()()(

)()()(

θθθ

θθθ

Jfff

fff

332211

332211

coscoscos

sinsinsin

lll

lll

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Differential KinematicsDifferential Kinematics

J is not always invertibleJ is not always invertible

Remedy : Pseudo InverseRemedy : Pseudo Inverse

1TT )(JJJJ

xJθ

Gaussian EliminationGaussian Elimination

(use MATLAB, etc.)(use MATLAB, etc.)

Calculating Pseudo Inverse?Calculating Pseudo Inverse?

Problems with IKProblems with IK

Will G(Will G() be always zero?) be always zero?

No : Unreachable WorkspaceNo : Unreachable Workspace

Will the solution be always found?Will the solution be always found?

No : Local Minima/Singular ConfigurationNo : Local Minima/Singular Configuration

Will the solution be always unique?Will the solution be always unique?

No : RedundancyNo : Redundancy

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Apply to arms and legsApply to arms and legs

Lee and Chen '99Lee and Chen '99

oo

end end effectoreffector

lengthlength

Hybrid SolutionsHybrid Solutions

Constrained optimization with fewer variablesConstrained optimization with fewer variables--oneone--variable parameterization for arms and legsvariable parameterization for arms and legs

Hybrid SolutionsHybrid Solutions

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““EElbowlbow CircleCircle””[[KoreinKorein and and BadlerBadler 82]82]

Hybrid SolutionsHybrid Solutions

coscos ((qqelbowelbow) = (L) = (L22 –– LL1122 -- LL22

2 2 ) / 2 L) / 2 L11 LL22Still must choose Still must choose ““swivel angleswivel angle””

Hybrid SolutionsHybrid Solutions

oo

end end effectoreffector

lengthlength

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Hybrid solution: IKANHybrid solution: IKAN

““Inverse Kinematics using Inverse Kinematics using ANalyticalANalytical MethodsMethods”” IK for an IK for an anthropomorphic arm or leganthropomorphic arm or leg

Combination of analytic and numerical methods to solve Combination of analytic and numerical methods to solve generalized inverse kinematics problems generalized inverse kinematics problems

Results faster and more reliable than conventional inverse Results faster and more reliable than conventional inverse jacobianjacobian and optimization based techniques.and optimization based techniques.

Download IKAN from Download IKAN from SourceForgeSourceForge

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Motion Capture Animation TechnologiesMotion Capture Animation TechnologiesMotion Capture Animation Technologies

Motivation Motivation

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What is motion capture?What is motion capture?

Recording data from the Recording data from the real world and using it to animatereal world and using it to animate

Usually, one of a few specific Usually, one of a few specific technologies used to capture a technologies used to capture a human actor in order to animate human actor in order to animate a charactera character

Got its start in biomechanicsGot its start in biomechanics

Why use motion capture?Why use motion capture?

Captures realistic movements, can beCaptures realistic movements, can bespecific to individuals, good for specific to individuals, good for athletics and physical activitiesathletics and physical activities

Can capture Can capture alotalot of data reasonably quicklyof data reasonably quickly

Can capture onCan capture on--thethe--fly for realfly for real--time time performance and interactivityperformance and interactivity

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Where is motion capture used? Many games, capture celebrities, lifelike motion

What are the issues? What are the issues?

Recording the data accurately and quicklyRecording the data accurately and quickly--types of technologiestypes of technologies--running a motion capture shootrunning a motion capture shoot

Applying the data to the characterApplying the data to the character--filtering the datafiltering the data--fitting to a skeletonfitting to a skeleton

Editing motion data postEditing motion data post--mortemmortem--changing and concatenatingchanging and concatenating--generalized motion from a generalized motion from a

databasedatabase

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Types of technologies Types of technologies -- Optical SystemsOptical Systems

ViconVicon (also Motion Analysis)(also Motion Analysis)

Types of technologies Types of technologies -- Optical SystemsOptical Systems

1010--24 cameras 24 cameras 1000 frames/sec at 1280x1024 resolution (!)1000 frames/sec at 1280x1024 resolution (!)4mm size marker @ 10m within < 1mm4mm size marker @ 10m within < 1mmCost: $30Cost: $30--150K+150K+

Plus: High data ratePlus: High data rateBest motion in the industry!Best motion in the industry!

Minus: Expense Minus: Expense OcclusionOcclusionRelies on software for data resolutionRelies on software for data resolution

AlternativeAlternative-- Rent a day in the studio: $10Rent a day in the studio: $10--20K20K

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Types of technologies Types of technologies -- Active Optical SystemsActive Optical Systems

Ascension's Reactor (Ascension's Reactor (OptotrakOptotrak, , PhaseSpacePhaseSpace))

Types of technologies Types of technologies -- Active Optical SystemsActive Optical Systems

540 cameras540 cameras900 measures/second (up to 60 frames/sec)900 measures/second (up to 60 frames/sec)

Capture region: 3x4meters Capture region: 3x4meters Cost: ~$70K Cost: ~$70K

Plus: Minimal data loss after occlusion rePlus: Minimal data loss after occlusion re--identifiesidentifiesNo environment restrictionsNo environment restrictionsReasonably priced ?Reasonably priced ?

Minus: Low capture rate, small regionMinus: Low capture rate, small region

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Types of technologies Types of technologies -- Electromagnetic SystemsElectromagnetic Systems

Ascension (Ascension (PolhemusPolhemus) ) –– tethered and tethered and tetherlesstetherless

Types of technologies Types of technologies -- Electromagnetic SystemsElectromagnetic Systems

18 sensors six 18 sensors six dof'sdof's120 frames/sec120 frames/sec<1 cm/~1degree accuracy<1 cm/~1degree accuracy3m circular capture area3m circular capture areaCost: ~$50KCost: ~$50K

Plus: No occlusionPlus: No occlusionOrientation information recordedOrientation information recorded

Minus: Environment restrictionsMinus: Environment restrictionsCan be bulky Can be bulky

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Types of technologies Types of technologies -- Mechanical SystemsMechanical Systems

ExoskeletonsExoskeletonsJoint sensors plus a gyroscope Joint sensors plus a gyroscope

Types of technologies Types of technologies -- Mechanical SystemsMechanical Systems

500 samples/second500 samples/secondNo range limits/Wired systemNo range limits/Wired systemCost: ~40KCost: ~40K

Plus: Fits a rigid body skeleton wellPlus: Fits a rigid body skeleton wellHigh data rateHigh data rate

Minus: TetheredMinus: TetheredNot accurate in body location/orientationNot accurate in body location/orientation

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Types of technologies Types of technologies -- Mechanical SystemsMechanical Systems

Monkeys and other input devices Monkeys and other input devices

The PipelineThe Pipeline

BodenheimerBodenheimer et al 97et al 97

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On limbs On limbs vsvs joints joints –– neither is idealneither is ideal

Over tight clothing or thin skinOver tight clothing or thin skin

In repeatable 'landmarks'In repeatable 'landmarks'

Using standard marker setsUsing standard marker sets

Marker placementMarker placement

Marker placementMarker placement

MagneticMagnetic OpticalOptical

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Using marker data Using marker data -- mappingmapping

Problems: no perfect match, jointProblems: no perfect match, joint--center and rigidcenter and rigid--body assumptions, body assumptions, limits on ranges of motion, aesthetic and production requiremlimits on ranges of motion, aesthetic and production requirementsents

Using marker data Using marker data -- skeleton estimationskeleton estimation

OO’’Brien et al 99Brien et al 99

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Sources of noiseSources of noise

Outliers Outliers

Joints are approximated as pivotsJoints are approximated as pivots

Simplifications (like a rigid back)Simplifications (like a rigid back)

Markers move on the skin, clothingMarkers move on the skin, clothing

Errors may accumulateErrors may accumulate

FilteringFiltering

Gets rid of outliersGets rid of outliers

Smoothes dataSmoothes data

But removes important details!But removes important details!

All data is filteredAll data is filtered

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Some notes about IK and Some notes about IK and mocapmocap

FullFull--body IK starting from rootbody IK starting from rootplaces feet on the ground places feet on the ground –– assumes bodyassumes bodyroot is correct, (foot slide becomes a new root is correct, (foot slide becomes a new problem)problem)

FrameFrame--toto--frame coherence achievedframe coherence achievedby initializing frame with previousby initializing frame with previous

Known problems with the dataKnown problems with the data

Correcting errors Correcting errors

Modifying data to fit your characterModifying data to fit your character

Edit the data to do something newEdit the data to do something new

Connecting data sequencesConnecting data sequences

Generalize a pool of dataGeneralize a pool of data