CS 231. Inverse Kinematics Intro to Motion Capture. 3D characters. Representation. 1) Skeleton Origin (root) Joint centers/ bones lengths

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1 CS Inverse Kinematics Intro to Motion Capture Representation D characters ) Skeeton Origin (root) Joint centers/ bones engths ) Keyframes Pos/Rot Root (x) Joint Anges (q)

2 Kinematics study of static movement x Forward: x = f( ) easy to compute Inverse: = f - (x) intuitive to contro positioning hand/feet higher-eve goas Forward Kinematics? End Effector Base x cos( ) y sin( ) cos( ) sin( ) cos( ) sin( )

3 Inverse Kinematics (IK) What is it? End Effector Base Soving IK Kinematic equations x cos( ) y sin( ) cos( ) sin( ) Number of equation : Unknown variabes : cos( ) sin( ) Infinite number of soutions!

4 Redundancy System DOF > End Effector DOF x cos( ) y sin( ) cos( ) sin( ) cos( ) sin( ) System DOF = End Effector DOF = Redundancy in humans? A redundant system has infinite number of soutions Human skeeton has 70 DOF Super redundant How to sove highy redundant system? 4

5 Some intuition: Naturaness Based on observation of natura human posture Neurophysioogica/ biomech experiments Exampe Hybrid/anaytica soution for human arm Comfort pose Panning Inverse Kinematics Sovers Anaytica - ony for simpest systems Optimization - requires performance criteria Hybrid - combine heuristic and optimization 5

6 Noninear Optimization Optimization Probem minimize Goa( θ) Avaiabe Optimization Packages MATLAB, Numerica Recipes Etc... Goa Potentia Function pg p e Position Goa distance Goa End Effector Base 6

7 7 Jacobian Jacobian Jacobian Jacobian Matrix Matrix Lineary reates end Lineary reates end-effector effector change to joint change to joint ange change ange change (θ) x f θ J x x J θ θ J f Differentia Kinematics Differentia Kinematics -ink arm exampe ink arm exampe sin sin sin cos cos cos ) ( ) ( f f y x θ θ J y x ) ( ) ( ) ( ) ( ) ( ) ( θ θ θ θ θ θ J f f f f f f cos cos cos sin sin sin

8 Differentia Kinematics J is not aways invertibe Remedy : Pseudo Inverse T J J (JJ θ J x T ) Cacuating Pseudo Inverse? Gaussian Eimination (use MATLAB, etc.) Probems with IK Wi G() ) be aways zero? No : Unreachabe Workspace Wi the soution be aways found? No : Loca Minima/Singuar Configuration Wi the soution be aways unique? No : Redundancy 8

9 Hybrid Soutions o ength end effector Appy to arms and egs Lee and Chen '99 Hybrid Soutions Constrained optimization with fewer variabes -one-variabe parameterization for arms and egs 9

10 Hybrid Soutions Ebow Circe [Korein and Bader 8] Hybrid Soutions o ength end effector cos (q ebow ) = (L L - L ) / L L Sti must choose swive ange 0

11 Hybrid soution: IKAN Inverse Kinematics using ANaytica Methods IK for an anthropomorphic arm or eg Combination of anaytic and numerica methods to sove generaized inverse kinematics probems Resuts faster and more reiabe than conventiona inverse jacobian and optimization based techniques. Downoad IKAN from SourceForge

12 Motion Capture Animation Technoogies Motivation

13 What is motion capture? Recording data from the rea word and using it to animate Usuay, one of a few specific technoogies used to capture a human actor in order to animate a character Got its start in biomechanics Why use motion capture? Captures reaistic movements, can be specific to individuas, good for athetics and physica activities Can capture aot of data reasonaby quicky Can capture on-the the-fy for rea-time performance and interactivity

14 Where is motion capture used? Many games, capture ceebrities, ifeike motion What are the issues? Recording the data accuratey and quicky -types of technoogies -running a motion capture shoot Appying the data to the character -fitering the data -fitting to a skeeton Editing motion data post-mortem -changing and concatenating -generaized motion from a database 4

15 Types of technoogies - Optica Systems Vicon (aso Motion Anaysis) Types of technoogies - Optica Systems 0-4 cameras 000 frames/sec at 80x04 resoution (!) 4mm size 0m within < mm Cost: $0-50K+ Pus: High data rate Best motion in the industry! Minus: Expense Occusion Reies on software for data resoution Aternative- Rent a day in the studio: $0-0K 5

16 Types of technoogies - Active Optica Systems Ascension's Reactor (Optotrak( Optotrak, PhaseSpace) Types of technoogies - Active Optica Systems 540 cameras 900 measures/second (up to 60 frames/sec) Capture region: x4meters Cost: ~$70K Pus: Minima data oss after occusion re-identifies No environment restrictions Reasonaby priced? Minus: Low capture rate, sma region 6

17 Types of technoogies - Eectromagnetic Systems Ascension (Pohemus( Pohemus) tethered and tetheress Types of technoogies - Eectromagnetic Systems 8 sensors six dof's 0 frames/sec < cm/~degree accuracy m circuar capture area Cost: ~$50K Pus: No occusion Orientation information recorded Minus: Environment restrictions Can be buky 7

18 Types of technoogies - Mechanica Systems Exoskeetons Joint sensors pus a gyroscope Types of technoogies - Mechanica Systems 500 sampes/second No range imits/wired system Cost: ~40K Pus: Fits a rigid body skeeton we High data rate Minus: Tethered Not accurate in body ocation/orientation 8

19 Types of technoogies - Mechanica Systems Monkeys and other input devices The Pipeine Bodenheimer et a 97 9

20 Marker pacement On imbs vs joints neither is idea Over tight cothing or thin skin In repeatabe 'andmarks' Using standard marker sets Marker pacement Magnetic Optica 0

21 Using marker data - mapping Probems: no perfect match, joint-center and rigid-body assumptions, imits on ranges of motion, aesthetic and production requirements ents Using marker data - skeeton estimation O Brien et a 99

22 Sources of noise Outiers Joints are approximated as pivots Simpifications (ike a rigid back) Markers move on the skin, cothing Errors may accumuate Fitering Gets rid of outiers Smoothes data But removes important detais! A data is fitered

23 Some notes about IK and mocap Fu-body IK starting from root paces feet on the ground assumes body root is correct, (foot side becomes a new probem) Frame-to to-frame coherence achieved by initiaizing frame with previous Known probems with the data Correcting errors Modifying data to fit your character Edit the data to do something new Connecting data sequences Generaize a poo of data