cnm 190 advanced digital animation lec 10 : inverse kinematics & automating animation

CNM 190CNM 190Advanced Digital AnimationAdvanced Digital Animation

Lec 10 : Inverse Kinematics & Automating Lec 10 : Inverse Kinematics & Automating AnimationAnimation

Dan GarciaDan Garcia, EECS (co-instructor), EECS (co-instructor)

Greg Niemeyer, Art (co-instructor)Greg Niemeyer, Art (co-instructor)

Jeremy HuddlestonJeremy Huddleston, EECS (TA), EECS (TA)

A ski-jumping Luxo, Jr. from A ski-jumping Luxo, Jr. from Spacetime Constraints,Spacetime Constraints, 1988 1988

2/12Inverse Kinematics & Automating Animationhttp://inst.eecs.berkeley.edu/~selfpace/CNM190

OverviewOverview

DanDan Forward vs Forward vs

Inverse Inverse KinematicsKinematics

Automating Automating AnimationAnimation

Short film studyShort film study BoundingBounding Mike’s new carMike’s new car For the BirdsFor the Birds In the RoughIn the Rough

JeremyJeremy Demo of Mel tools Demo of Mel tools

forfor Importing dataImporting data Creating UI elementsCreating UI elements


Background You Know Background You Know AlreadyAlready

3D rigid model3D rigid model Usually given in “da Vinci” Usually given in “da Vinci”

or “relaxed bind” poseor “relaxed bind” pose RiggingRigging

Designing a hierarchical Designing a hierarchical skeletonskeleton

Use fewest joints as Use fewest joints as possible!possible!

BindingBinding Connecting the character’s Connecting the character’s

geometry to its skeletongeometry to its skeleton AnimationAnimation

Moving skeleton moves Moving skeleton moves character due to bindingcharacter due to binding

How to animate?How to animate?

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.


Forward vs Inverse Forward vs Inverse KinematicsKinematics

Forward Forward KinematicsKinematics (x,y,z) (x,y,z) Rotate top-level Rotate top-level

joints and the joints and the children joints children joints follow follow automaticallyautomatically

No ambiguityNo ambiguity

Inverse Inverse KinematicsKinematics (x,y,z) (x,y,z) Position the end Position the end

joints and the joints and the inner joints bend inner joints bend to compensateto compensate

Usu lots of Usu lots of solutions!solutions!

(x,y,z)-(x,y,z)-spacespace

--spacespace

FK FK IKIK


How Does IK Work?How Does IK Work?

You are at point PYou are at point P00 in in N-dim N-dim jointjoint space space

You’re asked to move to You’re asked to move to (x,y,z,…) point P(x,y,z,…) point P11

It’s not clear what values of It’s not clear what values of yield that (x,y,z,…)yield that (x,y,z,…)

How do we get there?How do we get there? Answer: IK SolverAnswer: IK Solver

Any algorithm for doing this Any algorithm for doing this successfullysuccessfully

Must factor in torques, dead Must factor in torques, dead spaces due to constraints, spaces due to constraints, total energytotal energy

PP00

PP11


Let’s Look at a 2D Let’s Look at a 2D Example (1)Example (1)

Two-jointed, robot Two-jointed, robot arm with red targetarm with red target

We can measure how We can measure how close we are at any close we are at any point (from a,b->x,y)point (from a,b->x,y)

If we did this for all If we did this for all a,b angles, we’d get a,b angles, we’d get the graph to the rightthe graph to the right Brightness is distance Brightness is distance

to the red goalto the red goal We only know answer We only know answer

locally -- we search!locally -- we search!

freespace.virgin.net/hugo.elias/models/m_ik2.htm




are needed to see this picture. aa

bb



Two-jointed robot arm with Two-jointed robot arm with red goal targetred goal target

Rotating joint A moves the Rotating joint A moves the tip in tip in aa direction direction This gets us closer to the This gets us closer to the

solution solution Rotating joint B moves the Rotating joint B moves the

tip in tip in bb direction direction Here, this is of no useHere, this is of no use

Most joints can rotate both Most joints can rotate both clockwise and counter-clockwise and counter-clockwiseclockwise After After aa rotates a bit, we rotates a bit, we

need to reverse-rotate need to reverse-rotate b b to to extendextend

We do this entire process We do this entire process incrementally, with small incrementally, with small aa, , bb






Graph below shows error Graph below shows error (distance to target) with (distance to target) with contour equal value linescontour equal value lines

We examine local gradientWe examine local gradient Which direction leads us Which direction leads us

fastest downhill? Go there!fastest downhill? Go there! ““Simple Gradient Simple Gradient

Following”, also known as Following”, also known as “greedy”“greedy”

Do this over and over until Do this over and over until you can’t go anymoreyou can’t go anymore

When you stop, either When you stop, either you’reyou’re There, and you’re done!There, and you’re done! Not there, and you’ve Not there, and you’ve

reachedreached A local minimumA local minimum A constraint-based A constraint-based

minimumminimum








Pose PPose P





Two ways to calculate Two ways to calculate gradient:gradient: By measurement (move, calc)By measurement (move, calc) By calculation (thanks, By calculation (thanks,

Newton)Newton)


QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

for each joint if 3D: axis = axis of rotation for this joint if 2D: axis = (0, 0, 1)ToTip = tip - joint_centreToTarget = target - tipmovement_vector = crossproduct(ToTip, axis) gradient = dotproduct(movement_vector, ToTarget) end loop


Let’s Look at a 3D Let’s Look at a 3D ExampleExample

You don’t need to You don’t need to always specify a always specify a fixed point in space fixed point in space for your end joint.for your end joint.

Alternatively, you Alternatively, you could specify could specify another locus of another locus of points and move to points and move to the closest point on the closest point on the surfacethe surface









When to use FK vs IK?When to use FK vs IK?

FKFK Can control the Can control the

rotation of a single rotation of a single joint and lock joint and lock othersothers

No unexpected No unexpected elbow/knee flippingelbow/knee flipping

Natural “arcs” by Natural “arcs” by defaultdefault

Works with multi-Works with multi-joints as expectedjoints as expected

IKIK Only need to move Only need to move

a single object to a single object to posepose

Can lock down an Can lock down an end effector (like end effector (like wrist or ankle) while wrist or ankle) while rest of body movesrest of body moves

Good w/2-joint Good w/2-joint chainschains

Great for legs!Great for legs!


Automating AnimationAutomating Animation Delightful SIGGRAPH Delightful SIGGRAPH

1988 paper entitled: 1988 paper entitled: “Spacetime Constraints”“Spacetime Constraints” Set up a system with real Set up a system with real

physics (torques, gravity)physics (torques, gravity) ……with space AND time as with space AND time as

part of the object’s posepart of the object’s pose Let the system try to Let the system try to

figure out how to optimizefigure out how to optimize Automatic animation!Automatic animation!

Very powerful idea, Very powerful idea, could use it in Olympic could use it in Olympic training simulationtraining simulation

cnm 190 advanced digital animation lec 10 : inverse kinematics & automating animation

Documents

htmabinverse kinematics

htminverse kinematics

htmpose pinverse kinematics

spacefk ikinverse kinematics

joint b

d example

children joints

toplevel joints