Overview Overview Modeling Tension and Modeling Tension and Goal - - PowerPoint PPT Presentation

Modeling Tension and Modeling Tension and Relaxation for Computer Relaxation for Computer Animation Animation

Michael Neff Eugene Fiume University of Toronto

Overview Overview

Goal

– Expressive, realistic character animation

Approach

– Identify characteristics that make human motion expressive – Build them into an animation system

Tension and relaxation one important characteristic

What does modeling tension What does modeling tension buy us? buy us?

Control over the shape of a motion End effects

– Overshoot, pendular motion

Varied reactions to external forces Control of force transference between joints Vary influence of gravity and momentum

• n movements

Background -- Animation Background -- Animation

Hand tuned controllers

– (Hodgins et al. 95, Wooten 98, Faloutsos 01)

Control systems that track trajectories

– (Zordan and Hodgins 99, Kokkevis et al. 96, Lamouret and Cani 95)

Kinematic approaches

– (Chi et al. 00, Perlin 95)

Background Background – – Biomechanics Biomechanics

Human body organizes muscles in agonist- antagonist pairs

– Regulate joint stiffness

Spring-like behaviour an important attribute of muscles Equilibrium point hypothesis

– Humans may move limbs by varying the equilibrium point generated by the muscles around a limb

Many attributes of real muscle not included

Equilibrium Point Control Equilibrium Point Control

Joints are effected by two types of forces

– Active, or internal, forces – External forces

Equilibrium point control balances these forces to achieve the desired angle

– Avoids steady state error due to gravity

Antagonistic Formulation Antagonistic Formulation

2 angular springs in

• pposition and a

damper at each joint

Antagonistic Formulation Antagonistic Formulation

Set point of each spring is fixed and placed just past limit of the joint Position controlled by varying the two gains Equation for antagonistic control: Stiffness is the sum of the two gains

= kL(L ) + kH (H ) kd ˙

Gain Space Gain Space

Any angle is a line in gain space Spring gains for a given angle are related as follows:

kH = kL L eq eq H ExternalForce H eq

Figure of Gain Space Figure of Gain Space

Vary tension by moving along isoangle line.

Sample Isoangle Lines for a Limb

50 100 150 200 50 100 150 200

Gain KL Gain KH

• 10

10 30 50 70 90

PD and Antagonistic Control PD and Antagonistic Control

Since linear springs are used, there is an equivalence between the two.

– (However, interpolating in the two spaces is not necessarily equivalent)

We find antagonistic control to be a more natural parameterization.

– Separates stiffness and position control

Moving a Limb Moving a Limb

• Take the starting gains

Moving a Limb

50 100 150 200 50 100 150 200

Gain K L Gain K H

10

Moving a Limb Moving a Limb

• 2. Determine the isoangle line for the desired end

point.

Moving a Limb

50 100 150 200 50 100 150 200

Gain K L Gain KH

10 70

Moving a Limb Moving a Limb

• 3. Draw a line of slope –1 between the start point

and end line.

Moving a Limb

50 100 150 200 50 100 150 200

Gain KL Gain K H 10 70 Slope -1

Moving a Limb Moving a Limb

• 4. Vary gains by moving along this line in order to

move the limb.

Moving a Limb

50 100 150 200 50 100 150 200

Gain KL Gain K H 10 70 Slope -1

Moving a Limb Moving a Limb

For high tension, the movement of the limb will precisely track the trajectory of the the movement along the line. Low tension more loosely tracks the trajectory.

Effect of Tension on Tracking Effect of Tension on Tracking Shape Control Through Shape Control Through Tension Variation Tension Variation

Changing tension during a transition will change the shape of a trajectory Increasing tension causes the limb to move more quickly at the beginning and slowly at the end Decreasing tension causes the limb to move slowly at the beginning and quickly towards the end of the motion

Shape Control Through Shape Control Through Tension Variation Tension Variation Shape Control Through Shape Control Through Tension Variation Tension Variation

Sample Isoangle Lines for a Limb

50 100 150 200 50 100 150 200

Gain KL Gain KH

• 10

10 30 50 70 90 Slope -1 Reduce Tension

Shape Control Through Shape Control Through Tension Variation Tension Variation

High tension and relaxing nods

Results: Gestures Results: Gestures

Giving the direction “Go left”

Results: Kinematic vs. Tension Results: Kinematic vs. Tension Controlled Controlled

Giving the direction “Go left” - Kinematic

Results: Gestures vs. Tension Results: Gestures vs. Tension Controlled Controlled

Giving the direction “Go left” – w/Tension Control

Results: Postures Results: Postures

Shrug

Results: Anticipation of External Results: Anticipation of External Forces Forces

Shoves with varied tension

Results: Anticipation of External Results: Anticipation of External Forces Forces

Different shove reactions

Discussion Discussion

Shape control by varying tension seems to be easier than trying to adjust transition functions.

– Takes character to correct physical state.

Achieves nicely nuanced movement The techniques are low level, but are meant as a building block to create higher level systems.

Questions? Questions?

www.dgp.toronto.edu/~neff