Analyzing the Physical Correctness of Interpolated Human Motion

HEctor CuNat NUNezValentijn Muijers

Linear interpolation of human motions

Simple technique used over the past 10 years with surprisingly natural looking results…

…BUT……it has been said that the physics of the resulting motion are incorrect.

Linear interpolation of human motions

• Why does this technique produce such good results?

• Which input motions produce results that are physical correct? Which ones produce incorrect results?

• When the results are physically incorrect… is there any modification we can do in order to fix it?

Analysis

Linear interpolation of 2 motions (I)

interpolation of 2 motions, being each motion:

: position of the root segment.

Q(t): orientation of the root and the relative angles of the character’s joints.

t :time of a particular frame.

Requirements for interpolating 2 motions:

• The input motions must be scaled in time in order to align key events.

• These key events are located at changes in the contact with the environment (such as ground contact).

• Based on these key events, the motions are split into phases.

Linear interpolation of 2 motions (II)

Example:

We compute motion M by interpolating the root positions and all the joint angles of motions M1 and M2:

Analysis

1. During Flight phases:1.1. Linear Momentum

1.2. Angular Momentum

2. During contact phases:2.1. Non-sliding foot contact

2.2. Static Balance2.3. Friction cone.

3. Transition between phases.

Analysis

1.1. FLIGHT PHASE: Linear Momentum (I)

THE Z component SHOULD BE A straight line…

(the only external force acting on the character IS gravity (Y direction)).

…However, sometimes it is not:

(a) Forward jump with no turn.

(b) Forward jump with 360 ºturn.

(c) Result form interpolating the previous 2 motions.

Analysis1.1. FLIGHT PHASE: Linear Momentum (II)

: Interpolate the center of mass trajectories instead of the root positions…

(root position is now computed from the center of mass position and joint angles)

Gravity IS now the only net external force acting on the character during flight (computing the time of the flight phase AS ).

Analysis1.2. FLIGHT PHASE: Angular Momentum

should be constant during flight …

…BUT, in general that’s not true for a motion computed by interpolating 2 motions.

However…

: Do nothing :) (AS IS unnoticeable)

Even large changes in angular momentum (H)

small changes of angular velocity (Ω)

(cAUSE THE inertia (I) around the x-axis is very large)

2.1. CONTACT PHASE: non-sliding foot contact

Problem: Footsliding when interpolating

: interpolate only the non-redundant degrees of freedom.

Analysis

2.2. CONTACT PHASE: static balance

If projection of Com on ground is within support polygon of feet for both motions at time t…

Interpolated projection of Com is also within support polygon of feet and static balance is achieved.

Analysis

Analysis

To be physically valid ground contact should not require an unreasonably high coeffiction of friction.

Coulomb friction model to analyze the ground contact.

Ratio of ground reaction force and normal component should be smaller than static friction coefficient.

2.3. CONTACT PHASE: Friction cone

Analysis Results

1. During Flight phases:1.1. Linear Momentum (interpolate com instead of root)1.2. Angular Momentum (can be incorrect, but it’s almosT unnoticeable)

2. During contact phases:2.1. Non-sliding foot contact (interpolate only the non-redundant dofs and constrains of the character)2.2. Static Balance (already correct)2.3. Friction cone (already correct)

3. Transition between phases (already correct)

Analysis3. Transition between phases

discontinuity in velocities not noticeable.

rotation during flight phase causes problems because the orientation of the interpolated motion and original motions do not match.

Solution: rotate original motions to align them with the interpolated motion a the end of the flight phase.

this causes small discontinuity in velocity for CoM (see video).

Summary

Embed video provided with the paper

Discussion

• Is this method applicable to game technology?

• How appropiate IS THE pERFORMED ANALYSIS to determine the physical correctness of the motion?