Procedural Animation of Human Interaction

using Inverse Kinematics and Fuzzy Logic

Gaetan Deglorie

, Koen Samyn

, Peter Lambert

, Rik Van de Walle

and Soﬁe Van Hoecke

ELIS Department, Multimedia Lab, Ghent University-iMinds, Gaston Crommenlaan 8, Bus 201, B-9050 Gent, Belgium

DAE, University College West Flanders, Ghent University Association, Botenkopersstraat 2, 8500 Kortrijk, Belgium

Keywords:

Procedural Animation, Multi-character Interaction, Inverse Kinematics, Fuzzy Logic.

Abstract:

Nowadays, animation of human interaction is predominantly modelled statically. Animations are adapted

manually to each set of participating characters to ensure visual ﬁdelity. To automate this process, we propose

a novel procedural animation technique where character interactions are modelled dynamically with fuzzy

logic and compare our technique to conventional inverse kinematics. The ’handshake’ interaction is used as

an example interaction, in order to illustrate how basic animation rules are deﬁned, while leaving room for

parametrization of character speciﬁc properties. Our results show that, although inverse kinematics delivers

higher precision in positioning than fuzzy logic, they are dependent on paths describing the motion of the ﬁnal

element in the kinematic chain. Fuzzy logic, on the other hand, is independent of such motion paths and solves

towards the target location locally. The presented handshake model using fuzzy logic can serve as a basis for

future models for virtual-human interaction.

1 INTRODUCTION

Video games, movies and simulations often contain

scenes with character interaction. To create anima-

tions for these interactions, a large fraction of pro-

duction resources is spent on manually producing or

recording these animations through motion capture.

Although the resulting animations do not adapt at

runtime without extra processing steps, this property

is highly desirable in dynamic virtual environments.

One approach towards adaptive animation is procedu-

ral animation, where animations are generated algo-

rithmically. Two important problems exist for this ap-

proach: (1) synchronization of separate animation se-

quences of participating characters, and (2) real-time

synthesis in order to generate animations for a speciﬁc

context in a real-time environment.

In this paper, we compare two procedural anima-

tion techniques for animating human interactions:

1. inverse kinematics, where limbs are retargeted

based on joint parameters obtained from kine-

matic equations (Johansen, 2009)

2. fuzzy logic controllers, where the joint parameters

are locally controlled for each joint (Samyn et al.,

2012).

Both procedural animation approaches are compared

using a handshake test case.

The remainder of this paper is as follows. After

an overview of related work in Section 2, the method-

ology of our approach is presented in Section 3. Sec-

tion 4 describes a case study of real-life handshakes,

as well as the concluded rules for deﬁning the virtual

model. Next, in Section 5, the underlying framework

facilitating animations of human interactions is pre-

sented. In Section 6 the model of the handshake is

described in detail. The results are presented in Sec-

tion 7. Finally, the conclusions and future work are

summarised in Section 8.

2 RELATED WORK

In this section, the state-of-the-art on procedural

animation and multi-character animation is reviewed.

Procedural Animation

Multiple variants of procedural animation exist; we

list the ones most relevant to our work.

First, animation retargeting adapts an existing an-

imation to a new context or situation. E.g., the walk

cycle of a character on a ﬂat surface can be adapted to

slanted surfaces. This technique can be implemented

using inverse kinematics (Johansen, 2009).

340

Deglorie G., Samyn K., Lambert P., Van de Walle R. and Van Hoecke S..

Procedural Animation of Human Interaction using Inverse Kinematics and Fuzzy Logic.

DOI: 10.5220/0005310603400347

In Proceedings of the 10th International Conference on Computer Graphics Theory and Applications (GRAPP-2015), pages 340-347

ISBN: 978-989-758-087-1

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

Second, physics-based character animation uti-

lizes real-time physics simulation to animate the

limbs of articulated skeletons. This way, high visual

ﬁdelity is achieved, but the animations lack the high

level of control that is required by traditional anima-

tion artists (Geijtenbeek and Pronost, 2012).

Finally, a third approach procedurally animates

the walk cycle of a character using fuzzy logic

controllers (Samyn et al., 2012). In this paper we

extend this approach to be usable for multi-character

animation.

Multi-character Animation

The creation of animation for multi-character interac-

tions has been approached in literature in a number of

ways.

First, a combined physics-based and data-driven

approach creates multi-character motions from short

single-character sequences (Liu et al., 2006) and de-

ﬁnes the motion synthesis as a spacetime optimisation

problem. This method animates the approach of two

hands towards each other, by iteratively drawing them

together until convergence is reached. However, this

solution is not suitable for real-time synthesis.

Secondly, Kwon models competitive interac-

tion (i.e. Taekwondo) as a dynamic Bayesian net-

work (Kwon et al., 2008). It synchronizes the ani-

mation of multiple characters by timewarping the ap-

propriate sequences of motion capture data. Whereas

Kwon uses multi-character motion capture, Schum

uses motion capture data of a single person (Shum

et al., 2012). Here character interactions are simu-

lated by expanding a game tree of possible states and

evaluating these states towards the future to select the

appropriate animation sequence. Both approaches are

unable to adapt their respective animations to differ-

ent character conﬁgurations.

A novel Laplacian motion editing method lets

artists manipulate synchronized multi-character an-

imation through the use of synchronized motion

paths (Kim et al., 2009). These motion paths de-

scribe the position of the character in space and time,

while constraint-based displacement is used to con-

strain speciﬁed limbs to a target location (e.g., char-

acters’ hands constraints when carrying a chair).

to achieve synchronization, adaptation and real-

time synthesis.

3 METHODOLOGY

The state-of-the-art approaches to animate multi-

ple characters mostly address issues concerning syn-

chronization of individual animations and adaptation

through motion re-targeting. They however do not

deal with real-time synthesis, which will become a

necessity with the ever increasing variation of charac-

ters in virtual environments. To solve this shortcom-

ing, a novel procedural animation technique based on

fuzzy logic is presented to achieve synchronization,

adaptation and real-time synthesis.

We compare this fuzzy logic based techniques to

create multi-character animation using parametriza-

tion of procedural techniques with inverse kinematics

(IK). Whereas conventional IK is used to retarget ex-

isting animations (Johansen, 2009), we use it to retar-

get kinematic chains (i.e. the right arms of the charac-

ters) to keyframed motion paths in order to overcome

the need for captured data. The IK controller calcu-

lates the joint parameters of the kinematic chain for

each frame, based on the current path position. Con-

trary to IK, the fuzzy logic approach solves towards

the target location locally (i.e. considering joints in-

dependently) in incremental time steps and allows the

use of both motion paths and static targets.

Our method supports synchronization and adapta-

tion. To create believable animations of human inter-

actions, the individual animations of each character

have to be synchronized. By constraining the end ef-

fectors (i.e. ﬁnal joint in a kinematic chain) of mul-

tiple characters to the same motion path, they per-

form synchronized animations. The animation adapts

to all partaking characters by parametrizing the mo-

tion paths and/or targets, speciﬁcally to their position,

dimensions and personality (i.e. dominance).

4 CASE STUDY

Our animation model is based on a two-part case

study that captured handshake gestures between pairs

of people. We identify four phases within the hand-

shake interaction: dummy phase (the starting subject

invites the other subject to shake hands), approach

phase (both hands move towards each other to initiate

the grip), shake phase (the hands move up and down)

and retreat phase (the subjects retract their hands back

towards their body). The different phases are dis-

played in Figure 1.

In the case study, we focus on the shake phase, ex-

amining the ﬂow and dimensions of the shaking mo-

tion and the orientation of the hands during the hand

grip in particular.

4.1 Shaking Motion of the Hands

The test used ﬁve test subjects (named A-B-C-D-E),

paired into three groups: (1) male A - male B, (2) fe-

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(a) Dummy (b) Approach

Figure 1: The subsequent phases of the handshake.

male C - female D, and (3) male E - female D. The

handshake was performed ﬁve times by each group to

mitigate the effect of possible outliers in the captured

data. While performing the handshake experiments,

the subjects stood on pre-placed markers so that the

data on the arm movements could be compared. The

shake phase of each handshake was analysed using a

top and a side view (see Figure 2). We refer to the

starting point of the shake phase as the “point of con-

tact”.

Figure 2: Stills of the 3 groups during part one of the case

study.

Considering the overall ﬂow, we observed both

single-shake (group 1) and multi-shake (groups 2 and

3) interaction. In the latter two groups, the multiple

shakes can be separated as one large primary shake

and multiple smaller secondary shakes. These sec-

ondary shakes can be accredited to subject D. We only

focus here on the primary shake.

The video footage used for this part of the case

study can be found at http://vimeo.com/107897073.

4.1.1 Top View Analysis

During analysis of the top view, we observed two

characteristics. First, during the shake phase the

joined hands stay in line with both (right) elbows,

i.e. the handshake grip and elbows create an initial

plane perpendicular to the ﬂoor, in which the entire

shake phase occurs. Second, on average the point

of contact is centred in between the subjects. Slight

deviations can occur as a result of difference in arm

length (group male-male), subject position or dom-

inance between subjects. We infer dominance of a

person from the rule that a dominant person keeps

the shake away from his/her personal space (Lewis,

2012).

Table 1: Results of angle analysis for the 3 groups.

Group 1 Group 2 Group 3

male-male female-female male-female

Avg. Std. Avg. Std. Avg. Std.

Dev. Dev. Dev.

EF 3.2 1.2 0.5 3.0 3.9 2.2

SF 92.5 2.9 77.2 11.5 86.2 3.5

SE 89.4 2.2 76.7 14.2 82.3 3.9

4.1.2 Side View Analysis

The vector of travel for both hands was also stud-

ied, i.e. the direction and distance travelled during

the shake phase, referred to as “shake direction” and

“shake distance” respectively. To infer both, we used

the video frames corresponding to the lowest and

highest position during the shake phase. By over-

laying these frames, the ﬁgure can be simpliﬁed as

a quadrilateral (as represented in Figure 3). We ob-

served that in some cases the elbow moves between

the lowest and highest position. In that case, we

used the position of the lowest point to construct the

quadrilateral. Next, we determined the orientations

Figure 3: Side view handshake of group 3 with highlights.

of the diagonals (indicated by the dashed lines). The

horizontal diagonal is referred to as the elbow-line

and the vertical diagonal as the shake-line. We ob-

serve three angles (illustrated in Figure 3): (1) be-

tween the elbow-line and the ﬂoor (EF), (2) between

the shake-line and the ﬂoor (SF), and (3) between the

shake-line and the elbow-line (SE). As can be seen in

Table 1, EF is always close to zero. Deviations can be

explained by either the difference in height (e.g. for

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group 1) or a result of the personalities of the sub-

jects. The results of group 1 show that SE should be a

right angle. In the cases of group 2 and 3, we attribute

the deviations from this value to an implied difference

in mannerism. SF is the superposition of angles SE

and EF. For the direction of travel during the shake

phase, we use SE and constrain it to be a right angle

(i.e. shake-line perpendicular the elbow-line).

The shake distance is calculated as a proportion

of the elbow-line length. No large deviations are

observed for this proportion. On average across all

cases, the ﬁnal ratio of shake distance to distance be-

tween elbows is 35 percent. This value is used as an

input for the generation of the vector of travel during

the shake phase, i.e. the observed effect in the result-

ing animation. More detail is given in Section 7.

4.2 Orientation of the Hands

Next, we deﬁne the speciﬁc orientation and positional

offset required to model a handshake grip. In our

model both hands are assumed equal in size. To

Figure 4: Handshake grip with focal points (left) and single

hand analysis (right).

model the handshake grip, two focal points are iden-

tiﬁed. As can be seen on Figure 4, these focal points

on each hand coincide with the matching focal points

of the other hand and are aligned vertically during the

grip. The intersection of the line between the focal

points and the middle ﬁnger palm bone (i.e. third

metacarpal bone) serves as the center of rotation, in-

dicated by the “anchor point” square. The angle of

rotation is deﬁned as the required rotation to place

line F1-F2 in a vertical position. Next, a small offset

reduces the implicit clipping behaviour of both hands.

This offset is deﬁned as half the thickness of the palm,

in the direction of the normal vector leaving the palm.

4.3 Complete Handshake Model

Based on the case study of real life handshakes, a set

of rules is created for deﬁning a virtual handshake

model. These rules consist of:

1. the initial point of contact of both hands located

between the subjects (weighted according to dom-

inance);

2. the vector of travel of the shake phase (35 percent

of the distance between the elbows; in the direc-

tion perpendicular to the elbow-line); and

3. the orientation and offset of the hands during

the shake phase (based on the dimensions of the

hand).

5 FRAMEWORK

Based on the handshake case study, a framework for

the creation and playback of interaction animations is

designed.

We personify virtual humans through personal-

ity traits represented by key-value pairs (trait name

- trait value). Traits such as dominance can be spec-

iﬁed and compared in order to adapt animations ac-

cordingly. We parametrize the handshake animation

model through the personality trait of dominance.

A handshake is an example of an interaction

where one subject starts the interaction and the other

subject accepts (or refuses) this initiation. The ani-

mation framework should therefore support interac-

tions with an asynchronous start. Accordingly, an ar-

biter component is introduced (see Figure 5) in order

to support this behaviour while doubling as a skeletal

pose sharing service. For reusability, the arbiter is de-

signed to be animation- and controller type agnostic.

Figure 5: Interaction work ﬂow with arbiter.

The arbiter handles the asynchronous start and

shares information between both parties (more specif-

ically sharing the current skeletal pose of the other

subject). If the interaction is accepted, the arbiter

passes a reference to the data of each subject to the

other. The architecture of the arbiter is completely in-

dependent of the handshake animation and controller

type, allowing the arbiter to be used in future for other

similar types of animation (e.g. high ﬁves).

6 HANDSHAKE ANIMATION

We now show how to implement the handshake in-

teraction in our framework. We describe the motion

of the hands using the four handshake phases deﬁned

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in Section 4: dummy, approach, shake and retreat.

The initiating character starts with the dummy phase,

here the hand moves a short distance in front of the

character. Next, both characters go into the approach

phase, moving the hands from a neutral position (or

current position for the initiating subject) to the point

of contact. The shake phase then, calculates the vec-

tor of travel and moves the hands upward and down-

ward along this vector. During this phase, the motion

of both hands is synchronized using a shared motion

path. Furthermore, a geometric handle is used to en-

force rotation and offset of both hands. Finally, the

retreat phase makes the hands return to a neutral po-

sition or an ongoing overarching animation.

The transitions between phases are modelled as

a ﬁnite state machine (FSM) as shown in Figure 6.

State transitions are handled individually with the ex-

Figure 6: Handshake phases modelled as a ﬁnite state ma-

chine with states: N1 (neutral state of initiating subject),

N2 (neutral state of other subject), D (dummy phase), A

(approach phase), S (shake phase) and R (retreate phase).

ception of the transition from A1/A2 to S1/S2 where

both parties need to agree (i.e. synchronize) in order

to switch states.

For every phase, each character initializes a par-

tial animation and adapts it according to the position,

dimensions and personality of the character. As par-

tial animations are initialized right before the start of

each phase, the animation can adapt to parametrical

or environmental changes on a per-phase granularity.

In the following subsections, we discuss the use of

IK and fuzzy logic animation controllers in the frame-

work.

6.1 Inverse Kinematics

Our IK approach uses keyframed motion paths to

guide the character animation, i.e. the end effector

of the kinematic chain moves along this path. The

motion paths are represented by B-splines, facilitat-

ing personalisation of the animation. The path is con-

structed as the shortest distance between two points:

the current location of the hand and the target loca-

tion for the end of that phase (e.g. the point of contact

deﬁnes the end of the approach phase).

IK has many known implementations (Aristidou

and Lasenby, 2009), two of the more popular being

Jacobian Transpose IK and Cyclic Coordinate De-

scent IK (CCD). Both alternatives are compared in

Section 7.

6.2 Fuzzy Logic

In the fuzzy logic approach, a fuzzy logic controller

is attached to each individual joint of the kinematic

chain. The input of the fuzzy logic controllers is an-

gular error α

. Angular error is determined locally

for each joint, and is deﬁned by the rotation required

to move the end effector in line with the target posi-

tion (see Figure 7). We let the joint angles approach

Figure 7: Angular error α

of each joint in the kinematic

chain.

their target state at a speed that scales with the an-

gular error of their respective joint. Conceptually,

both the input and output have ﬁve membership func-

tions (Zadeh and Kacprzyk, 1992). Angular error has

memberships: Far(left), Near(left), Zero, Near(right)

and Far(right); speed has memberships: Fast(left),

Slow(left), Zero, Slow(right) and Fast(right).

Figure 8: Input and output memberships for the fuzzy logic

controllers.

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We use the following rules for each controller:

IF angularError IS FarL THEN speed IS FastR

IF angularError IS CloseL THEN speed IS SlowR

IF angularError IS Zero THEN speed IS Zero

IF angularError IS CloseR THEN speed IS SlowL

IF angularError IS FarR THEN speed IS FastL

From this, the controller returns a fuzzy output for

the speed of the joint. The output is defuzziﬁed us-

ing a centroid defuzziﬁer to obtain the matching scalar

value for the speed. By keeping the output values for

speed low, all joints rotate in small increments over

time.

Hence, it is possible to animate using only a static

target position, instead of requiring motion paths as

was the case with IK.

The animator has no exact control over the path

taken by the end effector towards such static target

positions. If however control is wanted, the animator

can choose to use motion paths instead.

By adding rotational information to the target po-

sition, we can extend our approach to support axial

rotation of the individual bones, which in turn can re-

duce artefacts during transitions between phases.

7 RESULTS

The handshake animation can be conﬁgured in two

important ways, on one hand the choice of animation

controllers in both characters, and on the other hand

the inﬂuence of character properties such as position,

scale and personality. Video footage of all conﬁgura-

tions can be found on http://vimeo.com/107897074.

7.1 Animation Controller Conﬁguration

We evaluated four test conﬁgurations for both anima-

tion controller independence and animation controller

performance.

Table 2: Four conﬁgurations of animation controllers.

# Controller 1 Controller 2

1 Jacobian Transpose Jacobian Transpose

2 CCD CCD

3 Fuzzy logic Fuzzy logic

4 CCD Fuzzy logic

For each test conﬁguration, we evaluated the po-

sitional precision of the end effector or right hand of

each character during the shake phase. Three metrics

were calculated as a measure of error: (1) the distance

between both end effectors, (2) the distance between

the hand of character 1 and the target, and (3) the dis-

tance between the hand of character 2 and the target.

The resulting values are presented in Figure 9.

Note that distance is expressed in engine units, cor-

responding to centimetres in the real world.

The summarized results for all graphs are dis-

played in Table 3. For errors, we calculated both the

mean and the standard deviation. Execution times

are also shown as a measure of performance (mea-

sured as number of CPU ticks per frame on an In-

tel(R) Core(TM) i7-2600 3.40GHz).

Conﬁguration 1 achieves an overall high accuracy

with only a small decrease halfway the animation, as

shown in Figure 9(a). However, this high level of pre-

cision comes at the cost of a comparatively higher ex-

ecution time (see Table 3).

Conﬁguration 2 has an overall lower precision

than Jacobian Transpose with a comparatively better

precision halfway the shake (see Figure 9(b)). Ad-

ditionally, the video footage shows that the hands do

not maintain their relative alignment. This is due to

the iterative rotation of joints in CCD, which makes

the ﬁnal bone in the chain align with the target. This

is particularly visible at the end of the approach phase

and start of the retreat phase.

Conﬁguration 3 has both subjects using fuzzy

logic controllers. As can be seen in Figure 9(c) and

Table 3, the precision of this conﬁguration has an

overall lower precision than with both IK methods.

The path of the gradient shows that fuzzy logic has

reactive behaviour. The error increases because it is

unable to keep up with the animation target. At the

peak of the shake phase, the target switches direction

and moves towards the delayed end-effector, decreas-

ing the error severely. After passing the end effec-

tor, the error increases again towards the end of the

shake phase. The complete error shows similar be-

haviour, which can be accredited to a small difference

in movement speed of both hands.

Conﬁguration 4 shows the hybrid controller ap-

proach. The performance, shown in Figure 9(d), is

not surprisingly a superposition of the separate er-

ror rates. It shows how our underlying interaction

framework operates independently of speciﬁc anima-

tion controller types. To our knowledge, this is not

possible in the current state-of-the-art.

As can be seen in Table 3, Jacobian Transpose IK

(conﬁguration 1) performs with the lowest error rate

in all cases, but at the expense of having the lowest

computational performance. CCD IK (conﬁguration

2) has a slightly higher error rate, but has the best

performance of all. Fuzzy logic (conﬁguration 3) of-

fers a tradeoff with an error rate that is higher than

CCD and a performance in between CCD and Jaco-

bian Transpose. The resulting precision of the hybrid

conﬁguration (conﬁguration 4) is an average between

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345

(a) Jacobian Tranpose (b) CCD

Figure 9: Error measurement for each conﬁguration.

Table 3: Summary of animation controller inﬂuence.

Conﬁguration Jacob. Transpose(1) CCD(2) Fuzzy logic(3) Hybrid(4)

Error Avg. Std.Dev. Avg. Std.Dev. Avg. Std.Dev. Avg. Std.Dev.

Complete 0.53 0.10 0.72 0.46 1.70 0.61 1.14 0.40

Hand 1 0.58 0.05 0.73 0.40 1.13 0.56 0.78 0.37

Hand 2 0.50 0.06 1.35 0.55 1.06 0.57 1.09 0.57

Performance (ticks/fr.) 1250 300 800 N/A

fuzzy logic and CCD. We believe that the fuzzy logic

approach can reach similar precision as CCD in the

future. The fuzzy logic error curve shows delayed fol-

lowing behaviour, which can be reduced by tweaking

the controller response speed.

7.2 Character Conﬁguration

We now discuss the adaptability of the animation to

changes in position, dimensions and personality. The

effect of changes in character position is presented in

Figure 10. As can be seen, the orientation and posi-

tion of the handshake adapts automatically according

to the model described in Section 4. However, as we

only animate from the clavicle to the hand, the current

model has a limited range of valid character positions.

Figure 11 shows the effect of scale difference. The

complete handshake automatically adapts to the scale,

except for the handshake grip. Again, the range of

possible scale differences is limited, as our human

model cannot bend over to shake hands with very

small characters.

Finally, in Figure 12 the effect of difference in per-

sonality is displayed. Both characters have a person-

ality trait “dominance” which inﬂuences the point of

Figure 10: Varying conﬁgurations of character position.

Figure 11: Variation of character scale.

contact. The handshake grip shifts towards the less

dominant character (the left character in this ﬁgure).

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Figure 12: Variation of character personality.

8 CONCLUSION AND FUTURE

WORK

In this paper, we presented a handshake animation

model as a use case for general multi-character in-

teractions. The model synchronizes speciﬁc parts of

the animation in order to achieve believable inter-

actions, whilst adapting to changes in position, di-

mensions and personality of the participating charac-

ters. Compared to the current state-of-the-art, our ap-

proach synchronizes multiple single character anima-

tions and is suitable for real-time animation synthesis.

We compared inverse kinematics with fuzzy logic.

Whereas inverse kinematics achieves a higher preci-

sion than fuzzy logic, it however relies completely on

motion paths. Contrary, fuzzy logic can operate with-

out them. When using static targets with fuzzy logic,

the animator cannot control the path taken by the end

effector towards these targets. In that case motion

paths can still be used to enforce a certain path.

Both presented approaches use motion paths to

facilitate synchronization in an animation controller

type agnostic manner. This enables us to create hy-

brid interactions where both characters use different

animation controller types.

Future work can encompass, on one hand, creating

alternative animations to handshakes and, on the other

hand, increasing the detail of this interaction model.

For fuzzy logic, future work can be the use of ma-

chine learning to tweak the individual controllers, the

addition of axial rotation control to the end effector,

and handling of non-constant speed values throughout

the phases. Furthermore, more in depth case studies

should be done in order to achieve animations with

higher (visual) ﬁdelity.

ACKNOWLEDGEMENTS

The authors would like to thank DigitalRune GmbH

for providing a non-commercial license of their li-

brary. This work was partly funded by the Friendly

Attac project (http://www.friendlyattac.be/), a project

of the Institute for the Promotion of Innovation

through Science and Technology in Flanders (IWT).

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