Introduction

References

Conclusion and Outlook

Forward Model (FM) Inverse Models

Cross-Level InteractionComputational Modeling

- Motor program graph:nodes = sequence of MCs

- Motor schema graph: nodes = flexible combination of

MPs of four body parts

Forward module recognizes and predicts the familiar movements (stored in graph) with the aid of probabilistic models. As a result, the most likely MCs can be performed sequentially possibly even during observation (active imitation).

Inverse module parametrizes and stores the novel movements in the according graph. Afterwards, the stored MCs can be performed with delay (passive imitation).

[1] Kopp S. (2008). From Communicators to Resonators - Making Embodied Conversational Agents Sociable. Proceedings of the Speech and Face to Face Communication Workshop in memory of Christian Benoît, Grenoble, France, pp. 34-36.[2] Oztop E., Franklin DW., Chaminade T., and Cheng G. (2005). Human-Humanoid Interaction: Is a Humanoid Robot Perceived as a Human? International Journal of Humanoid Robotics. World Scientific, pp. 537-559.[3] Kopp S., Wachsmuth I., Bonaiuto J., Arbib M. (2008). Imitation in Embodied Communication - From Monkey Mirror Neurons to Artificial Humans. In Wachsmuth I., Lenzen M. & Knoblich G. (eds.), Embodied Communication, Oxford University Press, pp. 357-390.

Humans rely on imitation on the one hand as a social learning mechanism for novel actions, and on the other hand, as social function that gets the interlocutors coordinated in their interactional characteristics in order to establish social resonance [1]. Observing humanoid robots can evoke motor resonance in the human mirror neuron system [2], depending on how the robots look and move. In this context, we propose a computational model, which enables humanoid agents to have motor resonances and imitate with a focus on social intransitive behaviors like hand-arm gestures.

Our model consists of four main modules:

Preprocessing module contains processing units for preparing the observed trajectories:- Sensory memory receives at each time step the perceived data from the virtual sensor

about the current position/configuration of supported body parts - Working memory stores received data from sensory memory over several time steps

in a chronological order as a trajectory- Segmenter decomposes a trajectory into segments depending on the velocity profile

Memory module contains the stored movements as hierarchically connected graphs:- Motor command graph: directed edges = movement segments (motor commands)

nodes = 3d spatial position (wrists) / configuration (hands)

The inverse models of motor command level use self-organizing feature map (SOM) to classify each segment of a movement onto prototypical forms, which will be added as MCs into the graph and also sent to the performer to be generated.

The SOM learns incrementally, whereupon the influence of newly presented segments is controlled by the SOMs' average classification error, in order to avoid the stability-plasticity dilemma.

The imitation process proceeds reciprocally across different levels of a hierarchy from kinematic features, to motor primitives (MCs), to motor sequences (MPs), and finally to motor schema (MSs).We use a Bayesian network to model the bottom-up cross-level activation by means of probabilistic relationships between components of each level. Furthermore, the top-down process is modeled through assigning the a priori probability of bottom levels, depending on the activation of upper levels.

The forward model attempts to relate a sequence of observed samples to the movement prototypes already encoded in the graph. A probabilistic model with a Expectation Maximization (EM) core is employed to generate a set of hypotheses each of which represents a distinct possible explanation for the observations. The hypothesis set is extended according to the freedoms granted by the preferably sparse graph, and dropped according to a set threshold. The FM can refuse the whole hypothesis set and recommend the activation of the Inverse Model instead.

Probability Density Functions for hypotheses at t =t0 and t =tn

MS

MPlw MPrw MPlh MPrh

MClw MCrw MClh MCrh

Xlw Xrw Xlh Xrh

P(X|MC)

P(MC|MP)

P(MP|MS)

Bayes network for bottom-up belief propagation

Using this computational model, the imitator is able to learn new gestures and recognize them by observation. The probabilistic modeling methods allow fast belief updating and imitating in real-time. Three hierarchical levels of the model facilitate comparing, recognizing and predicting observed movements in different time scales.However, an imitated act should also fulfill the intention of the demonstrator (while doing a gesture), which is not directly inferable. The motor schema, as a result of composing various expressions of the same gesture in different contexts, can be associated with context-dependent intentions.

Train seg.:

In order to compare the form of a segment with the prototypes of the SOM, it is necessary to normalize the input segments, that could be of any length and orientation, to values of a specific interval and to translate and rotate every segment inside the x-y-plane of the cartesian coordinate system. Consequently, the assigned prototype should be transformed back to the original length, orientation and position.

At each time step, the probability of each hypothesis at different motor levels, indicates the imitator's belief in recognizing a segment (MC), a movement (MP) or a gesture (MS).

Sensory MemoryWorking Memory

Segmenter

Motor Schema GraphMS1

Forward Models (FMs)

FMs for Motor

Programs

FMs for Motor

Schemata

FMs for Motor

Commands

Inverse Models (IMs)

Visual Stimuli

Performer

Feedback

Active Imitation

MSk

IMs for Motor

Programs

IMs for Motor

Commands

MSk

MPj

MCi

IMs for Motor

Schemata

Passive Imitation

The quality of observed hand strokes is matched with the prototypes with a Gaussian tubular "cloud" which, for each hypothesis, increasingly stretches along its trajectory (with reduced probability density) to accommodate for slight speed variances along with the expected positional inaccuracies.

P(xt|H)

drop hypotheses

H

h1 h2 h3

Recommendation

mc1mc2mc3

mc4

mc1mc2mc3

mc4

t0: P(X|H={mc1}) tn: P(X|H={mc1,mc2}), P(X|H={mc1,mc3,mc4})

RightHand

Motor Program Graph

Motor Command Graph LeftHand

Motor Program Graph

Motor Command Graph RightWrist

Motor Program Graph

Motor Command Graph LeftWrist

Motor Command Graph

MC1

Motor Program Graph

MP1

MCi

MPj

Contact:

Recommending the most significant probable active hypothesis

Rotation onto X

Normalization &Translation

Dimension reduction

Returned transform

Processing steps before and after classification with SOM

Y

XZ

X

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XZ

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XZ

X

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Imitation in social interactionAmir Sadeghipour, Andreas Rüter, Ramin Yaghoubzadeh, Stefan Kopp

Amir Sadeghipour, Sociable Agents Group, CITEC, Bielefeld University, PO-Box 10 01 31, 33501 Bielefeld, Germany, asadeghi@TechFak.Uni-Bielefeld.DE

PT (H) = P (H|xT ) =1T

T!

t=0

P (xt|H) · PT!1(H)"h P (xt|h) · PT!1(h)

1 2 3 4 5 6 7 8 9 100

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0.9Probabilities of MCs

mc3

mc1

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mc8

mc90 1 2 3 4 5 6 7

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5.5Motor Command Graph

mc1

mc2

mc3

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mc5mc6

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mc8mc9

mp1

mp2

mp3

1 2 3 4 5 6 7 8 9 100

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0.9Probabilities of MPs

mp1

mp2

mp3

1 2 3 4 5 6 7 8 9 100.1

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0.9Probabilities of MSs

ms1={mp2,mp3}

ms2={mp1}

Observation in MCG and Probability changes of hypotheses in 10 time steps