Deep Learning based Model Identiﬁcation System Exploits the Modular

Structure of a Bio-inspired Posture Control Model for Humans and

Humanoids

Vittorio Lippi

Neurological University Clinic, University of Freiburg, Freiburg im Breisgau, Germany

Keywords:

Posture Control, Deep Learning, System Identiﬁcation, Parametric Nonlinear System.

Abstract:

This work presents a system identiﬁcation procedure based on Convolutional Neural Networks (CNN) for

human posture control using the DEC (Disturbance Estimation and Compensation) parametric model. The

modular structure of the proposed control model inspired the design of a modular identiﬁcation procedure, in

the sense that the same neural network is used to identify the parameters of the modules controlling different

degrees of freedom. In this way the presented examples of body sway induced by external stimuli provide

several training samples at once.

1 INTRODUCTION

The application of convolutional neural networks

(CNN) in human movement analysis has produced

promising results in recent experiments (Batchuluun

et al., 2018; Karatzoglou et al., 2018; Abdu-Aguye

and Gomaa., 2019a; Abdu-Aguye and Gomaa., 2019b),

and in general deep learning is starting to be applied to

system identiﬁcation (De la Rosa and Yu, 2016; Ander-

sson et al., 2019; Miriyala and Mitra, 2020; De la Rosa

et al., 2015; Ljung et al., 2020). This work aims to ap-

ply CNN to the identiﬁcation of human posture control

models, that are used in several studies for the analy-

sis of human data and the control of humanoids, e.g.

(van der Kooij et al., 2007; van der Kooij et al., 2005;

van Asseldonk et al., 2006; Goodworth and Peterka,

2018; Mergner, 2010; Engelhart et al., 2014; Pasma

et al., 2014; Jeka et al., 2010; Boonstra et al., 2014).

Most of the studies on posture control use linear mod-

els like the independent channel (IC) model (Peterka,

2002), and make the assumption of linear and time-

invariant behavior (Engelhart et al., 2016). In this work

a nonlinear model will be considered. This makes the

use of deep learning more interesting, as the identiﬁ-

cation of nonlinear systems is more complex and in

general it is performed using computationally expen-

sive iterative algorithms as in (Assl

ander et al., 2015).

In a previous work, CNNs proved to be suitable to iden-

tify the parameters of a human posture control model

https://orcid.org/0000-0001-5520-8974

(Lippi. et al., 2020). Speciﬁcally, the CNN presented

in (Lippi. et al., 2020) was applied to a single inverted

pendulum (SIP) model, but it proved to work also in

identifying the parameters of a double inverted pendu-

lum system. In this work a triple inverted pendulum

(TIP) model of posture control will be used to show

how the identiﬁcation process can be extended to an ar-

bitrary number of degrees of freedom. The model used

here, the Disturbance Estimation and Compensation

(DEC) has a modular structure (Lippi and Mergner,

2017), i.e. each degree of freedom is controlled by a

module and all the modules share the same structure.

Exploiting this characteristic, one CNN is used to iden-

tify the parameters of the three modules controlling the

three degrees of freedom. In this way each simulation

provides three training samples at once.

2 METHODS

2.1 Posture Control Scenario

The scenario considered here models a human (or hu-

manoid) balancing on a tilting support surface as a TIP.

The three degrees of freedom considered in the sagittal

plane are the ankles, the knees and the hips (Fig. 1A).

The support surface tilt

represents the input of the

system and it is the same for all the simulations. The

proﬁle of the tilt of the support surface is the pseudo-

random ternary sequence, PRTS, shown in Fig. 1B.

540

Lippi, V.

Deep Learning based Model Identiﬁcation System Exploits the Modular Structure of a Bio-inspired Posture Control Model for Humans and Humanoids.

DOI: 10.5220/0010245405400547

In Proceedings of the 10th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2021), pages 540-547

ISBN: 978-989-758-486-2

Figure 1: Balance scenario and posture control system. (A)

The triple inverted pendulum model used to simulate human

posture control together with the control modules. The

represent the sway of the body COM around the ankle joint.

(B) The Pseudo-Random Ternary Signal, PRTS, the time

proﬁle for support surface tilt. (C) Schema of a control

module. The disturbances are compensated feeding them

in the form of an angle equivalent as input to the servo

controller (PID).

Such stimulus is used in human experiments because

it is not predictable for the subject (Peterka, 2002). It

is composed by a sequence of velocity steps suitable

to excite the dynamics of the system over several fre-

quencies. The output of the system is the sway of the

body segments: shank, thigh (leg) and trunk addressed

as α

, α

, and α

T S

respectively.

2.2 Human and Humanoid Posture

Control: The DEC Model

The DEC is a model of the human postural con-

trol mechanisms (Mergner, 2010; Lippi and Mergner,

2017). It has a modular structure that can be applied

to multiple DoF robots (Lippi and Mergner, 2017;

Zebenay et al., 2015; Ott et al., 2016; Lippi, 2018;

Hettich et al., 2013; Hettich et al., 2015). Here it

is implemented speciﬁcally on the TIP model, using

three control modules. A block diagram of the DEC

control is shown in Fig.1. A complete description of

the model is beyond the scope of this paper and can

be found in (Lippi and Mergner, 2017). In the fol-

lowing a general description of the model is provided

with particular emphasis on the components that have

an impact on the deﬁnition of the machine learning

problem. A control module based on the DEC concept

is implemented as servo loop, here implemented as

a PID controller (the neural controller in Fig. 1C).

The controlled variable can consist in the COM sway

of all the segments above the joint controlled by the

module with respect to the gravitational vertical pass-

ing through the controlled joint (e.g.

in Fig 1 for

the ankle joint). The sensory channels shown in Fig.1

for disturbance estimation. The disturbance estimates

are fed into the servo so that the joint torque on-line

compensates for the disturbances. The lumped delay

in Fig. 1 (C) represents all the delay effects that are

distributed in humans, and humanoids (Antritter et al.,

2014; Hettich et al., 2014). The model used in this

work considers gravity and support surface tilt as dis-

turbances. The gravity torque to be compensated is

assumed to be proportional to the sway of the COM

of groups of segments above the controlled joints. Ide-

ally the gain required to compensate gravity is

mgh

where

and

are the total mass and the COM height

of the controlled segments respectively, and

is the

gravity acceleration. The integral component of the

PID controller is not applied to the compensation as

in (Ott et al., 2016). The support surface tilt estimator

includes a non-linearity, introduced to represent the

behavior observed in humans (Mergner et al., 2009;

Mergner et al., 2003), deﬁned as:



vest

prop



(1)

where

prop

is the ankle joint angle signal from propri-

oception.

stands for Body-to-Foot. The function

is a dead-band threshold deﬁned as

(α) =







α + θ i f α < −θ

0 i f −θ < α < θ

α − θ i f α > θ

(2)

The estimated

is then up-channeled through the

control modules and used to control body position.

In this work the threshold is set as

θ = 0.0003rad/s

The disturbance compensation and the total torque

commanded by the servo controller for the ankle joint

is:

τ(s) = −e

−s∆



+ sK

+ K



(ε) + (K

+ sK

(3)

where

and

is the derivative coefﬁcient for the

PD controller, and

∆

is the lump delay. Notice that

the derivative component is also acting on gravity

representing a sort of anticipation of the disturbance.

Deep Learning based Model Identiﬁcation System Exploits the Modular Structure of a Bio-inspired Posture Control Model for Humans and

Humanoids

541

There is also a passive torque acting on the joints rep-

resented as a spring-damper model:

passive

= −(K

pass

+ sK

pass

)



prop



(4)

The coefﬁcients

pass

and

pass

are kept ﬁxed for all

the simulations. The standard parameters are shown

in Table 1. In general the gains are proportional to the

mgh

for the groups of segments above the controlled

joint, this will be used in the next section to normalize

the parameters. The anthropometric of the TIP model

is taken from previous works (Lippi et al., 2019b;

Lippi and Mergner, 2020).

2.3 The Training Set

Control Parameters and Target Set.

The training

set has been generated simulating the posture control

scenario with different parameters, these parameters

represent the target for the neural network and the

sway of the segments represents the input. In order

to exploit the modular structure of the DEC control

the CNN has been designed to identify the parame-

ters of a speciﬁc module. In this way each simulation

provides three training samples associated with the

three control modules. As explained in the previous

section, the gains of the controllers are proportional

to the

mgh

of the segments above the controlled joint,

and the lumped delay is larger for the ankle module

and smaller for the hip module. In order to use such

parameters for the training of the same CNN their

value is expressed as deviation from the default value

and normalized dividing it by the default value, e.g.

= (K

sample

− K

)/K

in Table 1. Besides the PID

gains the target vector includes the lumped delay and

a variable

that is set to

−1

when the controlled vari-

able is the joint angle and to

when the controlled

variable is the COM. This leads to a sample with the

following form:

T =



∆ C



(5)

where the˜indicates that the values are normalized.

The training samples are generated with random

parameters from normal distributions

X ∼ N (0, 0.5)

that is summed to the normalized parameters. The

variable

is sampled with equal probability (

0.5

) be-

tween the two cases. In order to avoid negative values

the absolute value of the obtained parameters is used

”‘warping”’ the normal distribution on positive values.

A set of parameters is used as a sample only if the

behavior it produces is stable: simulations with body

sway larger than

◦

are not considered realistic balanc-

ing scenarios and are discarded. Overall the obtained

data consist of

20730

samples,

14000

used as training

set,

3000

as validation set and

3730

as test set. The

three sets are normalized subtracting the average di-

vided by the variance of the training set. The resulting

distribution of the normalized

is shown in Fig. 2

together with the distribution of maximum body sway

amplitudes.

-2 -1 0 1 2 3 4

200

400

600

0 1 2 3 4 5 6

500

1000

1500

2000

2500

Figure 2: Output of the performed simulations. Above the

distribution of the normalized

parameter produced during

the stable simulations. Below the distribution of the body

sway amplitudes. The last column of the histogram on the

right includes the simulations that were aborted because the

body sway reached the threshold of 6

◦

The CNN Input.

The Input is a representation of

the system output, i.e the sway of the segments. The

simulation was performed with a ﬁxed integration step

2ms

and sampled at

50 Hz

, producing

6051

samples

with a resolution of

20 ms

. In order to adapt the signal

to the CNN the input was transformed into an image.

The data considered were the sway with respect to

the vertical of the two segments under and above the

controlled joint, e.g. for the ankle module they are

and

. The Spectrogram of the two signals is com-

puted with short-time Fourier transform over windows

of 250 samples overlapping for 135 computing 250

frequency points. This results in a 51 ×250 matrix of

complex values. The ﬁrst 51 columns of the matrix

are here considered, corresponding to a bandwidth of

approximately

10 Hz

. Due to the low-pass dynamics

of the body sway, the power spectrum of the signal

at higher frequency is very poor and hence not giving

important informations (i.e. almost black images inde-

pendently of the parameters) . The resulting

51 × 51

matrix is used to deﬁne the input image as follows: the

ICPRAM 2021 - 10th International Conference on Pattern Recognition Applications and Methods

542

Table 1: Default parameters.

Parameter Symbol Ankle Knee Hip unit

Active proportional gain K

465.98 245.25 73.575

N·m

rad

Active derivative gain K

116.49 18.394 18.394

N·m·s

rad

Active integrator gain K

11.649 6.1312 1.8394

N·m

rad·s

Passive stiffness K

pass

232.5000 61.2500 36.5000

N·m

rad

Passive damping K

pass

145.000 11.2500 11.2500

N·m·s

rad

Foot rotation velocity threshold θ

v f s

0.03 rad/s

Lumped delay ∆ 0.10 0.07 0.1210 s

module and the phase of the matrices associated to the

two segments sway are computed. The ﬁrst channel of

the image is the module of the matrix describing the

sway of the segment above, the second is the matrix

describing the segment below and the third channel is

the difference between the phases. The process is sum-

marized in Fig 3. Also the input images are normalized

subtracting the average and dividing by the variance

of the training set through element-wise operation (i.e.

pixel by pixel, channel by channel).

2.4 CNN Architecture

The neural network architecture is schematized in Fig

4. The network is implemented with Matlab

Deep

Learning Toolbox

. The network has been trained

using stochastic gradient descent with momentum as

policy. The training was set to a limit of 200 epochs.

The loss function is the Mean Squared Error MSE as

expected with a regression task, although the target

vector includes a categorical feature, the controlled

variable, that implies a classiﬁcation problem. The cat-

egorical variable produced by the CNN is interpreted

considering the sign (positive = COM sway, negative =

joint angle). The performance in regression and classi-

ﬁcation is discussed separately in the Results section.

3 RESULTS

3.1 Training and Test

The results of the training set are reported in Table 2.

Notice that there is a total RMSE on the training set,

including the error on the categorical variable, and a

Figure 3: Design of the input features for the CNN. In A the

spectrogram of a signal is given, the dashed line shows where

it is cut. In B it is shown how the spectrograms associated

with the sway of two body segments are combined to form

a three channel

51 × 51

pixel image. The image C shows

the normalization of the samples using the mean and the

variance of the training set, computed element-wise (pixel

by pixel).

ﬁt RMSE computed on the continuous variables. The

average absolute error and absolute variance is shown

in Fig. 5. The error is larger on

. The identiﬁcation

Deep Learning based Model Identiﬁcation System Exploits the Modular Structure of a Bio-inspired Posture Control Model for Humans and

Humanoids

543

Figure 4: Neural Network architecture. The group of layers addressed with x 5 is repeated 5 times.

error in this context can be deﬁned as the norm of

the difference between body sway obtained with the

target parameters (

) and the one associated with

the identiﬁed parameters (

) divided by the number

of samples N = 6051,

−

(6)

, where the bold text represents the fact that

a vector of samples. The MSE on the single sample

is computed considering the target error on the three

control modules used in the simulation. The prediction

error

on the 15 normalized parameters is computer

for each sample, leading to an MSE of

MSE =

/15 (7)

. The identiﬁcation error plotted versus the MSE is

shown in Fig. 6. On average the identiﬁcation error on

the training set is 0.0024

◦

0.2

0.4

0.6

0.8

1.2

average absolute error

Mean

Variance

Figure 5: Average and variance of the error on the parame-

ters.

Table 2: Training Results.

Dataset total RMSE ﬁt RMSE Accuracy

Training 1.3664 1.3296 85.79%

Validation 1.5186 1.4810 83.90%

Test 1.4846 1.4486 84.72%

0 0.1 0.2 0.3 0.4 0.5 0.6

MSE (by sample)

Average identification error [°]

-3

(0.1, 0.07)

Figure 6: Identiﬁcation Error for a set of 60 training sam-

ples. The identiﬁcation error is plotted versus the MSE error

on the parameters (target output). The arrow addresses a

point that is out of the scale of the axes (i.e MSE = 0.1,

error=0.07). The correlation between the two measures of

errors is

−0.1265

, which means in general larger MSE on

the parameters are not associated to the larger identiﬁcation

errors. This may suggest a certain degree of redundancy in

the model, allowing the system to reproduce a similar output

with different sets of parameters.

3.2 Identiﬁcation of Human Posture

Control Parameters

The neural network is used to identify the control pa-

rameters from a human experiment performed with

the same scenario simulated in the training set. The

human experiment had the user stand with straight

legs and hence the simulation was applied just to the

ankle and the hip module. The identiﬁed parameters

are reported in table 3 and the simulated sways of the

segments are shown in Fig. 7, the result shows a good

similarity between the simulation and the original data.

For both the control modules, i.e. hip and ankle, the

network proposed the sway in space of the segments

ICPRAM 2021 - 10th International Conference on Pattern Recognition Applications and Methods

544

as controlled variable, in according to previous studies

on support surface tilt (Hettich et al., 2014).

Table 3: Parameters identiﬁed for an example from a human

experiment.

Module K

∆ Var

Ankle 421.8574 74.6664 12.0254 0.0685 Sway Angle

Hip 74.5148 8.2559 1.8854 0.0219 Sway Angle

0 20 40 60 80 100

Time [s]

-1.5

-1

-0.5

0.5

1.5

Sway [°]

simulated

human

Figure 7: Human data compared with simulated responses.

3.3 Identiﬁcation with a Monolithic

Model

In order to evaluate the impact of the modular ap-

proach the experiment is repeated with a network that

considers the three DOF together. The target vector

incorporates the parameters for the 3 control modules,

i.e. 15 values; the input is encoded as a 5 channel

picture with with spectrograms as described in

2.3.

Support surface tilt

is not taken in account as it is

the same for all the samples. The channels represent

the modulus of the spectrogram for

, and

T S

and the phase difference between

and

as well

as between

and

T S

. The dataset, rearranged in

this way accounted for

2264

samples, i.e. one third of

the original set. The dataset was split into a training

set and a validation set of

1000

samples and a test set

264

samples.The network had the same structure

of the one used in the modular case, but the input and

the output layers were modiﬁed according to the di-

mensionality of the new dataset. Such network has

the disadvantage of having less training samples and

more parameters, but potentially the advantage of in-

tegrating more information about the global structure

of the system (e.g. distinguishing explicitly between

different DOFs). The results are shown in Table 4.

The performance is overall worse than in the modular

case, especially for the classiﬁcation accuracy, sug-

Table 4: Training Results with a monolithic model.

Dataset total RMSE ﬁt RMSE Accuracy

Training 4.0731 3.2723 60.20%

Validation 4.1597 3.3297 53.50%

Test 4.0531 3.2586 51.51%

gesting that a modular approach is advantageous with

this problem.

4 CONCLUSIONS AND FUTURE

WORK

In this work a method for posture control parameter

identiﬁcation based on CNN is presented. The sys-

tem provides an efﬁcient way to ﬁt a model of the

non-linear bio-inspired control system DEC on experi-

mental data. This represents an advantage with respect

to previous solutions relying on iterative methods. the

training set is produced with parameters from normal

distributions (although only the parameters producing

a stable simulation are selected). Future work will fo-

cus on the distribution of human data. An a posteriori

test can be performed comparing the distribution of the

parameters identiﬁed on the test set with the expected

distribution on real data. This can help the process of

choosing between different possible network hyperpa-

rameters sets as shown in (Sforza et al., 2011; Sforza

and Lippi, 2013).

Some parameters were better identiﬁed than others

as shown in Fig. 5. This may be due to the kind of

experimental set up or due to the choice of the input

features. For example the effect of

is mainly visible

just in the low pass components of the spectrogram.

Furthermore, simulations and robot experiments are

able to reproduce human behavior in the considered

set up (PRTS support surface tilt) without the integral

component of the neural controller (Mergner, 2010;

Hettich et al., 2015; Hettich et al., 2014). The inte-

gral component of the controller is more important in

analyzing transient behavior, e.g. reaching a desired

position, where it can be used to guarantee zero track-

ing error (Ott et al., 2016). A tracking task may be

better to identify K

more precisely.

The proposed CNN for posture control modeling

can ﬁnd application in bio-inspired humanoid control,

e.g. (Choi and Kim, 2007; Abedi and Shoushtari,

2012; Zebenay et al., 2015; Mergner and Lippi, 2018).

The CNN can also be helpful in setting up wearable

robots using the control parameters identiﬁed on the

user (Chugo et al., 2019; Mergner and Lippi, 2019).

The parameters can be a tool to benchmark humanoids

and wearable devices (Torricelli et al., 2020), in partic-

ular, in the framework of the COMTEST project (Lippi

Deep Learning based Model Identiﬁcation System Exploits the Modular Structure of a Bio-inspired Posture Control Model for Humans and

Humanoids

545

et al., 2019a; Lippi et al., 2020) that aims to make

a posture control testbed available for the humanoid

robotics community, and to deﬁne performance met-

rics.

ACKNOWLEDGEMENTS

This work is supported by the project

COMTEST, a sub-project of EUROBENCH

(European Robotic Framework for

Bipedal Locomotion Benchmarking,

www.eurobench2020.eu) funded by H2020

Topic ICT 27-2017 under grant agreement number

779963.

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Deep Learning based Model Identiﬁcation System Exploits the Modular Structure of a Bio-inspired Posture Control Model for Humans and

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