
 
positional output errors over each of the ten different 
cycles performed by the subject. The average of the 
output errors reflected the network’s ability to 
extrapolate its results on samples that were not 
directly included in the training set. After iteratively 
testing different sigmoid activation functions for the 
hidden layer of the network, numbers of epochs and 
numbers of hidden neurons, the final configuration 
of the network was determined.  
The resulting network comprised seven hidden 
neurons with the hyperbolic tangent as activation 
function and the number of epochs was set to 50. 
The reader is referred to previous publication 
(Barzilay and Wolf, 2009) for a detailed explanation 
on the setting of the network’s architecture. 
2.3.2  Network with Kinematic and EMG 
signals as Input 
In the second step of this research, we added the 
patient's biceps and triceps EMG signals to the input 
of the network, such that the new exercise would be 
designed with respect to the information on the 
muscles of the subject as well as the knowledge on 
the kinematic data of his limb. 
The data provided by the electromyograms 
contain useful information that can be deciphered by 
signal processing. There are numerous ways 
described in the literature to extract this information 
from the EMG signal, including analysis in time or 
frequency domains. We use the workflow described 
in Hodges and Bui (1996) to compute the linear 
envelope of the signal by processing it in the time 
domain. The processed signal is needed at every 
instant in our application and the processing time 
has to be minimized, all the more since several 
signals are needed simultaneously. We accelerated 
this operation by using the processed signals from 
the precedent instant and reduced the processing 
time by approximately 96% (Barzilay and Wolf, 
2011). This fast implementation allows providing 
the subject with continuous visual feedback on his 
own muscular performance during the training. 
The same parameters that were described in 
section 2.3.1 are used to evaluate the network, but 
now in addition to the 3D curve, the desired EMG 
performance specific to that trajectory should also be 
designed. We therefore determined a few desired 
cyclic trajectories for the limb of the subject and 
recorded the EMG performances of a dozen of 
healthy subjects. The average of this set of data is 
then used as the desired EMG performance over a 
specific trajectory, and fed as input to the neural 
network  together  with  the trajectory of the desired 
kinematic performance. 
The number of neurons in the hidden layer has 
been set to 17, according to the evaluation criteria 
which were previously used. 
2.3.3 System Evaluation 
The first network, described in section 2.3.1, 
considers only the endpoint kinematics of the subject 
and has obviously less physiotherapeutic interest 
than the network involving the subject’s muscular 
performance (section 2.3.2). Nevertheless, the 
optimistic results (section 3.1 and Barzilay and 
Wolf, 2009) suggested evidence of the feasibility of 
modeling human motor control with neural networks 
and brought us to expand the subject model to 
include muscular performance as well. 
From a therapeutic perspective, the muscles 
activation of the patient is more significant than his 
ability to accurately reproduce specific trajectories. 
For that reason, we focus our efforts on minimizing 
the error in the EMG performance, whereas the 
kinematics error is considered more moderately. 
Although the EMG signals are calibrated from 
measurement of the maximal voluntary contraction 
prior to the training, the signals’ amplitudes tend to 
differ between different subjects. Furthermore, we 
focus on the rhythmical patterns of the muscles more 
than on the activation intensity. To do that, we 
consider the error between the desired and actual 
EMG performance in the frequency domain. 
For the evaluation of the adaptive system, we 
thus consider the root mean squared deviation, in the 
frequency domain, between the desired EMG 
performance and the smoothed EMG performance of 
the subject. Each participant (n  = 16) performed 
motor training on two exercises: the patient-specific 
exercise produced by the trained neural network 
(adapted training), and a general exercise having for 
trajectory the desired kinematic performance. The 
latter resembles a standard physiotherapeutic session 
where the physiotherapist demonstrates to the 
patient, for example with his hand, the desired 
gesture to reproduce (conventional training). The 
primary criterion for the system evaluation was 
defined as the ratio of the errors obtained in the 
performances in both cases. 
3 RESULTS 
3.1  Network with Kinematic Input 
The  exercise  trajectory, designed  by  the  network, 
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