## 2 Materials and Methods
### Data Analysis  
Each dataset containing the values of ground reaction forces (GRF) and torque was acquired during one trial (with support of either left or right upper extremity and with eyes open and closed), resulting in four trials per subject. Moreover, the exercise was conducted three times, so there were twelve recordings per participant. The trials lasted 30 s, with a sampling frequency of the force plate set to 1000 Hz. To avoid the possible disruptions of the signal at the beginning of the trial, while the participant was preparing for the test, and at the end of the trial, when the participant was getting up from the position, the 2.5 s at the beginning and end of the signal were eliminated from the analysis. This provides a total of 25 (25,000 time frames) analyzed seconds of the trial.  
The noise in the signal was removed with the use of the low-pass 4 th order Butterworth filter with a 10 Hz cut-off frequency [16]. To obtain the COP position, the coordinates were calculated according to the following formula:  
\[COP_{x}(t)=\frac{-M_{y}(t)}{F_{z}(t)},\]  
\[COP_{y}(t)=\frac{M_{x}(t)}{F_{z}(t)},\]  
where \(COP\) is the center of pressure coordinates in the anterior-posterior (AP) direction (\(y\)) and medial-lateral (ML) direction (\(x\)) in the frame-sample of \(t\), the \(M\) are torques in consecutive directions \(x\) and \(y\) in the frame-sample of \(t\) [Nm], and \(F_{z}\) is the vertical ground reaction force in the frame-sample of \(t\) [N] [17].  
The parameters used for analysis were:  
* the total length of \(COP\), respectively in both directions (\(l_{AP\text{-}ML}\)) and separately anterior-posterior (\(l_{AP}\)) and medial-lateral (\(l_{ML}\)) direction:  
Figure 2: Subject position during measurement.  
\[l_{AP-ML}=\sum\limits_{t=1}^{n-1}\sqrt{\left(COP_{AP}(t+1)-COP_{AP}(t) \right)^{2}+\left(COP_{ML}(t+1)-COP_{ML}(t)\right)^{2}},\] \[l_{AP}=\sum\limits_{t=1}^{n-1}\left|COP_{AP}(t+1)-COP_{AP}(t)\right|,\] \[l_{AP}=\sum\limits_{t=1}^{n-1}\left|COP_{ML}(t+1)-COP_{ML}(t)\right|,\]  
where \(l\) are lengths in corresponding directions [mm], \(t\) is the current time frame, and \(n\) is the number of frames in the current dataset (\(n\) = 25,000);  
* the mean velocity of \(COP\) in both directions--\(v_{AP-ML}\)--and in each of direction separately (AP--\(v_{AP}\) and ML--\(v_{ML}\)): \[v=\frac{l}{T},\] where \(v\) is one of the velocities (AP or ML) [mm/s], \(l\) is the corresponding path length [mm], and \(T\) is the total trial time of 25 s;
* 95% confidence ellipse area (\(A_{95}\) [mm\({}^{2}\)]): \[A_{95}=2\pi\cdot\frac{n-1}{n-2}\cdot F_{0.95n-2}\cdot\sqrt{RMS_{ML}{}^{2}\cdot RMS _{AP}{}^{2}-COV^{2}},\] where \(F_{0.95n-1}\) is the 0.95-quantile of the Fisher distribution with 2 and \(n-2\) degrees of freedom, \(RMS\) are the root mean square for each of the directions, and \(COV\) is the covariance between the \(AP\) and \(ML\) variations of the \(COP\);
* the frequency value of the highest power spectral density of the COP trajectory signal in both directions (\(P_{AP}\), \(P_{ML}\)) [Hz];
* the total power of the frequency spectrum for both directions--the integrated area of the power spectrum (\(PT_{AP}\), \(PT_{ML}\));
* the median of power spectral density of the signal--the frequency at which half of the total power is concentrated below it (\(PM_{AP}\), \(PM_{ML}\));
* the frequency at which 95% of the power signal is concentrated (\(P\)95\({}_{AP}\), \(P\)95\({}_{ML}\)) [Hz]. The frequency-based parameters were obtained by using the fast Fourier transform [7; 16; 18].