## 2 Model Creation and Data Processing
### Composing a Repolarize  
The search for a suitable and undemanding solution to this situation rested on the following conditions:  
Figure 5: Illustration of the \(\mathbf{p_{7}}=[p_{7\times},\,p_{7\gamma},\,p_{7z}]^{\mathrm{T}}\) position vector (effector) depending on the joint coordinate vector \(\mathbf{\varphi}=[\varphi_{1},\,\varphi_{2},\,\varphi_{3},\,\varphi_{4},\,\varphi_{5 },\,\varphi_{6}]^{\mathrm{T}}\) and its effect on the trajectory: (**a**) before repolarization; (**b**) after repolarization; the value of the joint coordinate vector depending on time \(\mathbf{\varphi}=[\varphi_{1},\,\varphi_{2},\,\varphi_{3},\,\varphi_{4},\,\varphi_{ 5},\,\varphi_{6}]^{\mathrm{T}}\); (**c**) before repolarization; (**d**) after repolarization; effect on the trajectory; (**e**) before repolarization; (**f**) after repolarization. * To maintain the original trajectory, the initial values should not be skewed, i.e., if possible, they should not be averaged or approximated;
* There should be no phase shift of the initial values, as is the case with many filters. For these reasons, we were trying to apply different approaches in the simulation, starting with a change in the initial data \(\varphi=[\varphi_{1},\,\varphi_{2},\,\varphi_{3},\,\varphi_{4},\,\varphi_{5},\, \varphi_{6}]^{\text{T}}\), which was very labor-intensive. The rate limiter has not met the expectations either [28] in switching the data flow at the moment of reaching the limits of the angles of rotation \(+/-\pi\), because the characteristics of the \(p_{7}\) trajectory were undulated anyway. Rate limiter is a marginalized derivation of an infinitely small difference to a difference of finite size. Or similar approaches based on a sequential omission of the undesired sample, such as in [29]. Or through averaging the values [30,31]. Neither of the approaches mentioned in this case has met our expectations. The best, if not ideal, results were finally achieved by the system working on this principle Figure 6 and explained in Figure 7. Joint coordinate data were measured in the sampling period \(T_{\text{sp}}\) every 0.005 s.  
When the data were uploaded, it was first necessary to establish the moment of repolarization \(t_{\text{r}}\) with the precision of \(\delta=+/-0.0025\) s when the variable \(\varphi(t)=0\), i.e., cuts through the time axis. Under the assumption of reaching the upper or the lower working interval limit \(<-\pi\), \(+\pi\)\(>\) of the joint coordinate. The variable at the output from the repolarize is \(\varphi_{out}(t)\). It was necessary to meet the following conditions:  
\[t\leq t_{1}|\varphi_{out}(t)=\varphi(t) \tag{15}\]  
\[t_{1}<t_{2} \tag{16}\]  
Figure 6: Constructed repolarizer. Conditions for identification of the sign and carrying out repolarization over time \(t_{r}\):  
\[t\geq t_{2}\bigg{|}\varphi_{out}(t)=\left\{ \begin{array}{ll}2\pi-\varphi(t), \ \varphi(t)<0\\ \varphi(t)-2\pi,\ \varphi(t)>0\end{array} \right. \tag{17}\]  
For the condition that can be considered discontinuation in the angle variable data \(\varphi(t)\), the following applies:  
\[\frac{\big{|}\varphi\big{(}t+T_{sp}\big{)}-\varphi(t)\big{|}}{T_{sp}}=\frac{2 \pi}{T_{sp}} \tag{18}\]  
The model was thus \"excited\" by the values of the joint coordinate vector \(\varphi(t)=[\varphi_{1}(t),\ \varphi_{2}(t),\ \ldots,\ \varphi_{\rm n}(t)]^{\rm T}\) obtained from the model created in CoppeliaSim Edu in the period of time \(T_{\rm sp}\). Under the condition of the prescribed maximum permissible deviation \([\Delta_{\rm max\,\,x},\ \Delta_{\rm max\,\,y},\ \Delta_{\rm max\,\,z}]=+/-0.0035\) m between the real trajectory and the one calculated on the basis of inverse kinematics. The data of joint coordinates \(\varphi(t)\) correspond to the effectors of the trajectory traveled.