The main objective of this chapter is to evaluate the reliability of the application of stimuli using the developed concept; the importance of the initial conditions for the repeatability of the stimuli will be tested; different types of stimuli will be evaluated; and also different types of dynamixel commands will be used to control the servos. First, some stimuli will be applied to the pendulum controlling the servos position, torque and velocity to assess the differences of the stimuli produced by these commands. The second step is to narrow the control methods for the servos and test some stimuli with shorter durations.



\section{Procedure planning}

For all the trials data will be collected over 10 seconds and stored in a csv (comma separated values) file for later analysis. A script plots the information contained in the csv files to provide visual feedback at the end of each trial. This information consists of: sensor readings, applied command to the servos, and the pendulum's angle. Regarding the latter, vision is used to get the pole's angle, more detailed information can be seen in section \ref{subsection:vision}. When the trials were finished a script calculated Pearson's product moment correlation coefficient \cite{mukaka} between the repeated tests, the method used can be seen in equation \ref{equation:correlation}. Note that the correlation is done between every repeated test so , as an example, if the a trial is repeated five times this method will produce ten correlations, table \ref{table:corr_explain} shows this method.

\begin{equation}
 r=\frac{\sum_{i=1}^{n}{(x_i-\overline{x}).(y_i-\overline{y})}}{\sqrt{[\sum_{i=1}^{n}{(x_i-\overline{x})^2}].[\sum_{i=1}^{n}{(y_i-\overline{y})^2}]}},
 \label{equation:correlation}
\end{equation}
 where $x_1$, $x_2$, ..., $x_n$ and $y_1$, $y_2$, ..., $y_n$ are the measured values. $\overline{x}$ (equation \ref{equation:x_mean}) and $\overline{y}$ (equation \ref{equation:y_mean}) are the variables means.
 
 \begin{equation}
 \overline{x}=\frac{1}{n}.\sum_{i=1}^{n}x_i
 \label{equation:x_mean}
 \end{equation}
 
 \begin{equation}
 \overline{y}=\frac{1}{n}.\sum_{i=1}^{n}y_i
 \label{equation:y_mean}
 \end{equation}

\begin{table}[!hb]\centering
\ra{1.2}
\caption{Correlations between repeated trials.}
\label{table:corr_explain}
\begin{tabular}{@{}llllll@{}}\toprule
        & $x_1$ & $x_2$     & $x_3$     & $x_4$     & $x_5$     \\ \midrule
 $x_1$  &       & $r_{1-2}$ & $r_{1-3}$ & $r_{1-4}$ & $r_{1-5}$ \\
 $x_2$  &       &           & $r_{2-3}$ & $r_{2-4}$ & $r_{2-5}$ \\
 $x_3$  &       &           &           & $r_{3-4}$ & $r_{3-5}$ \\
 $x_4$  &       &           &           &           & $r_{4-5}$ \\
 $x_5$  &       &           &           &           &           \\
\bottomrule
\end{tabular}
\end{table}

The first trials will test different actuations more specifically ramp, ramp step, sawtooth and triangle and different control types such as position, torque and velocity. Only one servo is used, the other one is decoupled. This means that the rope is always loose so the servo actuation effect will be delayed and it is the reason why the pulse step wasn't used on these trials. Each trial was repeated five times to get a reliable correlation. This procedure is depicted in table \ref{table:procedure_1}

% 	\begin{figure}[!hb]
% 	\centering
% 	\includegraphics[scale=0.3]{Imagens/icones_graficos/pulse.png}
% 	\caption{Pulse step stimuli.}
% 	\label{figure:pulse_step}
% 	\end{figure}

\begin{table}[!hb]\centering
\ra{1.2}
\caption{Procedure plan for the first trials.}
\label{table:procedure_1}
\begin{tabular}{@{}llll@{}}\toprule
                                                                              & Position commands & Velocity commands & Torque commands \\ \midrule
 \includegraphics[scale=0.1]{Imagens/icones_graficos/ramp_step.png} Ramp step & $\times$5           & $\times$5           & $\times$5         \\                                                                             
 \includegraphics[scale=0.1]{Imagens/icones_graficos/ramp.png} Ramp           & $\times$5           & $\times$5           & $\times$5         \\
 \includegraphics[scale=0.1]{Imagens/icones_graficos/sawtooth.png} Sawtooth   & $\times$5           & $\times$5           & $\times$5         \\
 \includegraphics[scale=0.1]{Imagens/icones_graficos/triangle.png} Triangle   & $\times$5           & $\times$5           & $\times$5         \\
\bottomrule
\end{tabular}
\end{table}


The second trials had in mind the previous results, so only torque and velocity control were used. The only step used here was the pulse with three durations 0.1, 0.25 and 0.5 seconds and three different torque and speed values. This was decided based on the experience with the system and the experiments seen with other robot's balance test. For these set of trials the two servos were coupled, so the data collected was the force from the two sensors and the pendulum's angle. These trials had two distinct phases, one where the servos would adjust both rope's tension to about 4 N using the controller designed and some manual adjustments. The second phase was the stimulus application, where only servo 1 would pull the pole and servo 2 would just release the rope. When the stimulus time had finished servo 1 would unwind the rope at maximum speed to allow the pendulum to freely return to balance. Each trial was repeated only three times because they consumed some time and the previous ones proved to be reliable. The procedure for the second trials is depicted in table \ref{table:procedure_2}

\begin{table}[!hb]\centering
\ra{1.2}
\caption{Procedure plan for the second trials.}
\label{table:procedure_2}
\begin{tabular}{@{}llllclll@{}}\toprule
\multicolumn{1}{l}{\multirow{2}{*}{\includegraphics[scale=0.1]{Imagens/icones_graficos/pulse.png}}}   & \multicolumn{3}{c}{Torque commands} & & \multicolumn{3}{c}{Velocity commands} \\ \cmidrule{2-4}  \cmidrule{6-8} 
         & 800       & 900       & 1023       & & 800        & 900       & 1023       \\ \midrule
0.1      & $\times$3 & $\times$3 & $\times$3  & & $\times$3  & $\times$3 & $\times$3  \\ 
0.25     & $\times$3 & $\times$3 & $\times$3  & & $\times$3  & $\times$3 & $\times$3  \\ 
0.5      & $\times$3 & $\times$3 & $\times$3  & & $\times$3  & $\times$3 & $\times$3  \\
\bottomrule
\end{tabular}
\end{table}

\section{Measuring the Pole Angle with Vision} \label{subsection:vision}

%It is important to notice that this measure was made only to evaluate the reliability of the system, it can't not be used as another input for the %control method...

To get the pole's angle a simple 30 Hz web cam was used. Another node,\linebreak \verb|dyna_comm_camera|, was added to the \verb|dyna_comm| package to deal with the image processing and publish the pole's angle, this way the node \verb|dyna_comm| writes the csv file with synchronized data. OpenCV libraries were used to connect with the usb camera and do all the necessary steps to obtain the pole's angle. These steps are the following by order: transform the coloured image to grey scale; transform it to black and white and invert it because the pendulum is black; get all objects contours which are ordered from biggest to smallest, the pendulum being the biggest; get the orientation of the biggest object.

To assure that the pendulum is the biggest object the background is white and the pole was painted black, this way the lighting doesn't influence the image analysis process. These features and the pole's detection can be seen in figure \ref{figure:pole_detection}. To assure that the correct angle is published the camera is level with the horizontal.

	\begin{figure}[!hb]
	\centering
	\includegraphics[scale=0.3]{Imagens/pole_detection.png}
	\caption{Pole painted black and white background to favour its detection.}
	\label{figure:pole_detection}
	\end{figure}

\section{First Trials Results Presentation and Discussion}

% apresentar as tableas, alguns graficos, falar dos valores que la estao como foram calculados ou obtidos as freq de aquisicao, os tempos...
% 
% dizer que estao muita bons, os 1º's nao servem para concluir se devemos controlar os servos em pos torque ou vel. depois dizer que os estimulos tem de ser de curta duração para a vel dos servos nao afetar o ensaio, mas que isso e mais uma prova que as condiçoes dos ensaios tem de ser rigorosas para haver repititibilidade, e tambem que um estimulo com aquela duraçao pode ja ser um exagero, as colisoes que geralmente acontecem sao de curta duraçao (isto precisa de uma referencia, pesquisar sobre colisoes e tempo que elas duram)

Annex \ref{annex:first_stimuli} shows one set of graphics per trial, these sets were repeated five times. Each figure represents one trial, the left graphic is the sensor readings and the right graphic is the pendulum's angle. Figure \ref{graphic:rampsteptorque_} shows an example of these graphics. Tables \ref{table:position_control}, \ref{table:velocity_control} and \ref{table:torque_control} show the correlation mean and its standard deviation, using equation \ref{equation:r_mean} and equation \ref{equation:r_stdeviation}, respectively.

\begin{equation}
 \overline{r}=\frac{1}{n}.\sum_{i=1}^{n}r_i
 \label{equation:r_mean}
 \end{equation}
 
 \begin{equation}
 r_{\sigma}=\sqrt{\frac{1}{n}.\sum_{i=1}^{n}(r_i-\overline{r})^2}  
 \label{equation:r_stdeviation}
 \end{equation}

\begin{figure}[!hb]
	\centering
  \pgfplotstableread[col sep = comma]{Graficos/_rampstep_torque1.csv}\rampsteptorquecsv
  \subfloat[Tensile Force.]{
  \tikzsetnextfilename{Grafs-First/Torque/rampsteptorque_force}
      \begin{tikzpicture}
	\begin{axis}[
	  width=0.4\textwidth,
	  height=0.4\textwidth,
	  font=\scriptsize,
	  xmajorgrids,
	  ymajorgrids,
	  xlabel = Time (s),
	  ylabel = Force (N),
	  axis on top, % descriptions over filled area
	  legend pos=north east, % customize legend 
	  ]
	  \addplot[mark=none, color=blue, thick] table[x index = {0}, y index = {1}]{\rampsteptorquecsv};    
	  %\legend{Actuation Force}
	\end{axis}
      \end{tikzpicture}
  } %subfloat
   \subfloat[Angle of the pendulum.]{
   \tikzsetnextfilename{Grafs-First/Torque/rampsteptorque_angle}
      \begin{tikzpicture}
	\begin{axis}[
	  width=0.4\textwidth,
	  height=0.4\textwidth,
	  font=\scriptsize,
	  xmajorgrids,
	  ymajorgrids,
	  xlabel = Time (s),
	  ylabel = Angle (rad),
	  axis on top, % descriptions over filled area
	  legend pos=north east, % customize legend
	  ]
	  \addplot[mark=none, color=blue, thick] table[x index = {0}, y index = {2}]{\rampsteptorquecsv};    
	\end{axis}
      \end{tikzpicture}
}
  \caption{Ramp step with torque control.}
  \label{graphic:rampsteptorque_}
  
\end{figure}



On some of the ramp step, sawtooth and triangle graphics it is noticeable a spike in the tensile force; this is due to the pendulum's inertia. The sawtooth trials have the worst correlation because the servo couldn't unwind rope fast enough to allow the pendulum to freely return to the balance position. As for the decision to choose a control type for the servos it is still difficult to do; for now, only position will be discarded since it requires the definition of other parameters, namely velocity and torque.

As for the repeatability of the tests it can almost be assumed that the system is reliable because the initial conditions weren't exactly the same for every trial and still the correlations for the ramp and ramp step are good. As written before the initial conditions aren't exactly the same because the rope was loose. This somewhat acceptable correlation and the fact that these trials consume some time led to the decision of only repeating the second trials three times.

%Correlation of the results produced by different stimuli, controlling servo position.
\begin{table}[!hb]\centering
\ra{1.2}
\caption{Correlation of the results produced by different stimuli, controlling servo position.}
\label{table:position_control}
\begin{tabular}{@{}lllcll@{}}\toprule
\multirow{2}{*}{}             & \multicolumn{2}{l}{$\overline{r}$}&  & \multicolumn{2}{l}{$r_{\sigma}$}  \\ \cmidrule{2-3} \cmidrule{5-6}
                              & Force             & Angle           &  & Force                    & Angle                    \\ \midrule
\multicolumn{1}{l}{Ramp step} & 0.9421            & 0.9333          &  & 0.0127                   & 0.0457                   \\                              
\multicolumn{1}{l}{Ramp}      & 0.9623            & 0.9424          &  & 0.0055                   & 0.0741                   \\ 
\multicolumn{1}{l}{Sawtooth}  & 0.8598            & 0.9744          &  & 0.0798                   & 0.0221                   \\ 
\multicolumn{1}{l}{Triangle}  & 0.8547            & 0.9675          &  & 0.0235                   & 0.0393                   \\ 
\bottomrule
\end{tabular}
\end{table}

%Correlation of the results produced by different stimuli, controlling servo velocity.
\begin{table}[!hb]\centering
\ra{1.2}
\caption{Correlation of the results produced by different stimuli, controlling servo velocity.}
\label{table:velocity_control}
\begin{tabular}{@{}lllcll@{}}\toprule
\multirow{2}{*}{}               & \multicolumn{2}{l}{$\overline{r}$} && \multicolumn{2}{l}{$r_{\sigma}$} \\ \cmidrule{2-3} \cmidrule{5-6}
                                & Force             & Angle           & & Force                    & Angle                    \\ \midrule
\multicolumn{1}{l}{Ramp step} & 0.9410            & 0.9269            & & 0.0102                   & 0.0522                   \\                                 
\multicolumn{1}{l}{Ramp}      & 0.9141            & 0.9115            & & 0.0396                   & 0.0718                   \\ 
\multicolumn{1}{l}{Sawtooth}  & 0.4043            & 0.9280            & & 0.1601                   & 0.0558                   \\ 
\multicolumn{1}{l}{Triangle}  & 0.9192            & 0.6951            & & 0.0215                   & 0.2878                   \\ 
\bottomrule
\end{tabular}
\end{table}

%Correlation of the results produced by different stimuli, controlling servo torque.
\begin{table}[!hb]\centering
\ra{1.2}
\caption{Correlation of the results produced by different stimuli, controlling servo torque.}
\label{table:torque_control}
\begin{tabular}{@{}lllcll@{}}\toprule
\multirow{2}{*}{}               & \multicolumn{2}{l}{$\overline{r}$} & & \multicolumn{2}{l}{$r_{\sigma}$} \\ \cmidrule{2-3} \cmidrule{5-6}
                              & Force             & Angle             & & Force                    & Angle                    \\ \midrule
\multicolumn{1}{l}{Ramp step} & 0.9435            & 0.9538            & & 0.0214                   & 0.0396                   \\                               
\multicolumn{1}{l}{Ramp}      & 0.9411            & 0.9737            & & 0.0303                   & 0.0298                   \\ 
\multicolumn{1}{l}{Sawtooth}  & 0.3289            & 0.9201            & & 0.0673                   & 0.0845                   \\ 
\multicolumn{1}{l}{Triangle}  & 0.8238            & 0.6961            & & 0.0634                   & 0.3843                   \\ 
\bottomrule
\end{tabular}
\end{table}



\section{Second Trials Results Presentation and Discussion}

Annex \ref{annex:second_stimuli} shows one set of graphics per trial, these sets were repeated three times. From these graphics it can be concluded that the stimuli should be applied at maximum torque or velocity and for short durations to avoid the spikes seen in some of the actuating force graphics. The servos can't unwind rope at the same speed that the pendulum's elastic units react. Figure \ref{graphic:_pulse_t800_01_1__} shows a set of these graphics as an example.

\begin{figure}[!htb]
	\centering
  \pgfplotstableread[col sep = comma]{Graficos/torque/pulse_t800_01_1.csv}\pulsetoitocentosumcsv
  
  \subfloat[Tensile Force 1, actuating cable.]{
  \tikzsetnextfilename{Grafs-Second/torque800/_pulse_t800_01_1_force1}
      \begin{tikzpicture}
	\begin{axis}[
	  width=0.3\textwidth,
	  height=0.3\textwidth,
	  font=\scriptsize,
	  xmajorgrids,
	  ymajorgrids,
	  xlabel = Time (s),
	  ylabel = Force (N),
	  %ylabel style={overlay, anchor=north,},
	  axis on top, % descriptions over filled area
	  legend pos=north east, % customize legend 
	  ]
	  \addplot[mark=none, color=blue, thick] table[x index = {0}, y index = {1}]{\pulsetoitocentosumcsv};
	\end{axis}
      \end{tikzpicture}
      %\label{subfigure:step_actforce}
  } %subfloat
   \subfloat[Angle of the pendulum.]{
      \begin{tikzpicture}
      \tikzsetnextfilename{Grafs-Second/torque800/_pulse_t800_01_1_angle}
	\begin{axis}[
	  width=0.3\textwidth,
	  height=0.3\textwidth,
	  font=\scriptsize,
	  xmajorgrids,
	  ymajorgrids,
	  xlabel = Time (s),
	  ylabel = Angle (rad),
	  %ylabel style={overlay, anchor=north,},
	  axis on top, % descriptions over filled area
	  legend pos=north east, % customize legend
	  ]
	  \addplot[mark=none, color=blue, thick] table[x index = {0}, y index = {2}]{\pulsetoitocentosumcsv}; 
	\end{axis}
      \end{tikzpicture}
      %\label{subfigure:step_angle}
} %subfloat
     \subfloat[Tensile Force 2, passive cable.]{
     \tikzsetnextfilename{Grafs-Second/torque800/_pulse_t800_01_1_force2}
      \begin{tikzpicture}
	\begin{axis}[
	  width=0.3\textwidth,
	  height=0.3\textwidth,
	  font=\scriptsize,
	  xmajorgrids,
	  ymajorgrids,
	  xlabel = Time (s),
	  ylabel = Force (N),
	  %ylabel style={overlay, anchor=north,},
	  axis on top, % descriptions over filled area
	  legend pos=north east, % customize legend
	  ]
	  \addplot[mark=none, color=blue, thick] table[x index = {0}, y index = {3}]{\pulsetoitocentosumcsv};
	\end{axis}
      \end{tikzpicture}
      %\label{subfigure:step_angle}
} %subfloat
  
  \caption{Pulse with 800 torque and 0.1 s duration.}
  \label{graphic:_pulse_t800_01_1__}
  
\end{figure}



As for the quality of these results, it can be seen in tables \ref{table:pulse_torque_correlation} and \ref{table:pulse_velocity_correlation}, for torque and velocity respectively. The initial conditions and its variations can be seen in tables \ref{table:pulse_torque_initial} and \ref{table:pulse_velocity_initial}, for torque and velocity respectively.

Crossing the correlation tables with the respective initial values table makes it clear that the trial can be easily repeated because even though there were some high deviations of the initial tensile force this did not affect the test correlation. All the correlations coefficients are sufficiently high to consider enough the number of trial repetitions, which was three. It was considered that for statistical purposes three trials might not be enough but since the correlations are mostly above 0.99 these results are considered valid.

%Correlation of the results produced by pulse stimuli with different durations, controlling servo torque.
\begin{table}[!hb]\centering
\ra{1.2}
\caption{Correlation of the results produced by pulse stimuli with different durations, controlling servo torque.}
\label{table:pulse_torque_correlation}
\begin{tabular}{@{}lllllclll@{}}\toprule
\multicolumn{2}{l}{}                                            & \multicolumn{3}{c}{$\overline{r}$} & & \multicolumn{3}{c}{$r_{\sigma}$} \\ \cmidrule{3-5}  \cmidrule{7-9} 
\multicolumn{1}{l}{Torque}                                & Time (s) & Force 1     & Angle      & Force 2   & & Force 1          & Angle          & Force 2         \\ \midrule
\multicolumn{1}{l}{\multirow{3}{*}{800}}  & 0.1      & 0.9984      & 0.9947     & 0.9986    & & 0.0008           & 0.0021         & 0.0002          \\ 
\multicolumn{1}{l}{}                               & 0.25     & 0.9926      & 0.9642     & 0.9930   &  & 0.0046           & 0.0438         & 0.0055          \\ 
\multicolumn{1}{l}{}                               & 0.5      & 0.9956      & 0.9975     & 0.9972    & & 0.0007           & 0.0008         & 0.0004          \\ \hdashline
\multicolumn{1}{l}{\multirow{3}{*}{900}}  & 0.1      & 0.9947      & 0.9965     & 0.9954    & & 0.0017           & 0.0015         & 0.0030          \\  
\multicolumn{1}{l}{}                               & 0.25     & 0.9842      & 0.9957     & 0.9903    & & 0.0115           & 0.0005         & 0.0072          \\ 
\multicolumn{1}{l}{}                               & 0.5      & 0.9825      & 0.9943     & 0.9968    & & 0.0092           & 0.0032         & 0.0017          \\ \hdashline
\multicolumn{1}{l}{\multirow{3}{*}{1023}} & 0.1      & 0.9924      & 0.9974     & 0.9943    & & 0.0035           & 0.0012         & 0.0040          \\ 
\multicolumn{1}{l}{}                               & 0.25     & 0.9932      & 0.9958     & 0.9940    & & 0.0045           & 0.0012         & 0.0045          \\ 
\multicolumn{1}{l}{}                               & 0.5      & 0.9929      & 0.9970     & 0.9940    & & 0.0042           & 0.0006         & 0.0044          \\  \bottomrule
\end{tabular}
\end{table}

%Initial conditions of trials with the pulse stimuli with different durations, controlling servo torque.
\begin{table}[!hb]\centering
\ra{1.2}
\caption{Initial conditions of trials with the pulse stimuli with different durations, controlling servo torque.}
\label{table:pulse_torque_initial}
\resizebox{\textwidth}{!}{\begin{tabular}{@{}lllllclll@{}}\toprule
\multicolumn{2}{l}{}                                 & \multicolumn{3}{c}{Initial Values Mean}     & & \multicolumn{3}{c}{Initial Values Standard Deviation} \\ \cmidrule{3-5}  \cmidrule{7-9} 
\multicolumn{1}{l}{Torque}                & Time (s) & Force 1 (N) & Angle (\degree) & Force 2 (N) & & Force 1 (N)     & Angle(\degree)     & Force 2 (N)     \\ \midrule
\multicolumn{1}{l}{\multirow{3}{*}{800}}  & 0.1      & 4.0125      & 89.9958         & 3.8597      & & 0.0871          & 0.0740             & 0.0445          \\ 
\multicolumn{1}{l}{}                      & 0.25     & 3.7747      & 89.9719         & 4.1636      & & 0.1771          & 0.0683             & 0.0807          \\  
\multicolumn{1}{l}{}                      & 0.5      & 3.8791      & 90.0486         & 4.1636      & & 0.4013          & 0.0372             & 0.3078          \\ \hdashline
\multicolumn{1}{l}{\multirow{3}{*}{900}}  & 0.1      & 3.7717      & 89.9520         & 4.1923      & & 0.2287          & 0.0360             & 0.1487          \\  
\multicolumn{1}{l}{}                      & 0.25     & 3.9325      & 89.9476         & 4.0179      & & 0.3211          & 0.0441             & 0.1124          \\ 
\multicolumn{1}{l}{}                      & 0.5      & 3.7028      & 90.0218         & 4.0295      & & 0.1426          & 0.0545             & 0.1395          \\ \hdashline
\multicolumn{1}{l}{\multirow{3}{*}{1023}} & 0.1      & 3.7827      & 90.0120         & 4.0037      & & 0.0266          & 0.0146             & 0.1851          \\
\multicolumn{1}{l}{}                      & 0.25     & 3.8746      & 90.0398         & 3.9139      & & 0.1095          & 0.0751             & 0.2224          \\ 
\multicolumn{1}{l}{}                      & 0.5      & 3.5811      & 90.0284         & 3.8578      & & 0.01647         & 0.0482             & 0.2550          \\ 
\bottomrule
\end{tabular}}
\end{table}

%Correlation of the results produced by pulse stimuli with different durations, controlling servo velocity
\begin{table}[!hb]\centering
\ra{1.2}
\caption{Correlation of the results produced by pulse stimuli with different durations, controlling servo velocity.}
\label{table:pulse_velocity_correlation}
\begin{tabular}{@{}lllllclll@{}}\toprule
\multicolumn{2}{l}{}                                & \multicolumn{3}{c}{$\overline{r}$} & & \multicolumn{3}{c}{$r_{\sigma}$} \\  
\cmidrule{3-5}  \cmidrule{7-9}
\multicolumn{1}{l}{Velocity}                        & Time (s) & Force 1     & Angle      & Force 2    & & Force 1    & Angle   & Force 2         \\ 
\midrule
\multicolumn{1}{l}{\multirow{3}{*}{800}}            & 0.1      & 0.9965      & 0.9704     & 0.9970     & & 0.0005     & 0.0233  & 0.0012          \\  
\multicolumn{1}{l}{}                                & 0.25     & 0.9986      & 0.9836     & 0.9982     & & 0.0005     & 0.0061  & 0.0008          \\ 
\multicolumn{1}{l}{}                                & 0.5      & 0.9403      & 0.9866     & 0.9946     & & 0.0242     & 0.0038  & 0.0021          \\ 
\hdashline
\multicolumn{1}{l}{\multirow{3}{*}{900}}            & 0.1      & 0.9974      & 0.9477     & 0.9977     & & 0.0011     & 0.0428  & 0.0011          \\  
\multicolumn{1}{l}{}                                & 0.25     & 0.9939      & 0.9828     & 0.9971     & & 0.0035     & 0.0121  & 0.0015          \\ 
\multicolumn{1}{l}{}                                & 0.5      & 0.9804      & 0.9934     & 0.9915     & & 0.0131     & 0.0039  & 0.0059          \\ 
\hdashline
\multicolumn{1}{l}{\multirow{3}{*}{1023}}           & 0.1      & 0.9967      & 0.9810     & 0.9960     & & 0.0021     & 0.0133  & 0.0029          \\ 
\multicolumn{1}{l}{}                                & 0.25     & 0.9923      & 0.9969     & 0.9975     & & 0.0042     & 0.0006  & 0.0014          \\
\multicolumn{1}{l}{}                                & 0.5      & 0.9467      & 0.9884     & 0.9901     & & 0.0325     & 0.0085  & 0.0070          \\ \bottomrule
\end{tabular}
\end{table}

%Initial conditions of trials with the pulse stimuli with different durations, controlling servo velocity.
\begin{table}[!hb]\centering
\ra{1.2}
\caption{Initial conditions of trials with the pulse stimuli with different durations, controlling servo velocity.}
\label{table:pulse_velocity_initial}
\resizebox{\textwidth}{!}{\begin{tabular}{@{}lllllclll@{}}\toprule
\multicolumn{2}{l}{}     & \multicolumn{3}{c}{Initial Values Mean}   & & \multicolumn{3}{c}{Initial Values Standard Deviation} \\\cmidrule{3-5}  \cmidrule{7-9}
\multicolumn{1}{l}{Velocity}              & Time (s) & Force 1 (N) & Angle (\degree) & Force 2 (N) & & Force 1 (N) & Angle(\degree) & Force 2 (N)    \\
\midrule
\multicolumn{1}{l}{\multirow{3}{*}{800}}  & 0.1      & 3.7166      & 89.1194         & 4.0151      & & 0.1186      & 0.7606         & 0.1045         \\ 
\multicolumn{1}{l}{}                      & 0.25     & 3.6941      & 89.2527         & 3.9003      & & 0.0828      & 0.8207         & 0.2572         \\ 
\multicolumn{1}{l}{}                      & 0.5      & 3.6489      & 89.6939         & 3.9247      & & 0.1229      & 0.5049         & 0.2141         \\
\hdashline
\multicolumn{1}{l}{\multirow{3}{*}{900}}  & 0.1      & 3.6304      & 89.1316         & 3.8276      & & 0.1884      & 0.9508         & 0.1806         \\
\multicolumn{1}{l}{}                      & 0.25     & 3.7447      & 89.7734         & 4.0183      & & 0.2516      & 0.8168         & 0.2853         \\
\multicolumn{1}{l}{}                      & 0.5      & 3.6319      & 89.1251         & 3.9527      & & 0.1795      & 0.5337         & 0.2627         \\
\hdashline
\multicolumn{1}{l}{\multirow{3}{*}{1023}} & 0.1      & 4.0992      & 90.0413         & 4.1990      & & 0.1611      & 0.1963         & 0.4638         \\
\multicolumn{1}{l}{}                      & 0.25     & 3.9386      & 90.0330         & 3.8830      & & 0.1650      & 0.0994         & 0.1817         \\
\multicolumn{1}{l}{}                      & 0.5      & 3.7914      & 90.0630         & 3.9111      & & 0.2261      & 0.1279         & 0.3125         \\
\bottomrule
\end{tabular}}
\end{table}


And so, the evaluation of the application of stimuli proved that this concept satisfies the need for repeatability. When it comes to different types of stimuli there is a need to test is it can be repeatable,



