% ----------------------------------------------------
% ------------- Results and Discussion ---------------
% ----------------------------------------------------

	As mentioned on the first chapter, this project aims the development of a system able to comply several issues of concern, such as: flexibility, easy-to-use, non-invasiveness, robustness and real-time monitoring. To understand if the developed system fulfils these requirements, several experiments were performed. These experiments were conducted in two states: stationary driving and real driving situations.
	
	
\section{Stationary Driving Situations}

% --------- Stationary Driving Situation -------------
	
	In stationary driving conditions, it was possible to evaluate the fastening system in the pedals as well as the calibration process. To understand if the fastening system was working properly, the system was installed in a variety of pedals of several vehicles while they were turned off.

	In one of the tests, the system was installed in the clutch and brake pedals of a \textit{Peugeot 207} (Figure \ref{fig:peugeot_207}). The system was easily installed and the calibrations created for each pedal were intuitive and fast. The few errors while calibrating the brake pedal, were simply corrected by readjusting the orientation of the infrared (IR) sensors. 

\begin{figure}[htbp]
\centering
  	\includegraphics[width=0.6\textwidth]{images/peugeot_206.jpg}
  	\caption{Setup installed on a Peugeot 207.}\label{fig:peugeot_207}
\end{figure}	
	
	The system was also installed in the clutch and brake pedals of the \textit{AtlasCAR} (Figure \ref{fig:setup_atlascar}). In this case the installation was easier than in the \textit{Peugeot 207}, mainly due to the different materials of the pedals: metal for the \textit{Peugeot 207} and rubber for the \textit{AtlasCAR}.

\begin{figure}[htbp]
\centering
  	\includegraphics[width=0.6\textwidth]{images/setup_atlas_car.jpg}
  	\caption{Setup installed on the AtlasCAR.}\label{fig:setup_atlascar}
\end{figure}
		
	For all the tested pedals of vehicles, the system generally revealed an effortless and quick installation. Thus, it was possible to validate the flexibility and ease of use of the developed system to monitor the vehicle pedals. Regarding the calibration, the process was relatively fast and easy to follow. There were a few errors while calibrating due to the wrong orientation of the IR sensors, however, they were automatically identified by the interface and the driver was immediately warned to correct it.

% ----------------------------------------------------
	
\section{Real Driving Situations}

% --------------- Real Driving Situation -------------

	In real driving conditions, it was possible to test the non-invasiveness and robustness of the system. Importantly, it was also possible to test if the pedals could be monitored in real-time. As for the stationary driving conditions, these tests were also performed in several vehicles.
	
	In order to validate those conditions, the system was installed and tested in two different driving situations:
	
\begin{itemize}
\item The same driving route and vehicle for different drivers; 
\item Different velocities, stopping the car only using the brake pedal.\\
\end{itemize}

% ----------------------------------------------------


\subsection{Preliminary test}	

	Before performing the tests mentioned above, a preliminary test was made in order to observe the system capabilities. For this test, the \textit{AtlasCAR} was driven through the route shown in Figure \ref{fig:data_route}. Because the \textit{AtlasCAR} has an odometer system installed, it was also possible to obtain the velocity overtime. This is an advantage because it is possible to correlate the action on the pedals with its consequences in the velocity.

\begin{figure}[htbp]
        \centering
        \includegraphics[width=0.4\textwidth]{images/trajeto-preliminar.png}
        \caption[Route for the preliminary test.]{Route for the preliminary test \cite{google_maps}.}\label{fig:data_route}
\end{figure}

	With this preliminary test, it was possible to conclude about several characteristics of the system. Firstly, due to the fact that the system was not a nuisance to the driver, it was possible to confirm its non-invasiveness. Moreover, while driving, it was possible to test the robustness of the system. The system showed to be very robust in terms of collecting data, so that it was possible to infer the real actuation on the pedals just by looking at the displayed data on the monitoring interface. However, in terms of the fixation on the pedals it was not much effective. This lack of effectiveness was partially due to the non linear geometry of the pedal shaft, which makes it quite difficult to secure the system so it is firmly fixed. In order to improve this, it is possible to use other fixing systems, such as a belt.

	Finally, the velocity and force values were normalized to their maximum values. By comparing the data collected from the brake with data from the clutch (Figure \ref{fig:preliminar_test}) it was possible to analyse the behaviour of both pedals. 

\begin{figure}[htbp]
\centering
  	\includegraphics[width=\textwidth]{images/preliminary_test.eps}
  	\caption{Data of the preliminary test from brake (top) and clutch (bottom) pedals, with a median filter applied, between 100s and 250s.}\label{fig:preliminar_test}
\end{figure}
  

	Also, to understand if there was a correlation between the velocity and the pedal forces, the kinetic energy of the car and the braking energy were taking into account. These energies were calculated as shown in Equation \ref{eq:preliminary_eq}.
	
\begin{equation}
\Delta E_{braking} =\left | \Delta E_c \right | \Leftrightarrow \int_{0}^{t} F_{brake} \cdot v_{car} \cdot dt=\frac{1}{2}\cdot m_{car} \cdot \left |(v_f^2-v_i^2)\right |
\label{eq:preliminary_eq}
\end{equation}
\linebreak
	By assuming that the force applied on the brake pedal is proportional to the braking force, as shown in Equation \ref{eq:proportionality_eq}, it was possible to find the ratio between the kinetic energy of the car and the braking energy using the force applied on the brake pedal, shown in Equation \ref{eq:K_value}.
		
\begin{equation}
F_{braking} = K \cdot F_{pedal}
\label{eq:proportionality_eq}
\end{equation}

\begin{equation}
K=\frac{\frac{1}{2}\cdot m_{car} \cdot \left |(v_f^2-v_i^2)\right |}{\int_{0}^{t} F_{pedal} \cdot v_{car} \cdot dt}
\label{eq:K_value}
\end{equation}
\linebreak
	Due to the high amount of information collected in this test, only a selected part was analysed, between 100 and 250 seconds, shown in Table \ref{tb:preliminary_test}.
	

\begin{table}[htbp]
\centering
\begin{tabular}{|c|c|c|c|c|}
\hline
\textbf{$v_{i}$} & \textbf{$v_{f}$} & \textbf{$\left | v_{f}^2 - v_{i}^2 \right |$} & \textbf{$\int_{0}^{t} F_{pedal}.v_{car}.dt$} & \textbf{$K$} \\ \hline
0.629              & 0.257                      & 0.330                      & 0.530                   & 0.622                      \\ \hline
0.604              & 0.286                      & 0.283                      & 0.491                   & 0.577                      \\ \hline
0.542              & 0.345                      & 0.175                      & 0.365                   & 0.480                      \\ \hline
0.326              & 0.116                      & 0.093                      & 0.186                   & 0.501                      \\ \hline
0.515              & 0.283                      & 0.185                      & 0.263                   & 0.705                      \\ \hline
0.255              & 0.240                      & 0.007                      & 0.003                   & 2.8717                     \\ \hline
0.223              & 0.154                      & 0.026                      & 0.048                   & 0.544                      \\ \hline
0.805              & 0.714                      & 0.138                      & 0.161                   & 0.857                      \\ \hline
0.681              & 0.624                      & 0.075                      & 0.084                   & 0.891                      \\ \hline
0.573              & 0.549                      & 0.027                      & 0.041                   & 0.652                      \\ \hline
0.522              & 0.502                      & 0.020                      & 0.020                   & 1.016                      \\ \hline
0.485              & 0.362                      & 0.104                      & 0.156                   & 0.669                      \\ \hline
0.315              & 0.269                      & 0.027                      & 0.031                   & 0.871                      \\ \hline
\end{tabular}
\caption[Data of the preliminary test from brake pedal, between 100s and 250s.]{Data of the preliminary test from brake pedal, between 100s and 250s. For each braking situation: initial and final velocities, the kinetic energy, the energy of the pedals and the ratio K between the kinetic energy and the energy of the pedals.}
\label{tb:preliminary_test}
\end{table}


	By observing the spikes on the graph, it seems that generally the clutch is pressed much more times than the brake. Moreover, it was possible to find that the forces on the brake pedal and the velocity of the car are on average inversely correlated, meaning that generally when the force on the brake pedal increases, the velocity decreases. These values are not significantly correlated, maybe due to signal noise and other external variables, such as road slopes, engine braking, etc. By looking at the graph, it is possible to see that the Force Sensitive Resistors (FSRs) values reach saturation levels much faster than the Load Cells (LCs). Thus, for a more accurate analysis, only data from the LCs was taken into account. To attenuate the noise-to-signal ratio, a median filter was applied. A median filter is a non-linear digital filtering technique, which consists in replacing each entry with the median of neighbouring entries.

% ----------------------------------------------------


\subsection{Tests performed with different drivers for the same driving route and vehicle}		
  
	The tests regarding the validation of the system by collecting data on the same driving route (Figure \ref{fig:trajeto-subjectA_B}) and the same vehicle but with different drivers were performed in the \textit{AtlasCAR}. Eleven subjects tested the system in these conditions.\\ 

\begin{figure}[!h]
\centering
  	\includegraphics[width=0.5\textwidth]{images/trajeto-subjectA_B.png}
  	\caption[Route for the first test, for the same car and different drivers.]{Route for the first test, for the same car and different drivers \cite{google_maps}.}\label{fig:trajeto-subjectA_B}
\end{figure}

	By analysing the data collected from these tests, it was possible to evaluate the drivers behaviour. Three representative examples are shown in Figure \ref{fig:subjectA_subjectB_same_route}. It is possible to see that, for instance, Subject A uses much less the brake than Subject B or C. The brake intensity of Subject A is also inferior to the brake intensity of the other subjects, that reach high levels most of the times thus leading to the saturation point of the force sensors (Table \ref{tb:loadcell_intensity}). Thus, overall Subject A seems to have a sporty driving, while Subject B and C appear to have a more normal driving. With these tests it was possible to validate the robustness of the system in detecting different driving patterns from different subjects.

\begin{figure}[htbp]
\centering
  	\includegraphics[width=\textwidth]{images/subjectA_subjectB_same_route.eps}
  	\caption{Data collected in the first test, for the same route, same car and different drivers. Top: Subject A; Middle: Subject B; Bottom: Subject C.}\label{fig:subjectA_subjectB_same_route}
\end{figure}

\begin{table}[htbp]
\centering
\begin{tabular}{|c|c|c|c|}
\hline
\textbf{Subject} & \textbf{Pressed {[}Times{]}} & \textbf{Average {[}\%{]}} & \textbf{Max {[}\%{]}} \\ \hline
\textbf{A}       & 4                            & 1                         & 43                    \\ \hline
\textbf{B}       & 10                           & 9                         & 100                   \\ \hline
\textbf{C}       & 15                           & 9.6                       & 100                   \\ \hline
\textbf{D}       & 11                           & 11.6                      & 100                   \\ \hline
\textbf{E}       & 8                            & 9.8                       & 100                   \\ \hline
\textbf{F}       & 5                            & 0.8                       & 28.4                  \\ \hline
\textbf{G}       & 7                            & 1.8                       & 50                    \\ \hline
\textbf{H}       & 14                           & 8.4                       & 100                   \\ \hline
\textbf{I}       & 7                            & 3.1                       & 55                    \\ \hline
\textbf{J}       & 21                           & 3.4                       & 58                    \\ \hline
\end{tabular}
\caption[Data collected from the LoadCell for the subjects.]{Data collected from the LoadCell for the subjects. Number of times that the brake was pressed, the average and the maximum value of the applied force are presented.}
\label{tb:loadcell_intensity}
\end{table}
		
	After these tests each driver filled a form, in Figure \ref{fig:form}, in order to evaluate some features of the system, such as: 1) the ease of calibration and habituation (Figure \ref{fig:data_calib_habit}), 2) its interference with the normal driving (Figure \ref{fig:data_surveys}a), 3) its contribution for road safety (Figure \ref{fig:data_surveys}b) and 4) its use on a daily basis (Figure \ref{fig:data_surveys}c). The results of the inquiries confirm the ease of calibration and habituation to the system, seen before in the preliminary test. Also, it was possible to confirm its non-invasiveness, as for all subjects the system did not interfere with the normal driving. Finally, most of the subjects agree on the monitoring pedal system contribution for road safety and probably could use it on a daily basis.\\


\begin{figure}[!h]
\centering
  	\includegraphics[width=0.55\textwidth]{images/calibration_and_habituation.png}
  	\caption{Subjects evaluation of the calibration and habituation processes.}\label{fig:data_calib_habit}
\end{figure}

\begin{figure}[!h]
     \centering
     \subfloat[]{\includegraphics[width=0.25\textwidth]{images/system_interference.png}}
     \qquad
     \subfloat[]{\includegraphics[width=0.25\textwidth]{images/contribution_road_safety.png}}
     \qquad
     \subfloat[]{\includegraphics[width=0.25\textwidth]{images/use_daily_basis.png}}
     \caption{Subjects opinion of the system regarding its: a) interference with the normal driving, b) contribution for road safety and c) usage on daily basis.}\label{fig:data_surveys}
\end{figure}


\begin{figure}[htbp]
\centering
		\includegraphics[width=1.1\textwidth]{images/questionario.pdf}
	\caption{Form to evaluate the monitoring of vehicle pedals system.}
	\label{fig:form}
\end{figure}

% ----------------------------------------------------


\subsection{Tests done at different velocities, using only the brake pedal to stop the car}

	The tests using different velocities and only the brake pedal to stop the car, were performed in order to test if the force used on the brake pedal is actually proportional to the braking force and which would be the proportionality constant, K, as mentioned before. These tests were conducted under a velocity up to 60km/h and the brake was applied with the vehicle ungeared (with the clutch pedal fully pressed). This ungeared brake condition was necessary to reduce the influence of other variables for stopping the car, such as the engine braking.
	
	For the analysis of the collected data, a median filter was also applied to reduce the noite-to-signal ratio. In this case the velocity was normalized to 60km/h, which was the maximum velocity of these tests, as shown in Figure \ref{fig:braking_test_total}.
	
	First, the braking force periods were separated from the non-braking ones; for a braking force period to be considered for analysis the force applied on the pedal had to be higher than 1\%. To understand the correlation between the energy on the brake pedal and the energy to stop the car, the areas of the braking periods were calculated by integrating the product of the force with the velocity, for that time period. To look only to the relevant braking areas, the area values lower than the mean were discarded. With this, it was possible to find a proportionality constant that represents the average of the proportionality constants for each braking period. This constant was calculated by dividing the energy used to stop the car by the energy used on the brake pedal, as shown before in equation \ref{eq:K_value}. For these tests, the average of the proportionality constant value was $\sim$615.
	
	
\begin{figure}[htbp]
\centering
  	\includegraphics[width=\textwidth]{images/braking_test_total.pdf}
  	\caption{Data collected for different velocities using only the brake pedal to stop the car.}\label{fig:braking_test_total}
\end{figure}


	To diminish the variability associated with different velocities, the braking force periods were further sorted by a specific velocity, so that the starting point of each brake had to be comprised between $\pm$5km/h of the selected velocity. When analysing the group of braking force periods for 60$\pm$5km/h, as shown in Figure \ref{fig:braking_test_60}, the average of the proportionality constant found was $K=\sim677$ (Table \ref{tb:K_values_60}). The average of the proportionality constant for the braking force periods starting in 50$\pm$5km/h, as shown in Figure \ref{fig:braking_test_60}, was $K=\sim633$ (Table \ref{tb:K_values_50}). For the 40$\pm$5km/h and for the the 30$\pm$5km/h, as shown in Figures \ref{fig:braking_test_40} and \ref{fig:braking_test_30}, respectively, the average of the proportionality constant continues to decrease ($K=\sim526.50$ and $K=\sim510.40$), as shown in Table \ref{tb:K_values_40} and \ref{tb:K_values_30}. Unexpectedly, for the  20$\pm$5km/h velocity, as shown in Figure \ref{fig:braking_test_20}, the average of the proportionality constant increases ($K=\sim728.45$), as shown in Table \ref{tb:K_values_20}. 
	
	For the velocity of 40$\pm$5km/h the K values range considerably. This can be partially explained by the saturation of the load cells at certain time periods ($\sim$750-900s; Figure \ref{fig:braking_test_40}), which can be related to pressing the pedal over the calibration limits. Also, for the 30$\pm$5km/h and 20$\pm$5km/h velocities the K values continue to range considerably. This variations may be due to other variables that weren't taken into account, such as the energy transferred to the brakes and dampers, the kinetic friction between the wheels and the road. Moreover, it seems that for low velocities this kinetic friction has more impact in braking.

	Overall, it was possible to find a proportionality constant that appears to decrease with the velocity (Figure \ref{fig:linear_constant}). Meaning that perhaps the energy to stop the car decreases at the same rate as the velocity decreases.

\begin{figure}[!h]
\centering
  	\includegraphics[width=\textwidth]{images/braking_test_60.pdf}
  	\caption{Data analysis for 60 km/h using only the brake pedal to stop the car. Only the periods where there were relevant braking forces are shown, the dotted lines represent the excluded braking periods.}\label{fig:braking_test_60}
\end{figure}


\begin{table}[!h]
\centering
\begin{tabular}{c|c|}
\cline{2-2}
                                                         & \textbf{60 km/h} \\ \hline
\multicolumn{1}{|c|}{\multirow{5}{*}{\rotatebox[origin=c]{90}{\textbf{K values}}}} & 0.776                      \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.678                      \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.647                      \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.827                      \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.627                     \\ \hline
\multicolumn{1}{|c|}{\textbf{$\overline{K}$}}                   & \textbf{0.678}             \\ \hline
\end{tabular}
\caption{K values for 60 km/h.}
\label{tb:K_values_60}
\end{table}


\begin{figure}[!h]
\centering
  	\includegraphics[width=\textwidth]{images/braking_test_50.pdf}
  	\caption{Data analysis for 50 km/h using only the brake pedal to stop the car. Only the periods where there were relevant braking forces are shown, the dotted lines represent the excluded braking periods.}
  	\label{fig:braking_test_50}
\end{figure}

\begin{table}[!h]
\centering
\begin{tabular}{c|c|}
\cline{2-2}
                                                         & \textbf{50 km/h} \\ \hline
\multicolumn{1}{|c|}{\multirow{6}{*}{\rotatebox[origin=c]{90}{\textbf{K values}}}} & 0.671                      \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.648           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.547           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.577           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.711           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.619           \\ \hline
\multicolumn{1}{|c|}{\textbf{$\overline{K}$}}                   & \textbf{0.634}             \\ \hline
\end{tabular}
\caption{K values for 50 km/h.}
\label{tb:K_values_50}
\end{table}



\begin{figure}[!h]
\centering
  	\includegraphics[width=\textwidth]{images/braking_test_40.pdf}
  	\caption{Data analysis for 40 km/h using only the brake pedal to stop the car. Only the periods where there were relevant braking forces are shown, the dotted lines represent the excluded braking periods.}
  	\label{fig:braking_test_40}
\end{figure}


\begin{table}[!h]
\centering
\begin{tabular}{c|c|}
\cline{2-2}
                                                          & \textbf{40 km/h} \\ \hline
\multicolumn{1}{|c|}{\multirow{14}{*}{\rotatebox[origin=c]{90}{\textbf{K values}}}} & 0.843           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.524           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.646          \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.284           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.338           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.529           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.332           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.377           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.419           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.456           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 1.299         \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.842          \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.959           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                    & 0.544           \\ \hline
\multicolumn{1}{|c|}{\textbf{$\overline{K}$}}                    & \textbf{0.526}  \\ \hline
\end{tabular}
\caption{K values for 40 km/h.}
\label{tb:K_values_40}
\end{table}


\begin{figure}[!h]
\centering
  	\includegraphics[width=\textwidth]{images/braking_test_30.pdf}
  	\caption{Data analysis for 30 km/h using only the brake pedal to stop the car. Only the periods where there were relevant braking forces are shown, the dotted lines represent the excluded braking periods.}
  	\label{fig:braking_test_30}
\end{figure}

\begin{table}[!h]
\centering
\begin{tabular}{c|c|}
\cline{2-2}
                                                          & \textbf{30 km/h} \\ \hline
\multicolumn{1}{|c|}{\multirow{7}{*}{\rotatebox[origin=c]{90}{\textbf{K values}}}} & 0.888           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 1.181          \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.389          \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.298           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.670           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.510           \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.462           \\ \hline
\multicolumn{1}{|c|}{\textbf{$\overline{K}$}}                    & \textbf{0.510}  \\ \hline
\end{tabular}
\caption{K values for 30 km/h.}
\label{tb:K_values_30}
\end{table}


\begin{figure}[!h]
\centering
  	\includegraphics[width=\textwidth]{images/braking_test_20.pdf}
  	\caption{Data analysis for 20 km/h using only the brake pedal to stop the car. Only the periods where there were relevant braking forces are shown, the dotted lines represent the excluded braking periods.}
  	\label{fig:braking_test_20}
\end{figure}

\begin{table}[!h]
\centering
\begin{tabular}{c|c|}
\cline{2-2}
                                                          & \textbf{20 km/h} \\ \hline
\multicolumn{1}{|c|}{\multirow{8}{*}{\rotatebox[origin=c]{90}{\textbf{K values}}}} & 0.411          \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.575          \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.781          \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 1.065          \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.572          \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.782          \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 0.676         \\ \cline{2-2} 
\multicolumn{1}{|c|}{}                                   & 1.156          \\ \hline
\multicolumn{1}{|c|}{\textbf{$\overline{K}$}}                    & \textbf{0.728}  \\ \hline
\end{tabular}
\caption{K values for 20 km/h.}
\label{tb:K_values_20}
\end{table}
	
\begin{figure}[!h]
\centering
  	\includegraphics[width=\textwidth]{images/linear_constant.pdf}
  	\caption{Proportionality constant, K value, across the velocity.}\label{fig:linear_constant}
\end{figure}

	
% ----------------------------------------------------

\section{Application in Intelligent Monitoring context}

% --- Application in intelligent monitoring context --

	As mentioned before, there are several assistance driving systems. For example, a visual system to detect pedestrians can detect if an object is crossing the road and calculate and warn the driver about the estimated time to collision (ETC). These calculations are generally based on the velocity of the car, on the velocity of the object and on the distance to the object. Independently of the vehicle, if these variables are the same the ETC would also be the same. Nonetheless, the braking response is different in each vehicle, which could lead to a not sufficient and efficient braking. 
	
	By integrating the monitoring system with this visual system, it would be possible to improve these braking situations. For instance, by knowing the necessary time to brake in safety and replacing it by $t$ on the Equation \ref{eq:K_value_total} and assuming that the final velocity would be 0, $v_{f}=0$, it would be possible to find the required force to be applied on the brake pedal.\\
	
\begin{equation}
K=\frac{\frac{1}{2}\cdot m_{car} \cdot \left |(v_f^2-v_i^2)\right |}{\int_{0}^{t} F_{pedal} \cdot v_{car} \cdot dt} \Leftrightarrow  K=\frac{\frac{1}{2}\cdot m_{car} \cdot \left |-v_i^2\right |}{\int_{0}^{t} F_{pedal} \cdot v_{car} \cdot dt}
\label{eq:K_value_total}
\end{equation}
\linebreak
Also, assuming that while driving the mass of car can be considered constant, it is possible to simplify the Equation \ref{eq:K_value_total}:\\

\begin{equation}
K=\frac{\frac{1}{2}\cdot m_{car} \cdot \left |-v_i^2\right |}{\int_{0}^{t} F_{pedal} \cdot v_{car} \cdot dt} \Leftrightarrow  K_{2}=\frac{\left |-v_i^2\right |}{\int_{0}^{t} F_{pedal} \cdot v_{car} \cdot dt}
\label{eq:K_value_final}
\end{equation}
\linebreak
With this required force to brake safely and by knowing the force applied on the brake pedal in real time, this intelligent monitoring system could warn the driver accordingly if the force applied is more or less than the required to stop the vehicle safely.


% ----------------------------------------------------