For the vertical column approach with limited sensors 
% we
are defined as column vector $\mathbf{c}_j$:

\begin{equation}
\mathbf{c}_j^{(i,d)} = [S_{0+j}^{(i+d)}, S_{5+j}^{(i+d)}, S_{10+j}^{(i+d)}, S_{15+j}^{(i+d)}, S_{20+j}^{(i+d)}, S_{25+j}^{(i+d)}]^T
\end{equation}
\begin{equation}
\mathbf{D}^{(i)} = [\mathbf{c}_0^{(i,i+1)}, \mathbf{c}_1^{(i,i+6)}, \mathbf{c}_2^{(i,i+11)}, \mathbf{c}_3^{(i,i+16)}, \mathbf{c}_4^{(i,i+21)}]^T
\end{equation}

where $j \in \{0, 1,2,3,4\}$ represents the column index.

For the limited sensor case focusing on endpoints only, we use:

\begin{equation}
\mathbf{c}^{\text{limited}}_j = [S_{0+(j-1)}, S_{25+(j-1)}]^T
\end{equation}

representing only the lower sensor (sensor A) and upper sensor (sensor B) of column $j$.