Lattice stability - Lycée de la Salle (Alès)

We have a lattice with squared meshes. The bars which compose it are jointed. Without the addition of diagonal bars, such lattice is flexible.The questions that can be raised are as follow:
\begin{itemize}
\item What is the minimum number of diagonal bars required to make a lattice of $L$ mesh over $\ell$ meshes
\item Is there an algorithm which would enable to make such lattice rigid using as few bars as possible?
\item Is it possible to determine whether a given lattice is rigid or not?
\item How generalise all this with a lattice in dimension 3?
\end{itemize}