  The introduction and study of dispersing mobile robots across the nodes of an
anonymous graph have recently gained traction and have been explored within
various graph classes and settings. While optimal dispersion solution was
established for {\em oriented} grids [Kshemkalyani et al., WALCOM 2020], a
significant unresolved question pertains to whether achieving optimal
dispersion is feasible on an {\em unoriented} grid. This paper investigates the
dispersion problem on unoriented grids, considering both non-faulty and faulty
robots. The challenge posed by unoriented grids lies in the absence of a clear
sense of direction for a single robot moving between nodes, as opposed to the
straightforward navigation of oriented grids.
  We present three deterministic algorithms tailored to our robot model. The
first and second algorithms deal with the dispersion of faulty and non-faulty
robots, ensuring both time and memory optimization in oriented and unoriented
grids, respectively. Faulty robots that are prone to crashing at any time,
causing permanent failure. In both settings, we achieve dispersion in
$O(\sqrt{n})$ rounds while requiring $O(\log n)$ bits of memory per robot. The
third algorithm tackles faulty robots prone to crash faults in an unoriented
grid. In this scenario, our algorithm operates within $O(\sqrt{n} \log n)$ time
and uses $O(\sqrt{n} \log n)$ bits of memory per robot. The robots need to know
the value of $n$ for termination.
