  Leader Election is an important primitive for programmable matter, since it
is often an intermediate step for the solution of more complex problems.
Although the leader election problem itself is well studied even in the
specific context of programmable matter systems, research on fault tolerant
approaches is more limited. We consider the problem in the previously studied
Amoebot model on a triangular grid, when the configuration is connected but
contains nodes the particles cannot move to (e.g., obstacles). We assume that
particles agree on a common direction (i.e., the horizontal axis) but do not
have chirality (i.e., they do not agree on the other two directions of the
triangular grid). We begin by showing that an election algorithm with explicit
termination is not possible in this case, but we provide an implicitly
terminating algorithm that elects a unique leader without requiring any
movement. These results are in contrast to those in the more common model with
chirality but no agreement on directions, where explicit termination is always
possible but the number of elected leaders depends on the symmetry of the
initial configuration. Solving the problem under the assumption of one common
direction allows for a unique leader to be elected in a stationary and
deterministic way, which until now was only possible for simply connected
configurations under a sequential scheduler.
