  Self-stabilization is a versatile technique to withstand any transient fault
in a distributed system. Mobile robots (or agents) are one of the emerging
trends in distributed computing as they mimic autonomous biologic entities. The
contribution of this paper is threefold. First, we present a new model for
studying mobile entities in networks subject to transient faults. Our model
differs from the classical robot model because robots have constraints about
the paths they are allowed to follow, and from the classical agent model
because the number of agents remains fixed throughout the execution of the
protocol. Second, in this model, we study the possibility of designing
self-stabilizing algorithms when those algorithms are run by mobile robots (or
agents) evolving on a graph. We concentrate on the core building blocks of
robot and agents problems: naming and leader election. Not surprisingly, when
no constraints are given on the network graph topology and local execution
model, both problems are impossible to solve. Finally, using minimal hypothesis
with respect to impossibility results, we provide deterministic and
probabilistic solutions to both problems, and show equivalence of these
problems by an algorithmic reduction mechanism.
