  A mobile agent, modeled as a deterministic finite automaton, navigates in the
infinite anonymous oriented grid $\mathbb{Z} \times \mathbb{Z}$. It has to
explore a given infinite subgraph of the grid by visiting all of its nodes. We
focus on the simplest subgraphs, called {\em wedges}, spanned by all nodes of
the grid located between two half-lines in the plane, with a common origin.
Many wedges turn out to be impossible to explore by an automaton that cannot
mark nodes of the grid. Hence, we study the following question: Given a wedge
$W$, what is the smallest number $p$ of (movable) pebbles for which there
exists an automaton that can explore $W$ using $p$ pebbles? Our main
contribution is a complete solution of this problem. For each wedge $W$ we
determine this minimum number $p$, show an automaton that explores it using $p$
pebbles and show that fewer pebbles are not enough. We show that this smallest
number of pebbles can vary from 0 to 3, depending on the angle between
half-lines limiting the wedge and depending on whether the automaton can cross
these half-lines or not.
