Team of Automata with Universal Passability

Consider an integer-valued plane part of whose points are obstacles, while finite automata may be situated (and move about) at the remaining free points. The total number of automata on the plane is finite; each of these automata, at any free point, “knows” the direction toward point $(0, 0)$ (to within $90^{\circ}$), and also the presence and state of other automata at the same point. It is shown that there exists a team of four automata such that, if the automata are initially situated at any point $(i_0,j_0)$ such that there exists a path from $(i_0,j_0)$ to $(0,0)$, all automata will arrive at $(0,0)$. No single automaton with this property exists.