Consider a cube state space defined by $0<=,,<=$

$.$ Suppose you are piloting$/$programming a drone to learn how to land on a platform at the center of the $=0$

surface $($the bottom$).$ Some assumptions:

In this discrete world, if I say the drone is at $(,,)$

I mean that it is in the box centered at $(,,)$

$.$ And there are boxes $($states$)$ centered at $(,,)$

for all $0<=,,<=$

$.$ Each state is a $1$ unit cube. So when $=2$

$($for example$),$ there are cubes centered at each $=0,1,2$

$,=0,1,2$

and so on$,$ for a total state space size of $33=27$

states.

All of the states with $=0$

are terminal states.

The state at the center of the bottom of the cubic state space is the landing pad. So$,$ for example, when $=4$

$,$ the landing pad is at $(,,)=(2,2,0)$

$.$

All terminal states except the landing pad have a reward of $-1.$ The landing pad has a reward of $+1.$

All non$-$terminal states have a reward of $-0\mathrm{.}01.$

The drone takes up exactly $1$ cubic unit, and begins in a random non$-$terminal state.

The available actions in non$-$terminal states include moving exactly $1$ unit Up $(+$z$),$ Down $(-$z$),$ North $(+$y$),$ South $(-$y$),$ East $(+$x$)$ or West $(-$x$).$ In a terminal state, the training episode should end.