A diagram of the mechanical arrangement you want to implement would be very useful.
You don't say how big is the area to be cleaned
or how frequently it needs to be cleaned
or what will be doing the cleaning (a brush? a squeegee? what?)
or what forces are required to move the cleaning device.
If a servo is suitable then it is a very convenient option.
Maybe a simple geared DC motor would be adequate? It would have the advantage of consuming no power when not being used.
You have provided no information to support the idea that the precision of a stepper motor would be useful. And stepper motors are very inefficient.
...R