Controller for a Wireless 12v Battery Maintainer (Trickle Charger)

I've seen other write-ups on creating a battery charge controller, but this is a bit different.

I'd like to investigate the feasibility of creating a trickle charger, that operates over wireless coils, to maintain a 12v battery. Not to charge the battery if it's dead, but just to maintain the charge if left for an extended period of time.

The way I understand maintenance mode, or trickle charge mode, of typical 12v battery chargers ... is they go into some sort of square wave cycle mode, where they up the voltage (14v or so?), then reduce the voltage (12v), on a pulse frequency, to just maintain the battery charge.

With wired solutions, I believe there is a feedback signal from the battery to the controller, to tell it when to enter this maintenance mode. For my wireless idea, this feedback signal wouldn't be necessary as I only want it to maintain the battery ... so it would always be in this trickle, or maintenance, mode, and never need to supply higher voltage for charging a dead battery.

It needs to plug into the wall and use 110v as the power source (or I could just use a 12v wall wart transformer), and then using something like this coil setup, for the wireless connection to the battery:

WIRELESS COILS

I've done a pretty intensive Arduino project in the past, so this isn't completely new to me .. although I'm no expert by any means. Here's a LINK to my previous project.

Is the Arduino a good choice for this project? If so, which model would be a good starting point?