Efficiency could be a bit of a problem.
The induction power transfer is done through a high frequency EM field. This transfer is not 100% efficient as it radiates energy in other directions (careful design could increase transfer efficiency, but you'll never get a perfect transfer). The generation of the HF EM field consumes energy.
Therefore, you may get at best 80% \$^*\$ of the energy transferred from the battery to the device.
Then there is the cost. It's not a cheap system compared to what is essentially a bit of metal that is used currently.
Combine the two and what is maybe a 99.999% efficient piece of metal would be being replaced by a complex circuit costing many dollars and reducing the efficiency to maybe 75%.\$^*\$
Then of course, if the device is switched off, the battery will still be consuming power in generating a HF EM field that is not being used, so there would need to be a way for the device to turn off the battery - and turn it on again without any power (most easily done with good ol' wires...)
So nice as it would be, I can't see it really being practical.
\$^{*}\$These efficiencies are just made up off the top of my head and not to be quoted as accurate.
I've built several products around different chemistries. I have found LiPo the easiest to use since there are already specialised charger IC's that do all the work however, like you said, having them in series is not that straight forward. I believe the NiMH is a better solution if you don't have a lot of experience with chargers or if you don't find a good solution for charging LiPo in series.
Just one note, do not trickle charge NiMH indefinitely, use a timer at least to avoid overcharging the battery too much(even when you trickle them, they overcharge). You could also use, like Pwocky suggested, an LM317 to charge at a constant current and monitor the change in temperature in the battery pack, once the delta T becomes big enough (the temperature changes more rapidly) the battery is charged. You could also mix this method with delta V and a safety charge timer. This is what I do and it works perfectly. I charge my batteries fast and never overcharge them.
There is a lot of info online with graphs showing how the temperature changes when charging a NiMH battery.
Best Answer
Inductive charging stations is a very neat idea, and one I hope you are able to pull off with your robot platform.
Although I have never built a inductive charger myself, I have put together several home-made, from scratch RFID type devices and what I have learned is that the key to getting good coupling between the primary coil of the charging station and the pickup coil on your robot is having a well tuned (high-Q) resonant network on the primary. I think you will be best off coupling this with a non-resonant pickup coil on the robot, that way the load introduced by the robot will have minimal impact on the resonance of your primary coil.
Give this paper a read: Surface Based Wireless Power Transmission and Bidirectional Communication for Autonomous Robot Swarms
They have put together a basic system that should have all of the parts you need to provide power to charge your robot. On the base they use a two-coil setup with a primary driver coil being driven by a power MOSFET coupled to a resonant secondary coil. Since the secondary coil is electrically isolated from the driver they are able to preserve the resonance and improve the Q of the secondary system better than if they were just driving it directly.
On the receiver end they are using a non-resonant pickup coil (basically coiled wire) connected to a cascade multiplier which boosts the voltage picked up by the coil to a level they can use on their robots. I have built similar pickups for the RFID projects and they work surprisingly well with the right combination of Schottky diodes and capacitor values (ceramic work best here).
I think the challenge in your case would be to get the output voltage high enough to trickle charge whatever battery pack you are using. Since I don't know if you are using LiPo, NiMH, or even lead acid I couldn't say if this would work for sure. I imagine with enough tweaking you can easily get 4-5V out of this type of setup and that should be enough for LiPo or NiMH.