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.