The original idea sounds like a non-starter. The motor batteries for the robot are gonna
be discharging much quicker than the battery powering the Arduino - assuming spearate
batteries. Inductive charging will take forever, either way.
Many robots have been designed that plug into AC mains for charging, and also that
connect to +/- contacts inside a hutch, including some of the first robots ever built.
http://www.ias.uwe.ac.uk/Robots/gwonline/gwarkive.html
This sounds more practical. Any contacts on the floor and unprotected will likely be a
shorting-hazard.