Induction is cool for short distance low current applications... but I don't think it would work very well (excluding rules) for running a robot. Tesla devoted a lot of his work to wireless energy transmission, and never really got anything that was very efficient over much of an appreciable distance, plus when he tried to market some of his more long-range methods of transmitting large amounts of energy to the U.S., they were deemed unsafe.
But don't mistake me about him... nothing against Tesla. He did a TON of work with EMF that we use all the time today, it's just that long range energy transmission never really worked out for him (or anyone else for that matter).
Also, let's say the frequency you were using for transmission was somewhere up in the microwave spectrum, and let's assume your transmission in 100% efficient (it wouldn't be, it decays at the square of the distance your antenna is from your source, but just for fun). Also, let's say you want to run four CIM motors at up to 40A. 40A*12V= 480W, 480W*4motors=1.92kW.
As much fun as a 2kW microwave sounds, I don't think I want to be anywhere near it (unless lead shielding was provided for the operator stations).
Fun idea though...
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