What kind of connection to use between two circuit boards that move with respect to each other?
Automotive has this problem for the ABS wheel sensors. Their solution is a long lobe of thin, stranded copper wire in a thick rubber hose. That way most of the force is applied to the rubber instead of the conductors.

I would cut down the actual conductors to the power ones and do all else through radio. Or use a scheme where you can use the power wires for communication, too.