Looking at the PCB mounted on the drone, it appears to be a bridge rectifier and buck converter. I clearly see the chain of thought that went into the design: polarity could be either way - use a bridge rectifier to solve that, bridge rectifier drops too much voltage - use a higher voltage and regulate it down. Not bad for an artist with limited EE experience (also keeping in mind it's a proof of concept), but how would an experienced EE design it?
My take is that since weight is basically everything on a drone, the part that mounts on it could be simplified to just a MOSFET + few passives for reverse polarity protection. The base (without the strict weight requirement) would alternate the polarity to the contact grid while monitoring for current draw.