Standardized plates. Add DRM so no one can feed it knockoffs. That is how the coffee pots do it.

But seriously, standardized is the only way such a system could work unless you have a robot at the sink.

That said, a left and right washer is the easier approach. One is dirty,the other is clean. This obviates the need for putting dishes away. This also obviates the need for dishes to sit in the sink (ie because you hadn't put the clean dishes up yet.). Once the dirty is filled and the clean is empty, the washer runs, and the clean and dirty designations switch.