@sadraddini has requested this feature, and I'm planning to implement it myself soon. I'm creating the feature request because I wanted to solicit feedback before I do so. cc @RussTedrake

It seems like there are multiple ways to pull this off. One is to just have the user specify which joints are mimic joints. This seems ugly, but for simple setups (e.g. parallel jaw grippers), it would probably be the most convenient? We could also redo the parsing, but that seems very silly!

Another is to go into the MultibodyPlant and look for coupler constraints. But I'm worried this might turn into a footgun if the user has a discrete plant and isn't using SAP as the contact solver -- in that case, the mimic will be ignored, and the user could miss the warning. And in a more principled sense, it seems weird to make this (purely kinematic) method depend on what the user has selected as a solver for the contact dynamics in the plant.

However, inspecting the plant for the constraints also suggests the workflow of looking for weld constraints. This would be a much nicer workflow for IRIS regions in manipulation contexts, as the user could just weld free floating objects to make regions, instead of having to make an entirely separate set of directives.

Maybe the best option is to have two different setups?

1. Introspect the MultibodyPlant for coupler and weld constraints. Warn the user that discrete and not SAP will not see mimic joints.
2. Manually specify a list of mimic joints, along with their multipliers and offsets.