A tuned mass damper is really to reduce torsional vibration, this seems like an inefficient use of mass, it’s also nearly impossible to get the mass in the right spot geometrically to comply with the 16" extension limit while getting the desired effect.
Here’s what I mean in a free body diagram of a telescoping tilting climber the moment it releases from the mid rung. You can see a moment is created about the high rung equal to 24" (distance between rungs) * robot mass *g. In order to remove that moment the CG would need to be moved under the high rung, which means half the robot weight would need to be under the traversal rung (dotted vertical line). Unfortunately the 16" extension limit combined with the height limit struggles to reach there (drawing not to scale, but draw it out in CAD and you’ll see what I mean)
If swinging really is a problem for the traversal climb it seems easier to react the load of the robot against rung you’re letting go of until you are centered under the next rung with minimal kinetic energy. The windmill climbs are good at this and see less swinging because their CG can be moved independent of the release of the bar.
With a tilting telescoping climb you’d need to add something to react against the bar after your hooks release. We conceptualized something like this but never built it since we didn’t see swing as that bad. in the image below the green bar is sprung with a pivot low on the chassis and reacts the weight of the robot as it swings, this creates a moment opposite of the one created by robot mass but can be a light weight stick. Geometrically the bar should let go when CoM is centered under the next rung
