>>3017 (OP)
Robots like the one you posted that resemble humanoids are worthless in Trek, unless they're on Data's level of intelligence, in which case they would be androids, not robots. Think about it. Need something built in a hurry? Replicate it. Need some heavy lifting done? Transport it or use one of those gravity hand-trucks. Need to calculate something in a hurry? Ask the computer. Hostile forces are boarding the ship? Throw up some force-fields or grab a phaser. A slow, clunky robot wouldn't be much use against enemy boarding parties anyway.
Basically, any need a crew may have for a robot is already built into the ship. In rare cases where the built in tools of the ship aren't applicable, something new can be replicated, jury-rigged, or even be temporarily fabricated by a set of holo-emitters. The only robots that the Federation does use are non-humanoid, such as robotic arms that help assemble new star ships. So any kind of humanoid robot in Star Trek would just be obsolete.