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This sounds like an interesting project. I've done nothing like it myself. So long as what you are "moving" does not create a safety hazard, it seems like a unique, challenging little project. Do you want a robot arm to move based on voice commands? You probably should expect the unexpected when your voice recognition algorithm incorrectly processes the audio stream, and take precautions such that your bot doesn't damage anything.
Voice recognition software -> command parser -> GPIO ?
Or something like that.
Here's a project to control a roomba:
https://makezine.com/projects/use-raspb ... e-control/
It uses pocket-sphinx, which is speech recognition software. I know nothing about it though. I think there is a voice hat for the Pi that might factor into a setup. I'm just tossing bits collected from a quick search. Good luck and let us know about your results if you do a project.