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Why not use grippers to pull them? Probably more effective because there's no root to grow back from, shouldn't require too much force when they're small/the soil is damp, and you don't have to figure out torsion/"friendly fire" from a spinning blade.
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I think the project difficulty grows at least 10x with all the dust, insects wind, pollen in the air and whatnot even assuming you hide it for bad weather and you have secured very stable mount points. It sure would be cool though.
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Some 12ft T-post, shelter for it to park, update weak points were dust & water can intrude. I think it's doable.
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A small spinning blade? Sounds like the type 1 robots from Screamers https://www.imdb.com/title/tt0114367/
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I am picturing a drone, one with the fan at the bottom :) OR one that can do a roadster maneuver at the right time.

Edit: Isn't there already one that Zap's weed with a laser?

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I wonder if you could make it work vertically. It might ease the geometric challenges.

Naively, spraying targeted roundup from above or cutting a circle around the stem to kill roots kind of thing.

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Roundup is gross anywhere even in small amounts. If water and energy can be provided similarly to stringman, a heating element to deliver a small payload of boiling water usually suffices.
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weeds, dog poop, etc. could be useful in your yard.
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