There are a few Asimov books that take place in "near future" that vary from the introduction of robots but before we had much space travel capability, to the start of space travel all the way to some hundreds of thousands of years like with the foundation series.
Nemsis is a fairly recent one, set on the cusp of near light speed travel.
Another one that is "earthlike" in a sense is Nightfall, a planet with multiple suns that is always in eternal light, except that once every thousand years when things go wrong...
then there is the popular "I, Robot" and others in the robot series.
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