Amazon’s Prime Early Access Sale—aka October Prime Day—is a great time to buy your first robot vacuum, upgrade the one you have, or buy a second robot vacuum for another part of the house. Indeed, no smart appliance has brought us closer to a Jetsons-style utopia than the robot vacuum. Nobody enjoys pushing and pulling a noisy appliance across the floor or wrestling with tangled hoses and electrical cords. The solution: An autonomous robot, of course.. Here are some of the best deals we’ve spotted in four categories: Budget, mid-range, self-emptying models, and mop/vac hybrids. Note that the s…