When you say "Polaris" and "booster pump," that indicates you had a pressure-side cleaner, not a suction-side cleaner. Big difference. The booster pump pushes water through a pipe and down the cleaner's hose into the vacuum head, which uses Venturi action to send crud into a little bag attached to the vac head. You then periodically clean out the bag. The main pump must also be running while the booster pump runs, so a pressure-side vac system is the least energy efficient way to vacuum a pool, because two big pumps are running.
Robots work on their own, no extra pool pump needs to be running. Totally independent. But, yes, they plug in to a 120V outlet and so there is a cord running across your deck and into your pool (which is what I don't like about them). According to reports, reliability is not their strong suit.
Suction-side cleaners do not need a booster pump. Your main pump sucks water through the vac head and whatever gets sucked up ends up in your main pump's basket, or in your main pool filter. It can stay in your pool 24-7, but is easily removed for swimming, if you like. It's much lighter than a robot, so getting it out of the pool is less work. And there is no bag to clean, so once in the pool, you never have to remove it if you don't want to (I do, when it's more than just me swimming, but otherwise I ignore it). For the seven-ish non-pool-season months of the year, I don't even think about my pool vac, or need to do anything about it.
Others will tell you that running a robot uses less electricity than a suction-side vac, which needs the main pump running. And that is technically true, since a robot uses less energy than your main pump. But while a suction-side vac is cleaning, it is also filtering your water though your pool filter (a robot doesn't do that), so it can be considered part of your water filtering runtime. And while the main pump must run higher for vacuuming than for general filtering, it's not exactly fair to say a suction-side vac uses a whole lot more electricity than a robot, when you consider you'd be running your main pump anyway. This is truer if you have a variable speed pump (you don't specify). And, no, a suction-side vac does not tax your pump in any significant way, other than running it at slightly higher RPMs, which is what it is designed to do.
As
@JoyfulNoise describes, a leaf catcher is only used with a suction-side vac, when you have a lot of debris to clean up that you don't want to run through your pipes and into your pump basket and filter. I don't use one, because my pool stays relatively clean all year round, and I only have to clean my filter once a year (and have even skipped a year one time).
So between the weight and cord of a robot, and having to clean its little dirt catcher regularly (which means pulling it out of the water often), its expense and its tendency to need replacing, a robot isn't for me. My Pentair Rebel suction-side cleaner has been going strong for about five years and keeps my pool spotless. It is just now starting to get stuck once in a while, probably it's gears getting a little worn. Rather than trying to repair it, or waiting for it to die, I just this morning ordered another one, but only needed to replace the vac head (not all its other parts). That was about $225 (plus tax and shipping). Which works out to about $50 a year. Which is pretty darn affordable cleaning! I'll keep the mostly-still-working original as a backup.
Oh, sorry to go on, one other thing. I used to have a Polaris pressure-side cleaner, with that stupid tail that would spray me and my windows. A pool plumber was able to reroute my plumbing and convert my pressure-side plumbing to suction-side, so I was able to switch to a suction-side cleaner. The same may or may not be possible for your pool, but a decent pool plumber could determine that for you. The main thing is the diameter of pipes. Mine were 1.5", which, knock on wood, have so far been free from getting clogged up. I was able to get rid of a failing booster pump. And I found that the Rebel cleaned at least as well as the Polaris.