If you truly want no trimming at all, the only reliable way is a level edge the mower can straddle (paving flush with the lawn). Without that, every robot will leave a small strip.

The Luba Mini 2 AWD helps because it has a side cutting disc, so it reduces the amount left at the edge, but it still won’t be perfect unless it can overhang a flush border.

For the docking station, best practice is to place it on a hard, flat surface just off the lawn rather than in the grass.

On “best and cheapest,” there isn’t really a budget option that guarantees edge‑to‑edge cutting—your setup (flush edging) matters more than the mower.

Thanks
Mark