If you have the sprinkler which goes around int eh circle, you know the frustration of having to move it around to get coverage on non-circular lawns. I have designed a sprinkler which allows itself to be set for variable distances. The base piece is larger but has a set of sliders which cover separate holes (the more holes built in, the more customizsble the water coverage pattern). Cover a hole more and reduce flow but increase pressure, the water travels farther etc. You can get those pesky corners...
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Since water pressure is a source of power, it should be fairly simple to devise a sprinkler with water powered wheels that could follow a trail, say, a rope or flexible plastic cable laid down to permit the sprinkler to cover an entire lawn. It would also permit the spray to have a short range so as not to wet passers-by and be restricted to only the area of the lawn.
They do have variable pattern sprinklers of that source. They have a turret you turn which brings the hole pattern over the water pressure outlet. Semi mechanical sprinklers generally have pattern adjustment.
I like the robo waterer idea also.