There are a couple of difficult judgements that humans can make that a robot, to my knowledge, cannot. One is crosswinds down course. A sniper, a golfer, etc, all judge crosswinds down course because they will affect trajectory. A robot, I believe, would only be able to account for the wind around it, not changes in wind down course. At 500 yards, the winds can definitely change.
The other is slope an angles, GPS is good within sometimes inches, but usually a foot or two, and within a few degrees, but I have yet to see GPS capable of calculating exact slope and angle 500 yards downfield. You could pre-program your robot with the course layout via GPS within a certain accuracy, say 98%, but it'll never be perfect.
If he robot does miss, you now have to account for terrain changes. Proximity switches and the like could monitor immediate terrain height, such as long grass versus putting green, but it wouldn't be able to distinguish sand, or water, from putting green. Perhaps infrared imaging would be helpful in making a distinction between hazards, but your robot may be 500 yards from the intended area you want to analyze. If you want this to be a self-contained golfer, then good luck. You're robot would have to traverse the entire course using gps tracking of its location and plot a thermal map before golfing, or something to that effect.
You'd have to put some kind of homing device in the cup for it to recognize location of the cup.
Regardless of the above scenarios, putting, still, would be a nightmare. Pro courses have subtle changes in grade that GPS is incapable of projecting, at least to my knowledge. Ground penetrating radar wouldn't help you here. Radar would never provide you with the accuracy you'd need. You basically need airborne laser scanning of some kind, which is difficult given your self-contained golfer.
I don't know, what to say, I'd be hard pressed to think a robot could break par. I'm sure there is technology out there I know little about, but I can't think of anything that would make it realistic to expect the robot to break par, even with pre-programming of the course.
I'd venture to say if you had a par course of 72, your robot could get within 80%, or a 90 with as many factors taken into account as possible.
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