I had just read this article about how they were trying to figure out how to make a vibrating superconductor move in 1 direction, for propulsion, but it didn't sound too promising. So I thought of dust-shaking. Is vibration useful in shaking off Mars dust?
Yes, it would be, of course. I'm not sure why you'd need a superconductor for that though, when a lot simpler technologies such as piezoelectric, electrostatic, sonic (basically a "subwoofer"), compressed air, or other types of mechanical drives could be used. Also, simple rotation of solar panels should help too, and let the gravity do the rest, if that's permissible by the rover's design. And sometimes, even weather helps. With MER (Spirit and Opportunity) rovers, when they were caught into a dust storm, solar panels of one (don't remember which one) were cleaned by it, and the other one's were made even worse. So that's perhaps a bit moot point, but it goes to show that there's sufficient atmospheric pressure on Mars to somehow take advantage of winds there too with suitable design, say by designing them to be more flexible, e.g. by using thin-film solar cells.
The Mars rovers do not have any dust removing technology. And Opportunity worked fine for 10 years, so the dust problem should not be exaggerated. It is worse on the Moon (and on any asteroid) where there's no atmosphere which has eroded the dust. The regolith on the Moon is very fine, sharp as glass and sticky because of its electrostatic charge. The Apollo astronauts could not avoid bringing it into their lander, and it was even found in their lungs when they had returned to Earth. Thanks to the atmosphere of Mars the dust there is much less dangerous. (But could be full of poisonous chloride salts).
On the Moon the electrostatically charged (by the cosmic and solar radiation) dust which hoovers above ground might very well we removed/collected by a charged "broom" which sweeps over the ground. But the dust on Mars is more like the sand we know on earth.