After doing my background research for Exploring Space on Potential a range of ideas came to mind on how an asteroid threatening life on Earth might be redirected to a safer orbit. The ideas are in refinement but I thought I would put down outlines for right now.
__Potential Means of Moving Dust
_________Ablative propulsion, super heat the dust so that the vaporized material would provide a certain degree of thrust. Impact craters might serve as convenient regions for material vaporization
Kicking Up Dust
One of the cool results of dust on the surface of an asteroid becoming electrically charged under sunlight, is that dust particles will accumulate in regions of shadow. Impact craters will accumulate dusty deposits, similar to how dust stockpiles in the corners of your house (not quite in any real way but I think its a useful visual metaphor). These large dust deposits might have potential as a "fuel" for a redirection system. With the extremely low escape velocity found on asteroids, even ones large enough to cause a major environmental disasters hear on Earth, a small robotic system would be deployed on the surface of the target asteroid and spend its service life launching dust away from the asteroid and slowly change both the asteroid's mass and, at least minimally, the velocity of the asteroid as well. The combined effect of losing mass and gentle application of force, over a long enough time scale, would ensure the asteroid would miss the orbital window necessary to impact on the Earth.
__Potential Means of Moving Dust
____Shakerbot in the craters: The premise is relatively simple, a small robot or part of a larger robot would wander the surface of the asteroid going from impact crater to impact crater and begin to violently shake, the energy transferred from this shaking action would cause some of the dust particulates to gain enough energy to be ejected from the asteroid. Dust that wasn't ejected would still have the benefit of altering the rate at which sunlight was absorbed by the asteroids surface.
__________Swarm solution, many small shaker bots in craters, ruled over by a queen rover, who would supply power for the shaker bots and transport the smaller robots as needed to various sites of deployment
_________Lonely bot, instead of having multiple robots the asteroid would have a single rover transporting the shaker system from point to point
_________the Launcher: this robot would be a more straight forward in design than the shaker bot, the design would emphasize a mechanical launcher that would scoop up dust and launch it into space.
_________Ablative propulsion, super heat the dust so that the vaporized material would provide a certain degree of thrust. Impact craters might serve as convenient regions for material vaporization
________Ion Tether Drive: By docking a conductive tether onto the surface of the asteroid it might be possible to use charge of the local dust to create a type of ion drive. The tether would create a localized voltage gradient that dust particles could be attracted to, for this to work the pull of the tether would supply the local dust with enough additional energy to achieve escape velocity. (this idea I have the most faith in)
Nuclear thrust Cap Using a nuclear battery to redirect comets at extreme orbital distances into more convenient locations for future space mining.