Wandering across asteroids

Asteroids, comets, and meteorites are a new class of natural disaster, one that humans have the technological ability to prevent (whether we have the will to deflect these cosmic bullets is another story entirely (ok positive light).

A still from the nuking an Asteroid video

 Being the inventive species we are the range of potential solutions is truly astounding. Michael Bay's Armageddon had the most popular sound track of any movie about stopping an asteroid, it also had one of the more problematic solutions. that being said we have an excellent video of what that would look like, ok so it won't embed so please follow this link.  

More recently there was a proposal to use paintballs to coat the surface of an asteroid with varying colors of paint to very slightly alter the emissivity of the asteroid and over time change the path of the body just enough to avoid the earth.  In total Wikipedia lists about 14 different major ideas for preventing an asteroid mission.  I would like to humbly add my own idea to that mix.

Terrible drawing of a satellite walking on an asteroid 

The gentle tug of gravity connects every single large body (or collections of small bodies) in our universe, this force has been one of the more popular suggestions for changing an asteroids orbit.  By positioning a satellite on one side of the asteroid you very slowly tug the asteroid a little more to the left (I'm being arbitrary on terms here, so what).  This solution is extremely elegant and minimizes chances of creating surplus debris floating around our solar system.  My personal take on this idea is instead of having the satellite match course with the asteroid, a space agency could instead land a walking robot on the surface of the body, and create the gravitational tug a little closer to the surface.

The belief behind this approach stems from several factors; first off, I just think this idea is wicked awesome, it would be so cool to have a giant spindly legged robot wandering across the surface of a body where the force of gravity is so low (the original inspiration came from watching a TV show on deflecting killer space objects and I thought wouldn't using a pogo stick approach be cool, but as time went on a single point of contact at irratic intervals felt more and more dubious)  After the thoughts on the coolness factor mellowed out more rational design considerations came to the surface, a robot walking across the surface of an asteroid might in theory be able to have a lower overall launch mass as the legs can be electronically powered, while the gravity tug satellite would need a certain amount of fuel to allow it to maintain its course.  Another factor would be proximity to the original center of mass of the asteroid.  The inverse square law elegantly shows us that if you double the distance you are from a celestial body, the force of gravitational attraction is reduced to a fourth of the original value.  By having an automaton walking across the surface of an asteroid you could move your spacecraft much closer, drastically increasing the force of attraction between the two bodies, either reducing the overall launch mass of the machine, or increasing the overall change in ballistic trajectory per unit of time per unit mass.  A secondary consideration is flexibility in mission planning, a well designed asteroid walker could be launched at almost any time, sit on the surface of the asteroid for years if need be, and at a predetermined time stretch its legs after a long hibernation and begin wandering the axis of rotation and quietly protect humanity.  This feature could also allow the walker to avoid space debris during emergency situations, if the asteroid were to encounter a dust cloud that hadn't been seen during the original mission planning phase the robot could be able to hunker down in a quiet crater until the storm had passed.
I will try to follow up with some more math later, I just need to get back to looking for work.

Follow Up
Wired magazine has an article highlighting the concept of attaching a super massive tether to an asteroid to change its orbit.  The author of the article seems to indicate that an impacter being used at the right time would probably be more effective.  It also linked to a youtube video that showed that the gravitational tractor approach appears to require the probe be placed in front of the asteroid, making my idea appear less viable.