[Taylor]

Flamethrower.
Cigarettes are flammable, rocks are not.
Don't overcomplicate things.

OR

Have a steady stream of water coming out the front of the robot. Trash tends to float; simply have a sieve at the bottom of the hill for all the trash to float into and the water to pass through.
(same effect can be reached with a leaf blower. 30 bonus points if you can blow the trash up 12 inches in the air.)