Build a 1/20 cubic inch robot with a gripper that can pick up and move small objects. It is controlled by a Picaxe microcontroller. At this point in time, I believe this may be the world's smallest wheeled robot with a gripper. That will no doubt change, tomorrow or next week, when someone builds something smaller.
The main problem with building really small robots is the relatively large size of even the smallest motors and batteries. They take up most of the volume of a micro robot. I am experimenting with ways to eventually make robots that are truly microscopic. As an interim step, I made the three tiny robots and the controller described in this instructable. I believe with modifications, these proof of concept robots, could be scaled down to microscopic size.
After years of building small robots (see here: http://www.instructables.com/id/Building-Small-Robots-Making-One-Cubic-Inch-Micro/
) , I decided the only way to make the smallest robots possible, was to have the motors, batteries, and even the Picaxe microcontroller external to the robot.
pic 1 shows R-20 a 1/20 cubic inch robot on a dime.
pic 1b and 1c shows smallest wheeled robot lifting and holding an 8 pin IC.
THERE IS A VIDEO in step 3 that shows the robot picking up an 8 pin IC and moving it.
And another video in step 5 that shows the robot turning on a dime.