A surface mount version of the Picaxe 20x-2 is available to make even smaller microcontroller modules. For details on easily soldering surface mount components see here:
Remote Control Ring
The robot ant can be controlled by other Picaxe controllers configured to output infrared Sony signals. For details on how to make a remote control ring that can control the robot, see here: http://www.instructables.com/id/Make-A-Remote-Control-Ring/
A biological ant has between 200 to 3000 neurons working in parallel to control its movements. If we consider a microcontroller to be a very crude neuron, the robot ant has the equivelent of 4 neurons. The Picaxe, servo controller, motor controller, and infrared sensor each have a microcontroller as part of the module. Many more microcontrollers than this will be needed to achieve the incredible parallel processing of even simple biological systems.
Biological ants have hundreds of fine hairs and each one is a touch sensitive sensor. The main problem with robots today is not a lack of processing power , but the lack of sensitive sensors in large quantities. Many more sensors will be necessary to make this robot ant come closer to the incredibly fine manipulations of a real ant.
Laser Cutter and Smaller Robots
A laser cutter could be used to make some precision parts to make a micro 3d printer. The printer would then be used to make even smaller parts for a microscopic robot. The microscopic robot could then be used to manipulate objects on the scale of molecules.