Building a machine to mimic a robot...

[m_c]

As it's only polystyrene, cutting forces would be very minimal, so well designed lightweight should be more than acceptable.



Robot control is all about kinematics.
As long as a robot could be controlled by fairly common steppers/servos, there are controller options about that could handle it.
If it's something you did want to consider, I'd suggest having a look at Dynomotion, as their default CNC software can be made to handle kinematics, and TomK (Who run's Dynomotion) does like kinematics.

The major benefit of having a good kinematics setup in the controller, is you can program the machine using conventional Cartesian (XYZ) moves/positions, and the controller will handle converting that to the non-linear movements that something like a robot arm needs.