Creating an actuator based matrix with Arduino

So I know this is going to be pretty vague but bare with me… So I recently wanted to start experimenting with actuators to make modular robotic projects. I wanted to start with the most simple project I could think of and work my way up from there. I’m basically trying to make a 3x3 matrix of 3D printed cubes that are each connected by a series of actuators. Basically all I wanted to do was have the 3x3 Matrix of cubes shrink by half it’s original size. My method of achieving this would be to have the actuators shrink to half of their extended length, thus overall producing a half sized matrix. The actuators would be controlled by an Arduino or some sort of microcontroller. The problem I am having is debating what type of actuators I would use and how I would go about constructing one. I was thinking about using some sort of linear or even piezo electric actuator. This scale model will be in inches in scale in real life, but once I construct that I want to make one that will be microns in length. This will require software simulation because realistically, real life models cannot be constructed by hand. I have no idea where to begin with the equations of motion, and the formulas that would be required to undertake such a task. I want to first start with the life scale model and then begin working on the micron simulation. Does anyone have any ideas or where to start for absolute beginners on how to complete this project, as well as recommended software simulators that would help me along the way? I know this isn't exactly asll arduino based, but I'm just looking for a some places to start. Books, websites, forums, video tutorials, contacts, or anything that could be of help would be extremely appreciated. I know this is extremely vague, but I’m trying my best and all the material I seem to seek out is very overwhelming and I don’t even know where to start.

The problem with a piezo electric actuator is that it only responds to changes in voltage not absolute voltage. In other words you can’t get a steady DC displacement with them.

This leads you to linear actuators which are physical big, and so have a large minimum value of spacing.

Does this have any practical use in the micro version of this concept?

I can’t see what the problem is because surly all you do is to drive all the actuators to the same value to get your expansion or contraction of your cube.

You may look for "inchworm piezo" and an introduction paper. But even if the operating voltage dropped from originally 1000V to now 200V it's only for experienced people.