I can help you a bit. What are you looking to do? Someone walks up, it whooshes open, stays open a while, then closes? I could do that lots of ways, but the computer, ermm.. I don't like arduinos, and you would need to run a signal from a sensor to the computer to tell the computer to send a signal to a relay to open the solenoid ( or actuator) and open the door and then send another signal to the computer to tell it to close the door, via another signal to the solenoid or whathaveyou. Sheesh.
I would cut the computer right out of the equation, and just use a motion sensor, unless its critical that the door closes very quickly after the person walks through. Grainger has an adjustable inline pressure relief valve to keep the door from squishing someone in the event they just stand in the doorway. If its an actuator powered door, you will need a different way to prevent the door from closing on someone. I will think about it.
Just my .02 but there is a lot of difference between a swinging door prop that people watch and one they walk through. If it's just a prop, you can pretty much do what you want...window crank motor, garage door opener, air cylinder, what ever.
If people have to walk through it, that is a whole different ball game. You'd want to set it up so it either reverses when it contacts an object or has some type of 'slipper' clutch where it just can't make much force, or an electric 'eye' so it can't possibly close when someone is there. All this has to really 'work' as you don't want to close some 5 year old in the door accidentally.
If you can give us a bit more info about what you want, there are minds here much smarter than me who can help out!