Simple crude method
buy two 12v electric motors and some worm gear
see first few seconds of the video, attach the parts you want rotated to a spindle , attach a cog at the end of the spindle
attach worm drives to your electric motors, as the worm cog rotates it meshes with the standard looking cog and turn the shaft and parts mounted on that shaft
you will need something like a double pole double throw switch to reverse the current. you need forward,back, and off (or your motors will burn out)you may wish to attach resistors inline with your motors to lower the voltage and reduce speed of operation.
worm drives have a good advantage in that it is almost impossible to drive the in the oppostie direction, ie the cog cant turn the worm drive but the worm drive can easily turn the cog...so your rotated bits will stay in place with the power off. when you have the parts in your hand you will see what i mean. you will have to build a mounting box for the mechanism so it all holds tightly together.
component costs about 100 english pounds all in, time prolly 8 to 16 hours graft. The setup in the vid looks very slick, if its a one off & not a mass produced kit i would expect to be charged 300 punds plus drive in drive out. The poormans version is just to get the things to pop open with some powerfull magnets and springs, pull a lever, help the spring overcome the magnet and they pop up, to close them push them down by hand till the magnets bite and hold the lids shut.