In the (first) YouTube video, there is only one hydraulic cylinder per side. The associated column lifts the other columns by means of the central longitudinal beam. ... which I think has to be tubular, in order to resist a twisting flutter of the roof.
The hinge detail at the top of the column, and the hinge offset from the column and from the roof beams bears close examination. Stability of the pergola in the erected position depends on the end of the column in one direction, and on gravity, i.e., location of the roof CG relative to the hinge line, in the other direction. I would worry about the roof flopping to a vertical position with the columns upright in certain wind conditions.
I might be more comfortable with a parallellogram arrangement, i.e., two columns, or a column and a strut, at each column position, both for stability in windy conditions and to keep the roof always level so the accumulated crap doesn't fall into the water.
Talk to a commercial awning builder about doing up the roofs as fabric stretched and tied over steel pipe frames, instead of joists and plywood and membrane roofing.
With roofs framed lightly, built and skinned on site, over a perhaps shop-built metal skeleton of truckable size, and tractor/logsplitter hydraulics, it should be do-able for way less than 100 large.
Mike Halloran
Pembroke Pines, FL, USA