You have to make sure they are all lit to make the platform move- to do this you must use the hover vehicle. Line up and quickly go over the squares to get all at once.
You may have to do some shoving into place first. You should see a blue device in the hatchmarked area- shove this into the circle at the right end. Once that is done push on the green side of the panels sticking out of the structure in front of it. This activates a blue platform.