What mechanisms and technologies will be used to control the descent and movement of the falcon 9 rocket's booster stage on its way to the landing pad?
Key phases in the launch-and-landing plan for SpaceX Falcon 9 rocket. Image credit: Jon Ross, NBC News.com
After the first stage main engine cutoff, cold gas N2 thrusters are used to rotate the booster into the direction of flight, they reignite 3 of the Merlin 1D engines. (With 9 in the Octaweb alignment, the center and two on either side of it allow a 'line' of engines to fire).
They use this to kill forward momentum. They continue arcing upwards (since vertical and horizontal momentum components are independent) until they start falling down again.
They then fire three Merlin 1D engines to control descent through the hypersonic regime as they hit thick enough atmosphere to be problematic.
Finally they use the hypersonic grid fins at the top of the upper stage, the cold gas N2 thrusters in combination to try and steer the booster to its target. Time will tell if they have sufficient control to hit a small target that's 300 feet long by 170 feet wide (91 by 52 meters) precisely enough for Falcon 9's leg span of about 70 feet (21 meters).
Once they approach their landing surface, in the last few seconds (10-30 seconds?) they re-ignite the central Merlin 1D to decelerate from terminal velocity to a landing. Hopefully down to 4.5 mph (7.2 km/h) at the time of touchdown, a number that was mentioned during the recent CRS-5 pre-launch news conference. If not, bad things happen.
The landing legs will deploy during the final burn, according to SpaceX representatives. Here is a rendered video of this whole launch profile, from launch to landing of the Falcon 9 first stage on the Autonomous Spaceport Drone Ship (ASDS):
yes, lateral thrusts is the right keyword for this answer. Lateral thrusts has been introduced by Russia and US Ellon musk's spacex just copy/pasted it into their landing gear.
**at 0:02/0:08 : a procedure has been introduced named "lateral thrust", which turns it to right.
at 0:03/0:08 : a procedure has been introduced to stop it from further right.
at 0:04/0:08 : a full thursts procedure has been introduced to give it a right speed for the right side direction.**
Now this technique has been made public in late 2010 and these practices has been in action by Russia since late 2002 or 2003.
Ellon musk and spacex just copy/paste this "lateral thrusts" from Russians into their landing rockets and after several tests, rocket landed back with just addition of small step in a reverse engineering fashion.
control theory has no deep applications in Ellon musk's spacex, but what they do is copy/paste from other countries allied or core disciplines and do experiment to keep success in public eye and whatever they show to public, has been well experimented by other nations a lot long earlier.