Joaquim Hansen and Eddie Bravo were working techniques backstage at one of the early ADCC competitions. This half-guard sweep and sweep-to-back is one of Hansen's moves. More than anything, it underscores the importance of getting your hips clear when attempting to do work from the bottom in half-guard.
Hansen's Half Guard Sweep
From half-guard, you've got your outer arm across his throat to create space and your other arm in an underhook.
You are going to hip out to the outside as much as possible while maintaining the half-guard with your other leg. You are going to go at least perpendicular to his body--if not almost fully inverted--as you hip out away from him. I think you can use the underhook on the opposite side to help pull you around.
When you get your hips clear, you are going to kick your leg back toward his head.
Variation One: This move is the sweep. Once you get your knee on the other side of his head, you know you'll have the necessary leverage to sweep. Your underhooking arm goes between the guy's legs. The cross-throat arm helps push his head down so that you can get your leg on the other side. From here, use your underhook arm and your trapping leg to sweep him back towards your feet. Move your underhooking arm to outside the leg to hook outside the thigh.
Variation Two: The variation allows you to take the back instead of sweep. Same moves, only when you kick your leg back, you want to work your underhook under and use that arm to help push you over. You want to almost fully invert to give your arm room to get in the right place. Push and kick the leg back over his back. Follow your leg over into rear mount. Your half-guard hook leg will become the main/first hook for back control.
