Playing bottom half guard effectively often requires the student move somewhat continuously. This is one of the things that makes the positions difficult to learn. You have to remember to not get flattened out, (stay on your side), and not remain stationary. A common beginner mistake is to use an explosive type of movement as opposed to focusing on timing. As you saw with the pendulum sweeps it is a mistake to load up, hold your breath, and try to explode through the sweep. It is better to build momentum WITH your partner, and try and take them a direction they are not fighting.
It helps to understand that you have options on both ends of the position. If your partner keeps you down you can pursue the old school sweep. If they let you up you can try to go to their back. If however you get caught in the middle you can be in a bit of trouble. This position is commonly called dog fight, however that is a very poor name. You should still focus on the momentum and where your partner is trying to go then help them get there, versus attempting to overpower them to take them where you want.
One of the first obstacles you have to overcome to get to this position is to free your bottom knee. In order to do that you will need to un-weight your partners leg that is trapping your leg. The principle for this is similar to getting the single leg in a single leg take down - you give your partner a little bump which un-weights their leg. In the case of half guard you give a bump into your partner and free your trapped knee. You will see me do this in both examples below.
Two things to pay attention to here: 1) my partner is using the whizzer to establish his position. If he did not have the whizzer I would simple move to his back. 2) my motion is NOT ACROSS MY PARTNERS TORSO. Too often the bottom player will pop up into dog fight and move into their partner. You partner is higher than you and has great control with the whizzer. Pushing into them does nothing to improve your position and often gives them an advantage. I am moving backwards first and trying to weight my partners hips. Since they are focused on pushing down this is generally easy to do. Once their hips are weighted I begin to move behind them. The motion is like a J with me moving backwards first then across/behind the hips.
Sometimes though you just get stuck in the position and are unable to make the first move work. This is the time to roll through. Rolling through is pretty straightforward; hug your partners near leg and keep them close to you as possible. Then put your back on the mat as close to your partner as possible. Don't think of pulling your partner on top of you, instead try to pull them across you as you roll through.
There are a number of ways that you can get hurt, or hurt your partner, in this position IF one or both of you isn't paying attention. Part of Jiu Jitsu is learning how to stay safe. Often times we are so focused on winning or losing that we forget that the ability to concede the position is just as much Jiu Jitsu as is the front choke from mount. Focus on the body mechanics. First try to effect your move, then if your partner shuts you down feel where they are trying to go and help them on their way.
Just like everything else we do you want to get these down movements down smooth before you start pressing the accelerator. If in your training you focus on timing, balance, and momentum you will have an enviable half guard game in no time.
See everyone in class!