I had mentioned to BJJGrrl that controlling the hips was one of those things that was crucially important to a lot of aspects of JiuJitsu, and everyone told me that for years, but I never really understood what it MEANT or how to accomplish it until recently.
I've worked out that there are three ways to kill someones hip movement, the direct method, the indirect method, and retreating. With the direct method you are using solid pressure directly onto their hips. An example would be when you are in someones closed guard and you put your hands on their hip bones and drop your weight on them. You've directly shutdown their hips in order to work on opening their guard and passing. This method requires that you be able to solidly manage your weight, keep it centered, and "drive" down into your opponent. This is probably the first method that most people discover for controlling the hips.
The Indirect method is the method that I've actually found to be most useful though. With the indirect method I'm not attacking the hips directly, I'm removing the levers that control that hip motion, the legs. Every motion of the hips requires that the legs be involved to generate the torque and force required to accomplish anything. Shrimping, bridging, all of it involves driving with the legs. Because of this my primarily method of hip control has become the legs. An example is from mount when you grapevine the legs, it does add some direct pressure to kill the hips, but it mostly just takes the legs out of the equation. I expand on that concept whenever I'm on top and work to lift my opponents legs off of the ground to prevent shrimping. For example, in side control I will turn slightly towards my opponents feet and grab their FAR leg at the knee and pull it up off of the ground. This makes it very difficult for them to shrimp and makes it easier for me to transition to mount if I want to. I follow the same idea when I'm passing guard. I hug the knees, sprawl and then turn and lift to keep my opponents feet off of the ground. This stops them from shrimping away or chasing me with their legs.
The third method is retreating or transitioning. This is the method I use the most now and it's even LESS direct than the direct method. I feel like this method is best suited for a smaller person who is working against a larger person and is still applicable even against people of the same size or smaller, it's just not as necessary. With this method you just remove yourself from where their hips want you to be. If you are in side control and they start to shrimp to regain guard you transition towards north south then pop to Knee on Belly as they follow you. If they try to bridge you off there you spin and sit down on their head for headmount/northsouth. If they start to escape that you slide down to side control on the opposite side and start the process over again. You have to be pretty sensitive to when your opponent is moving to make this work though.
Now, the BEST method, and one I'm just starting to reliably be able to use, is a combination of all three. When I'm moving to KoB I like to grab the far leg at the knee and pull up to prevent shrimping away from me. At the same time I use the KoB to drive heavily into the hips to pin the hips. When I'm sweeping someone I maintain control of their hips either with leg pressure across the hips directly, or with a hook under the knee, or with a handful of pants. Concordantly I work to keep my hips AWAY From my opponent. This flipside of this entire thing is that controlling your OWN hips is just as important as controlling your opponents. If they have your hips locked down you can't do much to them. So again the legs come into play. If your hips are pinned by direct pressure you have to be explosive even if it's a tiny explosion. Just enough to unfreeze your hips on one side and pop out. If your legs are being lifting try to pull your knees up to your chest and pop them open like butterfly guard. If someone is using fast transitions then trick them. Fake shrimping one way the roll to your knees on the other side.
Above all look at ways to prevent your opponent from using their hips while finding ways to maximize your own hip movement.