This is an example of what you can do with the rig... whether my walk cycle however will look like this is another story.
The basic walk is as follows:
This image is from the "Animator's Survival Kit" this rule of basic locomotion is through out the animal kingdom too with slight variation.
When you start a walk cycle, select a starting position you would like to begin with. This could be either a stationary pose where the character hasn't moved or a mid step pose which captures the character moving and good way to start. Its a good way to start because it helps you follow a certain stride and speed plus which foot (or feet) are leading.
I started with a mid step pose:
The next stage is to show a little more push so the character is lifting his weight and pushing forward. A simple lean forward with a slight upwards motion will help simulate this.
In a quadruped walk cycle you still use the basic principles of a bipedal walk, it has a slight waddle as the hips and shoulders concertina so the characters body wiggles. This appears in bipedal walking but upright as our torso and hips move to balance us.
See the "S" shape, this is the quadruped balancing of the hips and shoulders. This goes back and forth like this :
An easy way of looking at the legs is by think they are two sets of bipedal walk cycles in sync with each other. So this would be diagonal, so the font left leg is up as is the back right leg then vice versa.
Heres an example:
In the previous video you can also see the squash and stretch I have attempted to do to give the walk a bit more character. Through squash and stretch you can also show where weight is being distributed through the body.
Things that could go wrong while trying to animate this sort of walk cycle is the breaking of the rig, which entails moving the joints in an awkward and unnatural manner causing the rig to go out of control when you play back the key frames. To keep this from happening keep the knee joints infront/behind their designated controller.
Another thing that could go wrong is if you lose the speed and stride of the character's walk. Try to time it just right so it stays within 25fps, this way when rendered it will flow much more nicely and more fluid. Sometimes that can be slow and padded out so if you want to make the character look like they are running faster; exaggerate their movements and skip some of the in-between poses that smooth out the animation.