http://www.oricomtech.com/projects/leg-time.htm lists three gaits:
- the tripod
- wave, and
Can these be improved, or can their relative pros and cons be altered, and are there other gaits worth considering?
Discrete gaits are a very limited way of implementing hexapod motion.
Imagine trying to limit a person to two speeds, walk and run. In reality we spend a lot of time meandering around with no defined gait or in transitions between various gaits.
There is a reasonable amount of research on insect gaits and the common discrete gaits you read about are essentially what insects settle upon as the optimal solution when spending a long time at a single speed.
A gait can be fully defined by the timings of its return strokes. In general, going faster requires performing more return strokes in a given amount of time (which is why a tripod gate will be faster than a tetrapod gait which will be faster than a wave/ripple).
I am not an expert in insect locomotion, but my understanding is that each leg independently decides when to return based on a set of simple rules.
As an example, a leg must return when it approaches the end of its stroke. To avoid having all the legs retract at once, legs are discouraged from performing their return stroke when its neighbours are retracting, or if the leg directly opposite is retracting.
As well, legs are mildly discouraged from retracting when any other leg is retracting so as many legs are on the ground as possible.
It is easy to see that both the tripod and ripple gait obey the above rules but you also get additional gaits and transitions as speed and direction changes.
TL;DR An insect will never use a single gait so if you want optimal creepyness (or efficiency since evolution is pretty good at that) there are a lot of books/papers on how insects walk.
EDIT: There are also a lot of per-leg rules that help traverse rough terrain. As an example, legs will always try to stand in a spot where a leg has already been (since it knows that place is solid). A typical insect will place its front legs in areas it knows are secure and all the subsequent legs will only use those locations.
I have never been a big fan of the traditional tripod gait. It usually looks clumsy, and doesn't really take into account the delicacy of walking over uneven terrain. Walking this way tends to be jerky since one tripod is reaching the end of its travel just as the next tripod is touching down. Exactly how smooth you can make the walk depends on the implementation of your robot. If you have 3 degrees of freedom on each leg, then you have great freedom bring one set of legs forward quickly, bring them carefully into contact with the ground, matching the motion of the ground, and gently taking the robot's weight on them before lifting the other tripod. Alternatively, if you have two fixed tripods, the robot is going to just clunk along like a toy. It also has the lowest payload carrying capacity, since only three legs are on the ground. However, it can be pretty fast, since you're moving three legs at once.
Ripple This is by far my preferred gait. What I like about this gait is that it's easier to make the walk smoother. At any one time, you have three legs taking the weight, one in flight, one touching down, and one lifting off. It also makes it easier to cope with rough terrain. When the terrain is rough, you may need a moment longer to touch the leg down carefully on the ground, begin to apply weight and see if it's stable. If so, take the weight fully, and continue walking. If not, then it's not a disaster to delay lifting another leg so that you can try to get this one stable.