>>14271342Real answer.
I wrote my thesis on locomotion based movement for robot applications. There is a small but growing amount of papers and interest on the subject. Probably the best source of actual mathematical models is anything written by researchers at Biomimetics Millisystems Lab at Berkeley - a lot of good papers and they aren't averse to assisting you if you have an interesting idea/research. The great thing about the lab is that they put theory into practice and develop new and groundbreaking robots. A few of the alumni of an earlier incarnation went on to form Boston Dynamics.
To answer your question succinctly, the answer is 'whatever works'. There's no 'naturality'. Consider a function with the following inputs: energy, current location, movement vector, locomotor arrangement, with the outputs your locomotor arrangement. Whatever works in terms of the 'given' locomotor/actuators, that's your naturality. Of course the team at Berkely study animals and propose different energy and actuator models. Jumping locomotion is a big deal at the moment, because it used to be difficult to calculate but with miniaturisation, on-board calculation of your launch angle/energy budget becomes quick and trivial.
Good luck, it's an interesting field.
