I guess that you're interested in a kind of breathing relevant to aikido (and any budo). If so, it is important how you breathe. I'd like to call it ki breathing.
It's belly breathing, more precisely with your center, and long extensions - especially of the exhalation, as mentioned by David above.
If you focus on exhalation and extension, it increases your power (as in budo, where almost every decisive movement is done when exhaling). If you focus on inhalation it leads to a strong sense of inspiration (as in the arts).
I have some ki breathing exercises on my website:
Check under the headline Breathing
Also check the Extension
exercises on the same webpage. There's one for walking.
I read through your webpage (very interesting I might add) and had a question about the belly breathing exercise (lying down), On the inhalation the belly presses against the hand and on the exhalation the belly also presses upwards against the hand. While I can generate both conditions I cannot do so without letting the belly relax (drop) between the inhale/exhale. If I end up with my belly extended on the inhale, there's no room for more extension on the exhale. Maybe I'm stating the obvious but is there an implied relaxation of the belly between in/exhale?