It seems to me that the most logical way to train piaffe is to train the hind legs to step under one at a time.
Using a long whip tap on the cannon bone of each hind leg tap until the horse picks it up. When that response is pretty reliable correct the horse (by repeating the tapping) when he places the foot either in the same place or behind where he had it originally. Very quickly he learns to pick up his hind feet on cue and place them slightly closer to his front feet.
Once the cue is reliable shift it to either side of the top of his rump. I did this by giving a light tap on the top of the right side of his rump, then applying the 'pick it up' cue on the right hind. Pretty soon he'll be picking up each hind leg in turn from light taps on the top of his rump.
Make sure the horse stays really calm through out this training. If he seems to be making steady progress that's great! Don't over do it. Lots of short sessions are the most effective way of training. If he seems to make no progress in his training, think about your own timing. Are you stopping tapping quickly enough? Maybe your tapping is too slow? Maybe its too hard or too soft? Make sure that your are applying only one aid at a time!!
Keep stroking him with the whip throughout so he doesn't develop any aversive behaviours.
Pretty soon you'll be able to get two hind leg steps, one after the other, in quick sequence.
Once the back legs are very clearly under stimulus control practice rapid, light transitions from trot to halt and back to trot again in hand. Once these are light you can add the taps on the back legs while doing the transition to really get some engagement from the hind legs.
Don't try and prevent the forward progression of the horse at this stage. If he gets heavy in your hand do a few "step back" steps but only two steps of the front legs (or one stride) at a time.
Wait until the horse is really alert and possibly a bit fresh before trying to get any actual piaffe. If he's a little bit excited its easier.
Once he's REALLY light in the trot/halt/trot transitions do a couple of transitions where you do a halt transition and then very quickly afterwards ask for two back leg steps - tap tap with the whip on the top of his rump. He'll be anticipating trot, so he should be prepared to travel forwards. Don't let him travel more than about 1m, repeat repeat repeat. Look for any diagonal trot steps and reward like crazy. (Note the tool bag full of carrots!)
Be patient, give many rewards and pretty quickly a nice little piaffe emerges. If your progress falters go back to the previous stage and consolidate. You are looking for nice regular rhythm and a lowered hindquarter. Its ok if he wants to carry his head a little high in the beginning, this probably helps him lower behind initially.
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