Since there's been a lot of interest in pedals recently I thought I'd offer my comments on the subject... Pedals have been a part of my warmup routine since they were introduced to me at a clinic in high school. During high school and college, few players around me had much knowledge or interest in them, but I kept doing them. Occasionally I would also use them to unwind after a hard session. They "felt good" and I think they helped my playing. But I don't think I was getting the main benefits that pedals can offer.
Fast forward 20 years, to the start of my comeback about 18 months ago. I discovered TPIN, and started learning about other methods for trumpet, and other approaches / benefits relating to pedals. My understanding of pedals has been growing, to the point that this is now becoming central to my entire approach to playing. Some important (for me) sources were the Claude Gordon materials, Clyde Hunt's web site and posts, and discussions on TPIN. However, I had to discover some of this for myself in order to (maybe) understand what everyone was talking about. Let's see if I can explain it now.
Try the following experiment. Play a low C (first one below the staff). Now, with valves open, bend the pitch down until you get a low G. The sound won't be great, but try to get it in tune. Then, while holding this pitch, press the first & third valves down. You should get a clear, centered G. This illustrates what I understand to be the underlying principle of the "constantly adjusting embouchure": there is a different "ideal" embouchure / oral cavity setting for every note on the horn. When you achieve that setting, you get a "centered" note, with good clear sound and no "clams" since your embouchure is in perfect agreement with the horn about the note to be played.
In the pedal range, the horn will not make the note for you. You have to make the note, by shaping your mouth and adjusting the lips. This is especially true of the "false pedals" from low F (octave below first-space F) down to C#. Try extending the above exercise, bending down to notes in the false-pedal range, while playing the note open. Then, while sustaining the note, press the valve combination you would use if the note were an octave higher (ie 1st and 2nd for false-pedal A, etc). While the note will still not be perfect, you should hear a dramatic improvement in tone due to resonance of the harmonics. But your embouchure is still forced to adjust to the note. You can't just press the valves and count on the horn to change the note.
For the "true pedals" (pedal C down to pedal F#, at least by my convention) you get some help from the horn, but you have to adjust the embouchure and oral cavity to bring them to pitch with full tone. This will seem impossible at first, but with practice you will discover how to do it. I think that's the key--you have to discover how to do it, and learn how it feels so you can do it again.
One of the biggest keys to getting this benefit is that you have to use the same setup for the pedals that you do for other playing. Claude Gordon forces this by having you play arpeggios etc beginning in the pedal register and ascending two or more octaves into the normal register, and descending from the normal register into the pedal register. Careful practice of this will train your embouchure to adjust to the optimum setting for each note in the normal register, in the same manner as you must do it in the pedal register.
The same training effect is possible in the normal register. I believe it was Nick Drozdoff's site where I heard sound clips of him playing full octave scales with no valves depressed in the normal register. I still cannot do this completely (I can descend from second-line G down to first-line Eb without valves, but the D still eludes me. And I have yet to master the intervals above first-line G. But Nick has it down--check it out!) I think this just extends what you can learn in the pedals--the "constantly adjusting embouchure".
I think this is making a big difference in my playing. I'm playing more "centered" even on faster-moving passages (Arban Characteristic study #1 for example) getting clearer notes and fewer 'clams' as a result. And I believe my playing is more efficient as well--ascending with less effort.