My definition of commitment is similar to BlackUnicorn's.
I went to check an example of wedding vows to analyze with that in mind:
In the presence of God, our family and friends, I offer you my solemn vow to be your faithful partner in sickness and in health, in good times and in bad, and in joy as well as in sorrow. I promise to love you unconditionally, to support you in your goals, to honor and respect you, to laugh with you and cry with you, and to cherish you for as long as we both shall live.
Now, unless you think of "faithful" as meaning "not poly", the rest is all the same. For me, committed means you vow to be there for that person if they get sick, if they lose their job, but also in happy times such as happy times with other partners they might have, and to include them in your happiness with others.
You will support them in their goals, as well, and give them your respect.
All of that applies. To me, the "till death do us part" section does not apply, and yet it does. What I mean by that is that for instance Raga and I broke up and I believe it's a good decision. But because we committed to one another I still feel committed to him in supporting him and being there for him and being part of each other's lives, even though we're not in a relationship anymore.
So I would replace the "till death do us part" with "if we were to break up, that part of my life would always remain part of me, and you would always remain someone who has been important to me and remain a part of my life". Or something to that effect.
I also believe that in poly relationships, committing to a partner also means committing to their existing partners (although in a different way) and committing to help them in their future dating, wooing and other such things.