It seems as though (I'm relying on the commentators in this instance) the KJV rendering of the same Heb. terms is given about 1/2 the time as "at your own will" and half the time as "that he/it may be accepted," or "accepted for him," something like that; and I'm guessing that most modern translations go with the one rendering, the latter.
It should be said, that this offering was in some sense the fundamental kind of offering for Israel's sacrificial system. It's origins are not less back in the past than Gen.4, and the offerings of Cain and Abel. Taking K&D's old introduction to Lev. as a basic and reliable, if dated, description: the aim of the essential offering is for fellowship (a re-establishment of the original fellowship in the garden).
"The true God did not require human sacrifice from His worshippers, but the surrender of the heart and the denial of the natural life, even though it should amount to a submission to death itself, and also that this act of surrender was to be perfected in the animal sacrifice; and that it was only when presented with these motives that sacrifice could be well-pleasing to God." Keil & Delitzsch.
Other than the admission that the gift (to man) of sacrifice is divine condescension, that it is a stand-in for a permanent solution, and that the presence of ineradicable sin is a barrier to uninhibited fellowship; this offering is certainly a "voluntary" dedication. It is not brought because of some specific sin or trespass (see chs. 4-5) for which atonement and forgiveness is sought. In fact, in the Israelite system, it should be brought only if there was no prior demand for one of those other offerings. In that sense, it was most voluntary.
These sorts of offerings (if I have the data correct) were the character of the regular priestly sacrfices, morning and evening, and other special occasions of Israel's calendar. They signified the national devotion to the Lord, constantly being before him; as well as offering the people in a general sense individually appropriated grace (divine favor), in spite of any personal limitations burdening them, that might not allow them even to draw near enough to the altar to make such an offering.
The regular offerings were commanded in the law, so not (in that sense) strictly voluntary; but they were a declaration also from the nation that (officially, anyway) it was (and the citizen-components were each) pleased to be in a Master-servant relation to God, so recognized in these offerings.
Poverty, sterility, habitual uncleanness, etc. would be the kinds of things that would prevent some Israelites from maybe ever (lifelong) enjoying the privilege of offering up such a personal gift on the altar, desire it as they might. NC expectations to lift those typological restrictions are some of the most precious promises of the OT, see Is.56:3-8.
