TL;DR: “Sweet madness” is an allusion to Milton’s Comus, which itself alludes to Homer’s Odyssey.
Aurobindo admired the works of John Milton, as we can see from his poetry criticism:
As [the magnificent Elizabethan outburst] dies away, we have the lonely figure of Milton with his strenuous effort at an intellectual poetry cast in the type of the ancients. The age which succeeds is that of a trivial intellectuality which does not follow the lead of Milton and is the exact contrary of the Elizabethan form and spirit, the thin and arid reign of Pope and Dryden.
Sri Aurobindo (1953). ‘The Course of English Poetry’. In The Future Poetry, pp. 72–73. Pondicherry: Sri Aurobindo Ashram.
Aurobindo emulated Milton by writing Savitri, a religious epic in blank verse, on the model of Milton’s Paradise Lost. So we should not be surprised when Aurobindo alludes to Milton. Here “sweet madness” comes from Milton’s masque Comus (1634), where Comus praises the song of the anonymous “Lady” thus:
I have oft heard
My mother Circe with the Sirens three,
Amidst the flowery-kirtled Naiades,
Culling their potent herbs and baleful drugs,
Who, as they sung, would take the prisoned soul,
And lap it in Elysium: Scylla wept,
And chid her barking waves into attention,
And fell Charybdis murmured soft applause.
Yet they in pleasing slumber lulled the sense,
And in sweet madness robbed it of itself;†
But such a sacred and home-felt delight,
Such sober certainty of waking bliss,
I never heard till now.
John Milton (1634). Comus, lines 252–264. Project Gutenberg.
† See this answer for a discussion of the puzzling phrase “robbed it of itself”.
In the passage from Comus, Milton references characters from Homer’s Odyssey: Circe was a sorceress who drugged Odysseus’ sailors and turned them into pigs; the Sirens were creatures who enchanted men with their beautiful singing; and Scylla and Charybdis were sea-monsters. Circe warned Odysseus of the Sirens thus:
First you will raise the island of the Sirens,
those creatures who spellbind any man alive,
whoever comes their way. Whoever draws too close,
off guard, and catches the Sirens' voices in the air—
no sailing home for him, no wife rising to meet him,
no happy children beaming up at their father's face.
The high, thrilling song of the Sirens will transfix him,
rotting away, rags of skin shriveling on their bones …
Homer. Odyssey, book XII. Translated by Robert Fagles (1996). Penguin.
So Milton’s “sweet madness” describes the enchantment of Circe’s drugs and the Sirens’ song. The phrase “sweet madness” is a paradox, an “apparently absurd or self-contradictory statement or proposition” (OED) which challenges the reader to figure out how to interpret it. Here the effect of the enchantments is “sweet” because it is pleasant, but “madness” because it robs the victims of “sense”, that is, their capacity for rational thought, leaving them as pigs on the island of Circe, or skeletons on the meadows of the Sirens.
The paradox works the same way in Aurobindo: love is “sweet” because it is pleasing, but “madness” because it leads to irrational behaviour. The word “rapturous” captures both of these ideas in a single term: rapture is both “a fit of intense delight” and “the fact of being carried onward or swept along”, as the rational mind is by the force of emotion.