The Animatrix was Square Studios' final project before it was broken up.  It's a link between The Matrix, the Enter the Matrix video game, and the Matrix sequel(s, depending on your view). It's short and bittersweet.

The main characters - Thaddeus and Jue - are introduced in a battle simulation.  They face off, blindfolded, in a stylized duel.  Though, as it turns out, it's less a stylized duel than, well... stylized foreplay.

Our lovers gradually strip one another's clothes off with graceful swordstrikes, until they are left just barely.  Before they can get closer, an alarm sounds.

Damn it! quoth dear Thaddeus, and they are pulled from the Construct.

Apparently a fellow named Robbie has picked up a good number of Sentinels.  The crew didn't know what to do, so called on the captain.  In an effort to outrun the machines, the Osiris runs, taking an uncharted tunnel which lands them on the surface...

...Where they find the machine army prepping to invade the last human city, Zion.

In worse trouble than they had been with the first few sentinels, the Osiris flees - and is soon pursued by a army of the buggers.

The rest of the clip is the struggle of the Osiris crew to buy time as Jue enters the Matrix to get word to the other rebels.

The Final Flight of the Osiris, as I said, is short and bittersweet.

Final Flight of the Osiris utilizes the same technology as resulted in the creation of The Spirits Within.  Thus, the animation is of the same kind.  A separate muscle system was used for Osiris, but that's all I know as being much different.

As it appears, a number of The Spirits Within's cast make cameos - Jane bears more than a passing resemblance to the gunner woman (who is voiced by Final Fantasy X's Rikku, unrelatedly).  Hein appears with a facial hair disguise (Easily noticed if you've seen a certain modified photo).  Neil is possibly there as the pilot.  I think I noticed Gray once.  Thaddeus is somewhat semblant of Ryan....  Though it could be coincidental, Square had said they wanted virtual actors capable of multiple roles - and multiple realistic deaths, if true.

Notoriously absent, although some might argue that, Aki got shaved and was used against a sentinel in a demo from Square Studios to the Wachowski Brothers.

For more on The Matrix, fandom and fiction, visit The Construct.  Their content, forum, and links should provide you with all the fix you need.