There is extensive halachas about taking cruises in general before, and during, shabbos (regardles of whether or not its a sail-boat)
Section by section, first:
Is it permissible to take a cruise over Shabbat? According to
Ashkenazim, many authorities forbid boarding a ship that will travel
on Shabbat unless one boards the boat during the first three days of
the week (Sunday through Tuesday), however, some permit boarding on
Friday. According to Sephardim, many authorities hold that one may not
board a boat within 3 days of Shabbat, meaning, preferably during the
first three days of the week and if that’s not possible then even on
Wednesday. However, some say that one is permitted to board a
cruise/boat even on Friday. 1This is all on condition that the
captain and crew are non-Jewish and that a majority of the passengers
are non-Jewish. 2 If the ship is owned by Jews, consult your local
Rabbi. 3
those notes are relevant:
- The Gemara Shabbat 19a quotes the Briatta which states that one may
not board a boat in order to travel on Shabbat unless one got on
before 3 days before Shabbat (whether or not this includes Wednesday
will be addressed later). The Rif (Shabbat 7a-b) explains that the
reason for this restriction is that if one boards a boat within 3 days
of Shabbat it will negatively impact the passenger’s oneg Shabbat
(enjoyment of Shabbat), however, if it’s started earlier the
passengers will get used to it and be able to enjoy Shabbat. The Rif
adds that if the boat will travel lower than 10 Tefachim (to the
ground of the river) there could be a violation of leaving the Techum
and in such a case one wouldn’t be able to leave any day of the week.
The Rosh (Shabbat 1:38) and Rambam (Shabbat 30:13) agree with this
reason. However, the Baal HaMoer (on Rif) explains that the reason
that one may not board a boat close to Shabbat is because it is likely
that there will be life threatening danger which will necessitate a
violation of Shabbat. However, when one enters the boat before 3 days
before Shabbat, there’s no issue because the obligation to prepare not
to violate Shabbat even for life threatening danger doesn’t begin
since the beginning of the week is not considered relevant to the
upcoming Shabbat (Mishna Brurah’s introduction to 248 and Mishna
Brurah 248:8). The Bet Yosef 248:1 writes that according to the Baal
HaMoer it seems that it would be forbidden to board the boat on
Wednesday because Gemara Gittin 77a says that Sunday through Tuesday
is part of the previous Shabbat and Wednesday to Friday is connected
to the upcoming Shabbat. Then the Bet Yosef infers from the Rosh that
it is permissible to board the boat on Wednesday. Mishna Brurah 248:8
writes that this question of whether Wednesday is a major dispute
between the Magen Avraham who forbids and the Gra who permits and
Mishna Brurah leaves it unresolved. Shemirat Shabbat KeHilchata 30:66
is strict only to allow entering the boat before Wednesday. Kaf
HaChaim 248:7 writes that preferably one should be strict not to board
on Wednesday but if it’s not possible one can be lenient. Menuchat
Ahava (vol 1, 1:1-2) is lenient to permit entering on Wednesday unless
it’s definite that there will be a violation of Shabbat (because life
threatening situations).
- Menuchat Ahava (vol 1, 1:2) writes that
nowadays since the boats are calmer and it’s less likely that it will
ruin one’s oneg Shabbat it’s permissible to board the boat on Friday.
Rabbi Yisrael Belsky (OU Kosher Webcast, December 2011, min 3-9) says
that nowadays the minhag is to be lenient and there is what to rely
on. However, Shemirat Shabbat KeHilchata 30:66 rules that trips for
vacation may only board the ship on the first three days of the week
even nowadays. (Rav Herschel Schachter (min 77) seems to agree.)
VeDaber Davar (Rav Shmuel Pinchasi, 1:25), Chut Sheni (Rav Nassim
Karlitz, vol 1, pg 72), and Daily Halacha by Rabbi Mansour agree with
Shemirat Shabbat KeHilchata. Similarly, Yalkut Yosef (Shabbat vol 1,
pg 48) argues that one should not be lenient unless one frequently
travels by boat and isn’t bothered by the travel. Menuchat Ahava (vol
1, 1:2) writes that if the crew or captain is Jewish and will work on
Shabbat it’s forbidden to board the boat any day of the week. Yalkut
Yosef (Shabbat, vol 1, pg 48), Sh”t Yechave Daat 6:16, and VeDaber
Davar (Rav Shmuel Pinchasi 1:22) agree. Menuchat Ahava (vol 1, 1:2)
writes that it is only permissible if a majority of the passengers are
non-Jewish, otherwise, the crew is working on Shabbat for the benefit
of Jewish and would be forbidden (as Amirah LeNochri). Shemirat
Shabbat KeHilchata 30:66 (and note 221) adds if the ship travels on a
schedule and would travel with or without passengers then it would be
permissible even if there’s a majority of Jews, but if without the
Jewish passengers they would cancel the trip it wouldn’t be forbidden.
and note 3:
Shemirat Shabbat KeHilchata 33:66 (not 222) writes that one should consult a Rabbi. See also http://www.yeshiva.org.il/ask/eng/?id=5290 who expressly forbids if it's owned by Jews.
although that link no longer works... but still seems to be dependant on if the ship is run by jews or not, so in this case of the sailboat, it would be a jew runnning it the whole time...
but all of this is regarding actually getting onto the boat, not just being on the boat (assuming one went on it sunday or even tuesday, for sure), you mentioned doing work such as "tie knots and pull the ropes of the sails" knot tying is problematic on shabbos, in fact that source explicitly mentions knots being tied for the sake of sailing:
If one ties a “permanent” knot on Shabbat, i.e. a knot that is not
meant to be undone within the next day or the next week (as we shall
soon explain), if this knot is “professionally done”, i.e. not all
individuals know how to tie such a knot, for it takes certain
knowledge and skill to tie such a knot, one is liable by Torah law as
a result of the knot he has tied, similar to any other form of Shabbat
desecration.
An example of a knot forbidden on Shabbat by Torah law is a
“Camel-Driver’s Knot.” This entailed making a hole in the saddle or
through the camel’s nose through which leather straps would be passed
and tied strongly such that it would never become untied. This kind of
knot is considered both “permanent” and “professional.” For this
reason, one who ties such a knot on Shabbat is liable by Torah law.
Similarly, a “sailor’s knot,” i.e. when rope is inserted in a hole
located in the front of a ship and tied very tightly so that it is
firm enough to tie another rope to it to hold the boat in place in the
dock, is considered a “permanent” and “professional” knot and is
forbidden to be tied on Shabbat by Torah law. In the next Halacha we
shall discuss several knots which are permitted by Torah law to be
tied on Shabbat but forbidden by a rabbinic enactment.
Although technically that was talking about tying it into the dock, which implies after sailing, but it may not apply (at least on the Torah level) if its tied temporarily to steer the boat, but if you look at the next halacha in that page, it discusses knots which are forbidden to be tied by rabbinic decree, which include knots taht are "professionally done", even if they're not permanent:
Knots Forbidden by Rabbinic Enactment: Permanent or Professional Knots
Our Sages enacted that even if a knot is not tied in a professional
manner, it is forbidden to be tied on Shabbat if it is permanent. This
means that even if this knot can be tied by anyone and requires no
special skill, nevertheless, if it is a permanent knot, one may not
tie it. (Shulchan Aruch Chapter 317, Section 1)
An example of such a knot would be the knot tied to the pail hanging
at the top of a well. Since the knot tied to the pail is never undone,
although tying such a knot requires no specific skill, it is forbidden
to tie it on Shabbat by rabbinic law.
Similarly, regarding a knot tied to a bit around an animal’s mouth,
although no special skill is required to tie the bit, it is forbidden
to tie such a knot on Shabbat if one never intends to untie it.
Additionally, if a knot is “professionally done” and requires some
skill to tie it, although it is not permanent, one may not tie such a
knot on Shabbat as a result of a rabbinic enactment.
Knots Permitted to be Tied on Shabbat A knot which is neither
professional nor permanent may indeed be tied on Shabbat, for our
Sages only decreed not to tie a knot which fits either one of the
Torah’s two criteria to forbid tying a knot on Shabbat, i.e. either it
is a professional knot or a permanent one. However, a knot which is
neither professional nor permanent may be tied on Shabbat. We shall
discuss this matter further in the following Halacha.
So even if its not permanent, but if its still done in a professional manner it seems to be forbidden by rabbinic decree.
So this is assuming the first part of the question, but the last part of "what if its all on autopilot" implies the sailor would be doing no actual work with the sails at all, which then depends on whether or not its permitted to use computers or robots to do melacha for someone on shabbos, which, according to Rabbi Moshe Feinstein (as quoted there), is in general only permitted for lights...
