A family travels to another planet in order to seed it with humanity. Meanwhile earth's technology surpasses that of the ship and gets to that planet before the ship. There's also a subplot involving robotic interface with humanity and immortality.
Okay so, there is a number of people on the ship. And in order to make it to the planet in the amount it would take this number is firm, so if anyone decides to have children the number of people on the ship can not go up. Before they lose contact with earth, humanity comes up with a way to freeze the rate of growth. What this means is they will not age anymore however their brains can still grow and learn. so in essence you can have an 15 year old with a brain of a 40 year old. This puts a bit of an ethical dilemma in the hands of the people on the ship because if they choose not to die...
They can not have children because they will never die. When they finally arrived at the planet hundreds of years later humanities science and research is overtaking the ship and they have beat the ship to the planet. However humanity as they knew it has changed completely. Most humans have inserted their thoughts and emotions into robots. Eventually you may discover is that instead of robots we can put ourselves into this giant hive mind and insert that hive mind into anybody so the individual and the concept of the individual kind of dies out.
There is one hold out however and it is one of the people from the ship. She has held out and stopped aging process at 40. She becomes kind of a pariah. Eventually she decides to become a robotic version of herself.
This is when the details get fuzzy. Something happens and eventually she becomes part of this group of robotic beings that goes out and into space. Humanity no longer needs space ships to travel they are capable of withstanding any atmosphere in anything because they are robotic themselves. This same character finds a planet and I think it's earth and decides to seed it and to switch things around so that life begins on it all over again.