I think that the fundamental plea Ulysses makes to his fellow mariners is to join him on a voyage where the destination is uncertain, the results in limbo, but the journey is the epitome of being worthy. In the Homeric myth, Ulysses' ability to convince his fellow mariners to strive towards Ithaca, towards home, had a directed end. It proved to be relatively easy to galvanize men into action with such a poignant and relatively simple selling point. Tennyson's retelling of Ulysses is much more complex. Home has turned out to be something representing banality. Home represents the "idle" and "barren crags." The voyage and spirit of intensity that accompanied it is lacking in home. To this end, Ulysses' pleas are geared towards instigating this spirit of what can be, of the conditional and of the possible, and of a realm where directed end products are not immediately apparent:
For my purpose holds/ to sail beyond the sunset, and the baths/ of all the western stars, until I die. It may be that the gulfs will wash us down.
This plea is followed by a potential promise to meet Achilles once again and "touch the Happy Isles." It is this plea, one of adventure, challenge, and inspiration, that Ulysses offers to his fellow mariners in the hope believing that consciousness can be an endeavor in which one commits "to strive, to seek, to find, and not to yield."