Although the details are obscure, Robert went to sea and ended up in Boston, Massachusetts. There, in September 1787, he was enrolled as third mate on the "Columbia Rediviva", a Boston vessel trading fur in the Pacific Northwest, under command of John Kendrick. At the Cape Verde Islands, Haswell's friend and mentor, first mate Joseph Woodruff, squabbled with Kendrick and was dismissed from the ship, but as a consequence Haswell became second mate. Haswell himself then ran afoul of Kendrick over the disciplining of a sailor, and he agreed to be sent home when they reached the Falkland Islands. However, no other ship was present, and Haswell agreed to move to the accompanying sloop, the "Lady Washington" (Captain Robert Gray). Although still second mate, the move to the much smaller vessel represented a demotion, which Haswell attributed to Kendrick's desire to promote his own son. In this role he cruised up and down the coast, trading for furs. In mid-1789, Gray and Kendrick exchanged ships, and Haswell accompanied Gray on the "Columbia" across the Pacific, stopping at the Sandwich Isles, and sailing on to Canton, China to sell the furs. They returned to Boston via the Cape of Good Hope and Saint Helena, the voyage being the first American circumnavigation of the globe.