In April 1430, King Sejong sent officials to Hamgil (here) and Gangwon (here) Provinces to find a rumored island named "Yodo." In October that year, the Hamgil governor reported that he sent people to Cape Muji to look for the island and that his men had seen what looked to be an island, but it was not confirmed. After that, there was no more mention of Yodo until its mention in the following record, which is dated July 26, 1438. Based on the following record, we know that Yodo had not yet been found, but King Sejong still had hope.
Source:『世宗實錄』 卷 八十二, 世宗二十年 七月 戊申條Notice that before asking the governor to do another search for Yodo, King Sejong referred to Muleungdo and how he worried about the risks of sending people there. He seemed to be trying to say that he knew the risk of searching the sea for Yodo, but that it was a risk that needed to be taken. The fact that he used Muleungdo as an example seems to show just how risky he considered the trip to Muleungdo to be. He seemed to be trying to convince the Gangwondo governer that his desire to find Yodo was not based on some selfish wish to travel to the mysterious island, himself, but was based on a need to know its location for the benefit of the country.
July 26, 1438
傳旨江原道監司 茂陵島 本人物所居之處 自昔徃來之地也 然近日差人經涉大洋 尙恐險阻 夙夜憂慮 况此蓼島 雖稱在某處 固無來徃之者 予以衰老之年 敢望尋覓 但本島諺稱在襄陽之東 不可不知其在何處也 卿宜更加訪問以達.
강원도 감사에게 전지하기를, “무릉도(茂陵島)는 본래 사람이 살던 곳이며, 옛날부터 왕래하던 땅이다. 그러나 근일에 사람을 파견하여 큰 바다를 건너게 하고서는, 오히려 그 험난함을 두려워하여 주야로 이를 우려하여 왔다. 하물며, 이 요도(蓼島)는 비록 모처에 있다고는 일컬어 왔으나, 본시 내왕하는 자가 없었으니, 내가 이미 쇠로한 나이에 감히 그의 탐방(探訪)을 바라겠는가. 다만 본 섬이 양양(襄陽) 동쪽에 있다고만 일컬어 왔을 뿐이니, 어느 곳에 있다는 사실만은 불가불 알아야 할 것이다. 경은 마땅히 다시 이를 탐문하여 계달하라” 고 하였다.
The King communicated the following to the governor of Gangwon Province:
"Muleungdo is a place where people once lived and have traveled to since ancient times. These days, however, when I dispatch people to cross the big sea, I fear the dangers and worry about this day and night. It is said that this Yodo is somewhere, but no one has travelled there. I am already too old and weak to dare hope to travel there, but I think we need to, at least, know where it is since it is said only to be east of Yangyang. Do another proper investigation and report."
King Sejong may have mentioned the journey to Muleungdo because he considered it the most dangerous of any journey to Korea's outlying islands. Of course, a trip to Dokdo/Takeshima is farther and more dangerous than a trip to Ulleungdo, so the fact that the king did not mention trips to any islands beyond Ulleungdo may be a indication that he did not know of any islands beyond Ulleungdo. I point this out just so that it is considered.
By the way, it sounds as if King Sejong might have wanted to travel to Yodo when he was younger. He must have heard some interesting stories about the island.