This kata (i.e. "form") was designed by Koichi Tohei (1920-2011). In the video below, Tohei is performing two different sequences, both counting in 22 (these are also known as "Jo 1" and "Jo 2"). The first one is more well-known outside ki-aikido.
Below, Kenjiro Yoshigasaki (1951-2021) performs "Jo 1" (All of Aikido 1999-2001) with some key points shown separately. The continuous kata starts at [1:30].
Again below, Yoshigasaki performs "Jo 2" (All of Aikido 1999-2001).
Obviously, there are always different interpretations of the same forms, depending on what each student has remembered. In the old days, before the video era, most teaching was obviously based on individual memory.
Fumio Toyoda (1947-2001) was Tohei's student from 1957 to 1984, when he founded his own organization. In search of video material of Toyoda, here's a Toyoda-style student Ed Haponick performing the first kata.
Michael Holm and Carsten Møller perform the "Jo 1" kata with all movements explained in detail as taught by Yoshigasaki.
Morihiro Saito's (1928-2002) jo-kata 31 has clear similarities with Tohei's jo-kata 22 ("Jo 1").
This is what Saito says about the kata in an interview with AikiNews (#88, 1991).
Q: "Was the present sanjuichi-jo (31-movement jo kata) finalized before O-Sensei’s death?"
A: "Yes, by the time I learned it the kata was already complete, but when Koichi Tohei Sensei [presently head of Shinshin Toitsu Aikido] came to practice in Iwama it had not yet been perfected. What he learned was different from what I learned, probably because O-Sensei’s way of instructing was not yet fully developed."
"...I used to teach the jo as a 27 or 28-movement form, but ended up with the 31-movement form as I found this was easier for students to understand. Just as my aikido has come to be called “Iwama-style,” the “sanjuichi-jo” name that I gave to this kata has stuck."
Saito started aikido in 1946, when Tohei was already one of the leading figures of the Aikikai (which was not yet called the "Aikikai" but "Kobukai" instead; see >History). However, Saito was studying intensively with O'Sensei Morihei Ueshiba, who put much focus on developing weapon techniques during his Iwama years.
"When Koichi Tohei and Morihiro Saito met for the last time - October 29, 2001" by Stanley Pranin. Aikido Journal.
Michael Winter performs the same with a partner in one sequence.