Gravity Rush

Gravity Rush a.k.a. Gravity Daze in Japan is a first installment in the Gravity Rush series published exclusively for PS Vita, followed by the second part released only on PS4 as well as remaster released on the same platform. The game is centered around an ability to change the gravity on the player's fancy.
Among the other gameplay features one may point out "gravity field" allowing the protagonist to grab and throw objects near her. There are also a certain amount of collectibles: ones that fill up your gravity gauge and gems used to power up abilities. The structure of a game represents an open-world which may be explored at once and many mission together with sidequests with the latter allowing you to complete them at any time.
The story follows Kat — a girl with superhuman abilities. Those she acquired by having a cat — Dusty, along with her. All of the missions are supposed to help Kat recover her memory and find out how did she end up in Hekseville.