Breakage(1999)

Breakage

In 2007, the inhabitants of Danger Planet II fight their battles using remote-controlled robots also known as virtual puppets. Kirio Nimura is a high school student and the strongest puppeteer on the planet who falls for Sairi Takahara; however, she insists that nobody may make advances until they have beaten her puppet, Benkei.

(Source: Anime Encyclopedia)