grope

(あいぶ) To stroke or caress your partner with the intention of arousing them.
 
もむ To grab someone with a full palm-and-fingers-open hand-motion for which there is no exact English equivalent. Usually used about grabbing boobs but not always sexual. If you grab a little kid’s plump cheeks, that’s also もむ。
 
まさぐる To grope blindly inside something looking for something. Usually used about reaching around inside clothes looking for your partner’s naughty bits, but can be used in a non-sexy situation:groping inside your purse feeling for your lighter.
 
いちゃつく More childish word. To be all over someone – not in a bad, hentai blind date way, but in a good, first-month-of-dating-make-your-friends-naseous way. To cuddle or do some PDA.