keep doing sth.是说继续做你刚刚做的事情,把做的状态继续保持下去.
keep on doing sth的意思则是“继续做某事”
go on doing sth 已开始干A停了一会继续干A
go on to do sth 已开始干A停了一会在继续干但是不干A了干B
continue to do是指曾经中断该动作（而做了其他事情）后继续再做此动作
比如,He continued to watch TV after opening the door for me.
而continue doing是未曾停止该动作（此动作是一直持续的）
比如,He continued watching TV,ignoring the loud knock on the door.