How to translate parent by child's axis

I have two object: parent and his child.
child can move by arrow key and aways look at parent
parent move by ‘w’ ‘s’ ‘a’ ‘d’ key
now parent can move by self (or world) axis, but how make parent move by child axis?

I guess you could just rotate the target direction vector according to the child’s rotation :

targetDirection.applyQuaternion( child.quaternion )