Accompany, attend and escort all mean to go along with.
Accompany when referring to persons, usually implies equality of status.
- Ken agreed to accompany me on a trip to Africa.
Attend implies a waiting upon in order to server usually as a subordinate. (see also: Tend vs Attend vs Mind vs Watch)
- The President was attended by several members of his staff.
Escort adds to accompany implications of protection, ceremony, or courtesy.
- Armed escorts are provided for visiting heads of state.