  When a team of agents, such as unmanned aerial/underwater vehicles, are
operating in $3$-dimensional space, their coordinated action in pursuit of a
cooperative task generally requires all agents to either share a common
coordinate system or know the orientations of their coordinate axes with regard
to the global coordinate frame. Given the coordinate axes that are initially
unaligned, this work proposes an orientation alignment scheme for multiple
agents with a type of leader-following graph typologies using only inter-agent
directional vectors, and the direction measurements to one or more landmarks of
the first two agents. The directional vectors are expressed in the agents'
body-fixed coordinate frames and the proposed alignment protocol works
exclusively with the directional vectors without the need of a global
coordinate frame common to all agents or the construction of the agents'
orientation matrices. Under the proposed alignment scheme, the orientations of
the agents converge almost globally and asymptotically to the orientation of
the leader agent. Finally, numerical simulations are also given to illustrate
the effectiveness of the proposed method.
