  In this paper, the problem of reaching formation for a network of rigid
agents over a special orthogonal group is investigated by considering
bearing-only constraints as the desired formation. Each agent is able to gather
the measurements with respect to other agents in its own body frame. So, the
agents are coordinated-free concerning a global reference frame. Attracting to
the desired formation is founded on solving an optimization problem for
minimizing the difference between the instantaneous bearing between agents and
their desired bearing. In order to have a unique global solution, the convex
optimization method is implemented. Since the rotation matrices are not convex,
the method of convex relaxation of rotation matrices space is used to embed the
rotation matrices on the convex hull of the Lie group. Then the control law is
designed to achieve the desired bearing with minimum energy consumption.
Finally, a simulation example is provided to verify the results.
