  Rigidity of the interaction graph is a fundamental condition for achieving
the desired formation which can be defined in terms of distance or bearing
constraints between agents. In this paper, for reaching a unique formation with
the same scaling and orientation as the target formation, both distance and
bearing constraints are considered for defining the desired formation. Besides,
both distance and bearing measurements are also available. 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. On the
other hand, the framework is embedded in SE(3). The control signal is designed
based on a gradient descent method by introducing a cost function. Firstly, the
formation problem is considered for bearing-only constraints in SE(3)
configuration. Then, the formation control is expressed for the general case of
both bearing and distance constraints. Furthermore, the essential conditions
that guarantee reaching the desired formation are discussed. Finally, the
validity of the proposed formation control is verified by numerical
simulations.
