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Rigidity of the interaction graph is a fundamental condition for achievingthe desired formation which can be defined in terms of distance or bearingconstraints between agents. In this paper, for reaching a unique formation withthe same scaling and orientation as the target formation, both distance andbearing constraints are considered for defining the desired formation. Besides,both distance and bearing measurements are also available. Each agent is ableto 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 theother hand, the framework is embedded in SE(3). The control signal is designedbased on a gradient descent method by introducing a cost function. Firstly, theformation problem is considered for bearing-only constraints in SE(3)configuration. Then, the formation control is expressed for the general case ofboth bearing and distance constraints. Furthermore, the essential conditionsthat guarantee reaching the desired formation are discussed. Finally, thevalidity of the proposed formation control is verified by numericalsimulations.

Bearing and Distance Formation Control of Rigid Bodies in SE(3) with Bearing and Distance Constraints