Formation control of mobile agents without an initial common sense of orientation

In this paper, we study formation control of single-integrator modeled agents in the plane. The agents maintain their own local reference frames, whose orientations are not aligned due to the lack of a common sense of orientation. Assuming that the agents measure the relative positions of their neighbors and exchange their local information with their neighbors, we propose an orientation estimation, a position estimation, and a position control law to achieve the desired formation. If the graph associated with the agents has a spanning tree and all initial orientation angles belong to an interval with length less than π, the orientations are exponentially estimated up to translation, the estimated position exponentially converges to actual position up to congruence, and the desired formation is asymptotically achieved up to congruence.