Unified Formulation of Multiagent Coordination With Relative Measurements

This article provides a unified solution to a general coordination problem of multiagent systems with relative measurements, including uncertain transformations in translation, rotation, reflection, and scale. First, we introduce relative measurements described by a matrix group expressing such transformations in a unified way. Then, we derive a necessary, and sufficient condition to achieve a coordination task by relative, distributed control according to a network topology, and a class of measurement information. Especially, a strict class of all realizable coordination tasks is characterized with an orbit associated with the transformation matrix group on measurement. Next, we show that the network topology required to coordination is the clique rigidity. Then, the clique rigidity for concrete coordination tasks is associated with conventional connectivity, e.g., connectedness and rigidity. Moreover, an intuitive condition is derived as a connectivity condition of the intersection graph of the maximal cliques (i.e., complete subgraphs). Finally, the new method is applied to formation control with unknown, heterogeneous scale factors and its effectiveness is demonstrated through simulations for both 2-D and 3-D spaces.