Formation Control

Formation control is a topic that has been widely studied in multi-agent systems. Agents measure distances, displacements, bearing vectors, or angles of the neighboring agents with respect to a local or global coordinate frame. After comparing the magnitude of these measurements with the desired ones, agents seek to minimize the errors of control variables. The agents are supposed to achieve a desired configuration of the locations of agents by minimizing the errors of control variables. To achieve a unique configuration by relative control variables, the underlying topology of the graph should be characterized by a rigidity property. There are distance rigidity, bearing rigidity, and angle rigidity, or combinations of these rigidities. Based on some mathematical properties of the graph rigidity, a distributed formation control problem is formulated.