Structural persistence of three dimensional autonomous formations
Built upon a recently developed theoretical framework, we consider some practical issues raised in multi-agent formation control in three dimensional space. We introduce the partial equilibrium problem, which is associated with unsafe control of a formation in practical 3-dimensional applications. We define structurally persistent graphs, a class of persistent graphs free of any partial equi- librium problem. In real deployment of control of multi-agent systems, forma- tions with underlying structurally persistent graphs are of interest. We study the connections between the allocation of degrees of freedom (DOFs) across agents and the characteristics of persistence and/or structural persistence of a directed graph. We also show how to transfer degrees of freedom between agents, when the formation changes with new agent(s) added, to preserve persistence and/or structural persistence