Rigid Formations with Leader-Follower Architecture

This paper is concerned with information structures used in rigid formations of autonomous agents that have leaderfollower architecture. The focus of this paper is on sensor/network topologies to secure control of rigidity. We extend our previous approach for formations with symmetric neighbor relations to include formations with leader-follower architecture. Necessary and sufficient conditions for stably rigid directed formations are given including both cyclic and acyclic directed formations. Some useful steps for creating topologies of directed rigid formations are developed. An algorithm to determine the directions of links to create stably rigid directed formations from rigid undirected formations is presented. It is shown that k-cycles (k ≥ 3) do not cause inconsistencies when measurements are noisy, while 2cycles do. Simulation results are presented for (i) a rigid acyclic formation, (i) a flexible formation, and (iii) a rigid formation with cycles.