Persistent Formations

Abstract

As studied in Chaps. 3 and 4, the goal of formation control is to achieve a unique desired configuration by satisfying distance constraints between agents. To achieve a desired distance constraint between two neighboring agents, if both agents work cooperatively in terms of sensing, communications, and actuation, then it may be considered as an undirected case. But, if only one of two neighboring agents connected by an edge works for this task, it may be considered as a directed case. In Chaps. 3 and 4, we studied global stabilization and local stabilization for undirected cases except Sect. 3.3. In Sect. 3.3, we studied a polygon formation under directed sensing and control topologies. However, even though we could satisfy the desired constraints, the formation would not be unique. The main goal of Sect. 3.3 was to achieve a desired polygon formation. That is, although the desired distance constraints between neighboring agents are satisfied, the realized configuration may not be unique in polygon graphs (cycle graphs). It may be realistic to suppose that only an agent can control an edge; so each edge of a graph may have a direction in the general setup (for sensings, communications, and actuations). By adding a requirement of achieving a unique configuration into directed graph setup, we may define a unique formation under directed graphs. This chapter is dedicated to address formation control problems under directed sensing and actuation topologies.