Sign rigidity theory and application to formation specification control

This paper develops a sign rigidity theory to characterize and examine multi-agent rigid formations consistent with a formation specification including distance- and signed area-constraints, and to control an arbitrarily positioned set of agents to take up the specifications. The sign rigidity theory can be viewed as an extended version of the standard distance rigidity theory with the addition of signed area constraints. This property enables elimination of possible formation specification ambiguities arising when a formation specification includes distance constraints only. As an application of the sign rigidity theory, this paper explores formation specification control in 2-D space. Under the proposed gradient-based formation control law, almost global convergence (from arbitrary initial positions) can be achieved when a target formation consists of triangulated sub-formations defined by distance- and signed area-constraints; the formation control law is applied for either single-integrator models or unicycle models.