Toward robust control of minimally rigid undirected formations

Abstract

Gradient control is a method based on potential functions to locally stabilize rigid undirected formations. However, when there is a mismatch in two neighboring agents' understandings of what the target distance between them is supposed to be, such a potential-based control will typically cause a rigid undirected formation to rotate in the plane. This paper investigates an appropriate modification of the gradient control, which eliminates this rotation and locally stabilizes the triangular formation with no restriction on the number of mismatches and any minimally rigid formation consisting of four or more agents with only one mismatch.