Generalized Controller for directed triangle formations

Abstract

This paper proposes and analyzes a distributed control law which generalizes three different previously considered control laws for maintaining a triangular formation in the plane consisting of three point-modeled, mobile autonomous agents. It is shown that the control law under consideration can cause any initially non-collinear, positively-oriented (resp. negatively-oriented) triangular formation to converge exponentially fast to a desired positively-oriented (resp. negatively-oriented) triangular formation. These findings clarify and extend earlier results.