Controlling a triangular formation of mobile autonomous agents

This paper proposes a distributed control law for maintaining a triangular formation in the plane consisting of three mobile autonomous agents. It is shown that the control law can cause any initially non-collinear, positively-oriented {resp. negatively-oriented} triangular formation to converge exponentially fast to a desired positively-oriented {resp. negativelyoriented} triangular formation. It is also shown that there is a thin set of initially collinear formations which remain collinear and may drift off to infinity as t → ∞. These findings complement and extend earlier findings cited below.