Maintaining a Directed, Triangular Formation of Mobile Autonomous Agents

This paper analyzes a class of distributed control laws which encompasses and generalizes three previously considered types of control laws for maintaining a triangular formation in the plane consisting of three point-modeled, mobile autonomous agents. It is shown that the control laws considered can cause any initially non-collinear, positively-oriented {resp. negatively-oriented} three agent formation to converge exponentially fast to a desired positively-oriented {resp. negatively-oriented} triangular formation. These findings extend earlier results and provide an alternative perspective.