A New Orthogonal Control Law for Shaping Acyclic Triangle Formations

A new orthogonal control law is proposed in this paper which is applied to the agent with two co-leaders in an acyclic triangle formation, while the other agents still using gradient-like control law; the dynamical system with the control laws assigned like this with the intention of forming a prescribed acyclic triangle formation approaches to its desired edge lengths starting from any point except initially agent 1 being in the same place with agent 2 and/or agent 3 . The orientation of triangle is also concerned, and the only stable formation with desired edge lengths is positively oriented while the formation with desired lengths and negative orientation is unstable. The stable properties related with orientations swap over if the sign (negative or positive) in the orthogonal control law is changed. A simulation result shows the convergent process of forming a given acyclic triangle formation.