Control of acyclic triangle formations with orthogonal control law

This paper proposes a distributed control law for three mobile autonomous agents to shape an acyclic triangle formation. Agents move themselves autonomously in two orthogonal axes to pursue and maintain the prescribed distances to their co-leaders. The dynamical system approaches exactly to the desired edge lengths and the orientation of the triangle in any initial condition except initial collocation of agent 1 and 2. For minimally rigid graphs with more than three agents constructed by the Henneberg sequence, using orthogonal control law leads to the exact formation desired. Stability analysis of the dynamical system shows the exponential convergence to the only stable equilibrium which corresponds to the desired formation. A set of three variables is defined to describe floating triangle formation, which neglects the translation and rotation of triangles but not its flipping over in the plane . These variables are also used as a set of state variables of the floating triangular formation to show the trajectories of the dynamical system.