Collision free and permutation invariant formation control using the root locus principle
In this paper, permutation invariant and collision free trajectories for a formation control problem are generated by using the root locus principle. A polynomial based representation space of multiple robots in two dimensional space is proposed, and the invariant properties in this space are analyzed. The formation control problem is solved in the representation space. A set of permutation invariant trajectories is generated by the generalized root locus dynamics. This method can be realized without the knowledge of global coordinates, but only with the local interaction between robots. In addition, the generalized root locus principle gives one degree of freedom to choose a different assignment in the formation. At the end, an example of permutation invariant safe control is provided.