Merging Multiple Formations: A Meta-Formation Prospective

This paper considers the problem of merging of more than two (minimally) rigid formations which do not have any common agent to obtain a single (minimally) rigid formation in R2 and R3. Following previously developed strategies for sequential merging of two rigid formations, a new set of enhanced merging operations is developed. They can be performed in a formalized meta-formation framework, where the individual rigid formations are considered as meta-vertices and they can be merged into a meta-formation. These operations for growing meta-formations offer a level of control to the merging quality and optimality, in the sense of minimizing the number of meta-edges (that is, edges between different meta-vertices) required. It is also proved that all minimally rigid meta-formations in R2 can be obtained by successively merging two or more meta-vertices using the proposed set of meta-operations.