Principles to control autonomous formation merging

This paper provides a complete description of possible scenarios of merging two minimally rigid or globally rigid formations to obtain a single minimally rigid or globally rigid formation, respectively, both in ℛ² and ℛ³. A strategy is developed based on simplification of the merging problem to a problem of growing a minimally or globally rigid graph. Based on this strategy, three principles are provided to control the merging efficiently and optimally, in the sense of minimizing the number of added edges and the number of vertices incident to these edges. Any possible scenario of merging two given minimally or globally rigid formations can be handled using a combination of these three principles. Although the main results are provided for merging two formations, application of the proposed techniques to merging of more than two formations is briefly discussed as well.