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This paper focuses on developing techniques and strategies for the analysis and design of sensor and network topologies required to achieve rigid formations of mobile autonomous agents for cooperative tasks. These strategies ensure minimum number of changes in the set of sensing and communication links between agents during splitting and merging operations. That is, in splitting, all the links between agents in the same post-split sub-formation are preserved and a minimum number of links are inserted into each post-split sub-formation to regain minimal rigidity. In merging, all the links in each pre-merged rigid sub-formation are preserved and a minimum number of links are inserted between sub-formations to create one single post-merged minimally rigid formation.