© 2020 IEEE. Localization between a swarm of AUVs can be entirely estimated through the use of range measurements between neighboring AUVs via a class of techniques commonly referred to as sensor network localization. However, the localization quality depends on network topology, with degenerate topologies, referred to as low-rigidity configurations, leading to ambiguous or highly uncertain localization results. This paper presents tools for rigidity-based analysis, planning, and control of a multi-AUV network which account for sensor noise and limited sensing range. We evaluate our long-term planning framework in several two-dimensional simulated environments and show we are able to generate paths in feasible time and guarantee a minimum network rigidity over the full course of the paths.