  An optimization problem is at the heart of many robotics estimating,
planning, and optimum control problems. Several attempts have been made at
model-based multi-robot localization, and few have formulated the multi-robot
collaborative localization problem as a factor graph problem to solve through
graph optimization. Here, the optimization objective is to minimize the errors
of estimating the relative location estimates in a distributed manner. Our
novel graph-theoretic approach to solving this problem consists of three major
components; (connectivity) graph formation, expansion through transition model,
and optimization of relative poses. First, we estimate the relative
pose-connectivity graph using the received signal strength between the
connected robots, indicating relative ranges between them. Then, we apply a
motion model to formulate graph expansion and optimize them using g$^2$o graph
optimization as a distributed solver over dynamic networks. Finally, we
theoretically analyze the algorithm and numerically validate its optimality and
performance through extensive simulations. The results demonstrate the
practicality of the proposed solution compared to a state-of-the-art algorithm
for collaborative localization in multi-robot systems.
