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Distance measurements demonstrate distinctive scalability when used forrelative state estimation in large-scale multi-robot systems. Despite theattractiveness of distance measurements, multi-robot relative state estimationbased on distance measurements raises a tricky optimization problem, especiallyin the context of large-scale systems. Motivated by this, we aim to developspecialized computational techniques that enable robust and efficientestimation when deploying distance measurements at scale. We first reveal thecommonality between the estimation problem and the one that finds realizationof a sensor network, from which we draw crucial lesson to inspire the proposedmethods. However, solving the latter problem in large-scale (still) requiresdistributed optimization schemes with scalability natures, efficientcomputational procedures, and fast convergence rates. Towards this goal, wepropose a complementary pair of distributed computational techniques with theclassical block coordinate descent (BCD) algorithm as a unified backbone. Inthe first method, we treat Burer-Monteiro factorization as a rank-restrictedheuristic for rank-constrained semidefinite programming (SDP), where aspecialized BCD-type algorithm that analytically solve each block updatesubproblem is employed. Although this method enables robust and (extremely)fast recovery of estimates from initial guesses, it inevitably fails as theinitialization becomes disorganized. We therefore propose the second method,derived from a convex formulation named anchored edge-based semidefiniteprogramming} (ESDP), to complement it, at the expense of a certain loss ofefficiency. This formulation is structurally decomposable so that BCD can benaturally employed, where each subproblem is convex and (again) solvedexactly...

Distributed Optimization in Sensor Network for Scalable Multi-Robot Relative State Estimation