| Summary: | © 2016 IEEE. We present Asynchronous Stochastic Parallel Pose Graph Optimization ($\textsc {ASAPP}$), the first asynchronous algorithm for distributed pose graph optimization (PGO) in multi-robot simultaneous localization and mapping. By enabling robots to optimize their local trajectory estimates without synchronization, $\textsc {ASAPP}$ offers resiliency against communication delays and alleviates the need to wait for stragglers in the network. Furthermore, $\textsc {ASAPP}$ can be applied on the rank-restricted relaxations of PGO, a crucial class of non-convex Riemannian optimization problems that underlies recent breakthroughs on globally optimal PGO. Under bounded delay, we establish the global first-order convergence of $\textsc {ASAPP}$ using a sufficiently small stepsize. The derived stepsize depends on the worst-case delay and inherent problem sparsity, and furthermore matches known result for synchronous algorithms when there is no delay. Numerical evaluations on simulated and real-world datasets demonstrate favorable performance compared to state-of-the-art synchronous approach, and show $\textsc {ASAPP}$'s resilience against a wide range of delays in practice.
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