  We present Asynchronous Stochastic Parallel Pose Graph Optimization (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, ASAPP offers
resiliency against communication delays and alleviates the need to wait for
stragglers in the network. Furthermore, 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
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 ASAPP's resilience against a
wide range of delays in practice.
