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.

翻译：我们提出了异步随机并行位姿图优化算法（ASAPP），这是首个用于多机器人同步定位与地图构建中分布式位姿图优化（PGO）的异步算法。通过使机器人能够无需同步即可优化其局部轨迹估计，ASAPP具备应对通信延迟的韧性，并消除了等待网络中掉队节点的需求。此外，ASAPP可应用于PGO的秩限制松弛问题——这是一类关键的非凸黎曼优化问题，近年来全球最优PGO的突破性成果正是基于此。在有限延迟条件下，我们采用足够小的步长证明了ASAPP的全局一阶收敛性。导出的步长取决于最坏情况延迟和固有问题稀疏性，且当不存在延迟时与同步算法的已知结果一致。在仿真与真实数据集上的数值评估表明，该方法相较于最先进的同步方法具有优越性能，并展现了ASAPP在实践中对广泛延迟的鲁棒性。