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.

中文翻译：

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异步并行分布式姿态图优化

我们提出了异步随机并行姿态图优化 (ASAPP)，这是第一个用于多机器人同时定位和映射中的分布式姿态图优化 (PGO) 的异步算法。通过使机器人能够在不同步的情况下优化其本地轨迹估计，ASAPP 提供了针对通信延迟的弹性，并减少了等待网络中落后者的需要。此外，ASAPP 可以应用于 PGO 的秩限制松弛，这是一类关键的非凸黎曼优化问题，是最近在全局最优 PGO 上取得突破的基础。在有界延迟下，我们使用足够小的步长建立 ASAPP 的全局一阶收敛。导出的步长取决于最坏情况延迟和固有问题稀疏性，并且在没有延迟时匹配同步算法的已知结果。与最先进的同步方法相比，模拟和现实世界数据集的数值评估显示出良好的性能，并显示了 ASAPP 在实践中对广泛延迟的弹性。