Asynchronous and Parallel Distributed Pose Graph Optimization
Proposes ASAPP, an asynchronous distributed pose graph optimization algorithm, enhancing multi-robot SLAM robustness against communication delays.
Key Findings
Methodology
• Each robot maintains a local cache of its pose variables and receives asynchronous updates from neighbors. • Robots trigger local optimization steps based on Poisson clocks, independently computing Riemannian gradients of their local cost functions. • Gradient steps are performed via retraction on the manifold, ensuring updates stay within the feasible space. • The stepsize is carefully chosen based on maximum delay and problem sparsity, balancing convergence speed and stability. • Theoretical analysis employs Lyapunov functions and delay bounds to prove convergence to first-order critical points. • The algorithm accommodates rank-restricted relaxations, enabling near-global optimal solutions with reduced computational complexity. • Empirical validation confirms robustness against delays and noise, with theoretical bounds matching observed performance.
Significance
This work addresses a critical bottleneck in multi-robot SLAM—synchronization overhead—by enabling fully asynchronous pose graph optimization. It bridges the gap between theoretical convergence guarantees and practical robustness in communication-constrained environments. The proposed ASAPP algorithm enhances scalability, reduces latency sensitivity, and improves fault tolerance, making large-scale autonomous navigation feasible. It opens new avenues for deploying distributed SLAM in real-world applications like drone swarms, autonomous vehicles, and industrial robots, where communication delays are inevitable. The theoretical contributions also advance the understanding of non-convex Riemannian optimization under asynchronous settings, with potential impacts beyond SLAM.
Technical Contribution
The paper pioneers the integration of asynchronous stochastic coordinate descent with Riemannian pose graph optimization, providing the first convergence proof under bounded delay for non-convex problems on matrix manifolds. It introduces a delay-aware stepsize scheme that adapts to network latency and problem sparsity, ensuring stability and convergence. The method extends to rank-restricted relaxations, connecting local non-convex solutions with global optimality conditions. Theoretical analysis employs Lyapunov functions and delay-dependent bounds, establishing sublinear convergence rates. This work significantly broadens the scope of asynchronous algorithms in non-convex geometric optimization, offering practical algorithms with rigorous guarantees.
Novelty
This is the first work to develop an asynchronous distributed algorithm for pose graph optimization on Riemannian manifolds with theoretical convergence guarantees under bounded delays. Unlike prior synchronous methods, ASAPP operates without global synchronization, greatly enhancing scalability and robustness. It innovatively combines Poisson-driven asynchronous updates, rank relaxations, and delay-dependent convergence analysis, bridging the gap between theory and real-world multi-robot systems. This approach opens new research directions in asynchronous non-convex optimization in geometric settings, with broad implications for robotics and machine learning.
AI Executive Summary
Deep Dive
Plain Language Accessible to non-experts
想象你和朋友们在厨房里准备一顿大餐。传统的方法是大家必须等所有人都准备好后才能一起吃饭，这就像同步算法，等待所有人同步完成。而异步方法就像每个人可以自己先开始做菜，不用等待别人，等到菜都做好了再一起享用。这样不仅节省时间，还更灵活。即使有人做得慢一点，也不会影响整体进度。这个新方法让厨房合作变得更高效、更顺畅，特别适合多人同时合作的复杂任务，比如无人机飞行或自动驾驶汽车的导航。
ELI14 Explained like you're 14
你知道在学校里，大家一起做项目时，如果每个人都要等别人完成才能继续，就会很慢，对吧？这就像传统的同步算法，要等所有人都准备好才能开始下一步。而新方法就像每个人都可以自己先做自己的部分，不用等别人，等到所有人都完成后再一起检查。这样就快多了，也不用担心有人做得慢会拖大家。这个新点子让团队合作变得更灵活、更高效，特别适合很多人同时合作的复杂任务，比如无人机飞行或自动驾驶汽车的导航。
Abstract
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.