Generalized Proximal Methods for Pose Graph Optimization

Fan, Taosha; Murphey, Todd D.

doi:10.1007/978-3-030-95459-8_24

Cited by 6 publications

(16 citation statements)

References 13 publications

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“…The proposed solver performs distributed block-coordinate descent over the product of Riemannian manifolds, and provably converges to first-order critical points with global sublinear rate. In a separate line of research, Fan and Murphey [18] propose an accelerated PGO solver suitable for distributed optimization based on generalized proximal methods.…”

Section: A Distributed and Parallel Pgomentioning

confidence: 99%

Asynchronous and Parallel Distributed Pose Graph Optimization

Tian,

Koppel,

Bedi

et al. 2020

Preprint

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We present Asynchronous Stochastic Parallel Pose Graph Optimization (ASAPP), the first asynchronous algorithm for distributed pose graph optimization (PGO) in multirobot 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, the same algorithm can be used to solve the so-called rank-restricted semidefinite relaxations of PGO, a crucial class of non-convex Riemannian optimization problems at the center of recent PGO solvers with global optimality guarantees. Under bounded delay, we establish the global firstorder 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 delay is zero. Numerical evaluations on both simulated and real-world SLAM datasets demonstrate the speedup achieved with ASAPP and show the algorithm's resilience against a wide range of communication delays in practice. I. INTRODUCTIONMulti-robot simultaneous localization and mapping (SLAM) is a fundamental capability for many real-world robotic applications. Pose graph optimization (PGO) is the backbone of state of the art approaches to multirobot SLAM, which fuses individual trajectories together and endows participating robots with a common spatial understanding of the environment. Many approaches to multi-robot PGO require the centralized processing of observations at a base station, which is communication intensive and vulnerable to single point of failure. In contrast, decentralized approaches are favorable as they effectively mitigate communication, privacy, and vulnerability concerns associated with centralization.Recent works on distributed PGO have achieved important progress; see e.g., [1], [2] and the references therein. However, to the best of our knowledge, existing distributed algorithms are inherently synchronous, which necessitates that robots, for instance, pass messages over the network or wait at predetermined points, in order to ensure upto-date information sharing during distributed optimization. Doing so may incur considerable communication overhead and increase the complexity of implementation. On the other hand, simply dropping synchronization in the execution of Supported in part by ARL DCIST under Cooperative Agreement Number W911NF-17-2-0181 and by NASA Convergent Aeronautics Solutions project Design Environment for Novel Vertical Lift Vehicles (DELIVER).

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Section: A Distributed and Parallel Pgomentioning

confidence: 99%

Asynchronous and Parallel Distributed Pose Graph Optimization

Tian,

Koppel,

Bedi

et al. 2020

Preprint

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Section: Introductionmentioning

confidence: 96%

“…In this paper, we propose majorization minimization methods [15] to distributed PGO that extend our previous work [16], in which proximal methods to PGO are proposed that converge to first-order critical points for both centralized and distributed PGO. In [16], each pose is represented as a single node and updated independently. Even though proximal methods to PGO in [16] converge fast for centralized PGO and apply to any distributed PGO, it might have slow convergence for multi-robot SLAM, in which each robot usually has more than one poses and it is more reasonable to represent poses of the same robot rather than each individual pose as a node.…”

Section: Introductionmentioning

confidence: 96%

“…In [16], each pose is represented as a single node and updated independently. Even though proximal methods to PGO in [16] converge fast for centralized PGO and apply to any distributed PGO, it might have slow convergence for multi-robot SLAM, in which each robot usually has more than one poses and it is more reasonable to represent poses of the same robot rather than each individual pose as a node. In this paper, poses of the same robot are represented as the same node and are updated as a whole, which makes use of more information in optimization and is expected to converge faster than [16] for distributed PGO in multi-robot SLAM.…”

Section: Introductionmentioning

confidence: 99%

“…Even though proximal methods to PGO in [16] converge fast for centralized PGO and apply to any distributed PGO, it might have slow convergence for multi-robot SLAM, in which each robot usually has more than one poses and it is more reasonable to represent poses of the same robot rather than each individual pose as a node. In this paper, poses of the same robot are represented as the same node and are updated as a whole, which makes use of more information in optimization and is expected to converge faster than [16] for distributed PGO in multi-robot SLAM. Furthermore, we redesign the accelerated algorithm using Nesterov's method for distributed PGO such that the inefficient objective evaluation is avoided and the inter-node communication is significantly reduced.…”

Section: Introductionmentioning

confidence: 99%

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Majorization Minimization Methods for Distributed Pose Graph Optimization with Convergence Guarantees

Fan,

Murphey

2020

Preprint

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In this paper, we consider the problem of distributed pose graph optimization (PGO) that has extensive applications in multi-robot simultaneous localization and mapping (SLAM). We propose majorization minimization methods to distributed PGO and show that our proposed methods are guaranteed to converge to first-order critical points under mild conditions. Furthermore, since our proposed methods rely a proximal operator of distributed PGO, the convergence rate can be significantly accelerated with Nesterov's method, and more importantly, the acceleration induces no compromise of theoretical guarantees. In addition, we also present accelerated majorization minimization methods to the distributed chordal initialization that have a quadratic convergence, which can be used to compute an initial guess for distributed PGO. The efficacy of this work is validated through applications on a number of 2D and 3D SLAM datasets and comparisons with existing state-of-the-art methods, which indicates that our proposed methods have faster convergence and result in better solutions to distributed PGO.

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