Exactly sparse memory efficient SLAM using the multi-block alternating direction method of multipliers

Choudhary, Siddharth; Carlone, Luca; Christensen, Henrik I.; Dellaert, Frank

doi:10.1109/iros.2015.7353543

Cited by 16 publications

(14 citation statements)

References 26 publications

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“…ADMM has been applied to bundle adjustment and pose graph optimization problems which involve the recovery of the 3D positions and orientations of a map and camera [107], [108], [109], informative path planning [110]. However, these works require a central node for the dual variable updates.…”

Section: Applications Of C-admmmentioning

confidence: 99%

A Survey of Distributed Optimization Methods for Multi-Robot Systems

Halsted¹,

Shorinwa²,

Yu³

et al. 2021

Preprint

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Distributed optimization consists of multiple computation nodes working together to minimize a common objective function through local computation iterations and networkconstrained communication steps. In the context of robotics, distributed optimization algorithms can enable multi-robot systems to accomplish tasks in the absence of centralized coordination. We present a general framework for applying distributed optimization as a module in a robotics pipeline. We survey several classes of distributed optimization algorithms and assess their practical suitability for multi-robot applications. We further compare the performance of different classes of algorithms in simulations for three prototypical multi-robot problem scenarios. The Consensus Alternating Direction Method of Multipliers (C-ADMM) emerges as a particularly attractive and versatile distributed optimization method for multi-robot systems.

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Section: Applications Of C-admmmentioning

confidence: 99%

A Survey of Distributed Optimization Methods for Multi-Robot Systems

Halsted¹,

Shorinwa²,

Yu³

et al. 2021

Preprint

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“…A similar gradient-based method with line-search has also been proposed [15]. Choudhary et al [16] propose the alternating direction method of multipliers (ADMM) as a decentralized method to solve PGO. However, convergence of ADMM is not established due to the nonconvex nature of the optimization problem.…”

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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“…where g and h are defined in (5) and (4), respectively. Summing these two cost functions and imposing the common feature constraints yields:…”

Section: E Sub-map Relaxationmentioning

confidence: 99%

“…Additionally, and in order to reduce the processing requirements of the C-SKF -between linear and quadratic in the map's size -we introduce a consistent relaxation of the C-SKF, the sub-map (s)C-SKF, which trades localization accuracy for processing speed by operating on the Cholesky factors of the partitioned Hessians resulting from dividing the original map into independent sub-maps. Note that the sub-maps used throughout this work are generated from the method of [8], however, other methods that produce submaps (i.e., [5]) could be employed as well. This approximation allows mapping larger areas and/or operating on resourceconstrained mobile devices, such as cell phones and tablets.…”

Section: Introductionmentioning

confidence: 99%

Consistent map-based 3D localization on mobile devices

DuToit

Hesch

Nerurkar

et al. 2017

2017 IEEE International Conference on Robotics and Automation (ICRA)

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The objective of this paper is to provide consistent, real-time 3D localization capabilities to mobile devices navigating within previously mapped areas. To this end, we introduce the Cholesky-Schmidt-Kalman filter (C-SKF), which explicitly considers the uncertainty of the prior map, by employing the sparse Cholesky factor of the map's Hessian, instead of its dense covariance-as is the case for the Schmidt-Kalman filter (SKF). By doing so, the C-SKF has memory requirements typically linear in the size of the map, as opposed to quadratic for storing the map's covariance. Moreover, and in order to bound the processing needs of the C-SKF (between linear and quadratic in the size of the map), we introduce a relaxation of the C-SKF algorithm, the sC-SKF, which operates on the Cholesky factors of independent submaps resulting from dividing the trajectory and observations used for constructing the map into overlapping segments. Lastly, we assess the processing and memory requirements of the proposed C-SKF and sC-SKF algorithms, and compare their positioning accuracy against other approximate map-based localization approaches that employ measurement-noise-covariance inflation to compensate for the map's uncertainty.• We introduce the Cholesky-Schmidt-Kalman filter (C-SKF), which employs the Hessian's Cholesky factor to compactly represent the map's uncertainty, and efficiently compute consistent map-based updates.• We introduce the sub-map (s)C-SKF, a relaxation of the C-SKF, which employs multiple, independent sub-maps

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Exactly sparse memory efficient SLAM using the multi-block alternating direction method of multipliers

Cited by 16 publications

References 26 publications

A Survey of Distributed Optimization Methods for Multi-Robot Systems

A Survey of Distributed Optimization Methods for Multi-Robot Systems

Asynchronous and Parallel Distributed Pose Graph Optimization

Consistent map-based 3D localization on mobile devices

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