Direct Relative Edge Optimization, A Robust Alternative for Pose Graph Optimization

Jackson, James S.; Brink, Kevin; Forsgren, Brendon; Wheeler, David O.; McLain, Timothy W.

doi:10.1109/lra.2019.2896478

Cited by 8 publications

(7 citation statements)

References 19 publications

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“…We exploit the fact that graphs in PGO (and other similar applications) are sparse, with positive (integer) weights, to design a tailored MCB algorithm that can greatly mitigate this issue, in particular for sparse graphs that are encountered in real SLAM/PGO applications. It can be shown that relative formulations have faster convergence compared with the vertex-based ones in the absolute frame (both in this work and the work in [20]). Therefore, for sparse graphs, based on the MCB, the cycle-based approach can attain faster (or comparable at least) computational time compared with the vertex-based ones, due to the reduced dimension in the cycle space and the sparsity forced by the MCB.…”

mentioning

confidence: 54%

“…Later, Bai et al [19] formulated PGO explicitly as a constrained optimization problem by using cycles in the graph. The cycle structure in graph optimization is typically presented as relative formulations [18], [19], which have been used in the work [17], [20], [24], [25], [56]- [60] as well.…”

Section: Related Workmentioning

confidence: 99%

“…A common issue in the relative parameterization is that it is not necessarily sparse [17]- [20]. It turns out this issue can be resolved by using a minimum cycle basis (MCB); however, the computation of an MCB itself is a hard problem.…”

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confidence: 99%

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Sparse Pose Graph Optimization in Cycle Space

2021

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The state-of-the-art modern pose-graph optimization (PGO) systems are vertex based. In this context, the number of variables might be high, albeit the number of cycles in the graph (loop closures) is relatively low. For sparse problems particularly, the cycle space has a significantly smaller dimension than the number of vertices. By exploiting this observation, in this article, we propose an alternative solution to PGO that directly exploits the cycle space. We characterize the topology of the graph as a cycle matrix, and reparameterize the problem using relative poses, which are further constrained by a cycle basis of the graph. We show that by using a minimum cycle basis, the cycle-based approach has superior convergence properties against its vertex-based counterpart, in terms of convergence speed and convergence to the global minimum. For sparse graphs, our cycle-based approach is also more time efficient than the vertex-based. As an additional contribution of this work, we present an effective algorithm to compute the minimum cycle basis. Albeit known in computer science, we believe that this algorithm is not familiar to the robotics community. All the claims are validated by experiments on both standard benchmarks and simulated datasets. To foster the reproduction of the results, we provide a complete open-source C++ implementation 1 of our approach. Index Terms-Minimum cycle basis, pose graph optimization (PGO), special Euclidean group (SE(3)), simultaneous localization and mapping (SLAM). I. INTRODUCTION P OSE graph optimization (PGO) is a fundamental problem, which arises in various research disciplines, such as simultaneous localization and mapping (SLAM) [1]-[5], structure from motion [6]-[8], calibration of multicamera rig [9], and sensor network localization [10], [11].A pose graph is a graph whose vertices encode positions and orientations of 3-D poses, and whose edges represent spatial constraints between the connected vertices. Taking a graph-based SLAM system as an example, the system processes the raw measurements to construct local maps. These local maps are Manuscript

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confidence: 54%

Section: Related Workmentioning

confidence: 99%

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Sparse Pose Graph Optimization in Cycle Space

2021

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“…To optimize the global pose graph, the least squares expression of the objective function, G(T), based on the error term is constructed, that is [34]:…”

Section: Pose Graph Optimizationmentioning

confidence: 99%

Research on Visual Positioning of a Roadheader and Construction of an Environment Map

et al. 2021

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The autonomous positioning of tunneling equipment is the key to intellectualization and robotization of a tunneling face. In this paper, a method based on simultaneous localization and mapping (SLAM) to estimate the body pose of a roadheader and build a navigation map of a roadway is presented. In terms of pose estimation, an RGB-D camera is used to collect images, and a pose calculation model of a roadheader is established based on random sample consensus (RANSAC) and iterative closest point (ICP); constructing a pose graph optimization model with closed-loop constraints. An iterative equation based on Levenberg–Marquadt is derived-, which can achieve the optimal estimation of the body pose. In terms of mapping, LiDAR is used to experimentally construct the grid map based on open-source algorithms, such as Gmapping, Cartographer, Karto, and Hector. A point cloud map, octree map, and compound map are experimentally constructed based on the open-source library RTAB-MAP. By setting parameters, such as the expansion radius of an obstacle and the updating frequency of the map, a cost map for the navigation of a roadheader is established. Combined with algorithms, such as Dijskra and timed-elastic-band, simulation experiments show that the combination of octree map and cost map can support global path planning and local obstacle avoidance.

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“…A common issue in the relative parameterization is that it is not necessarily sparse [17]- [20]. It turns out this issue can be resolved by using a minimum cycle basis (MCB); however the computation of a MCB itself is a hard problem.…”

Section: Introductionmentioning

confidence: 99%

Sparse Pose Graph Optimization in Cycle Space

Bai,

Vidal-Calleja,

Grisetti

2022

Preprint

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The state-of-the-art modern pose-graph optimization (PGO) systems are vertex based. In this context the number of variables might be high, albeit the number of cycles in the graph (loop closures) is relatively low. For sparse problems particularly, the cycle space has a significantly smaller dimension than the number of vertices. By exploiting this observation, in this paper we propose an alternative solution to PGO, that directly exploits the cycle space. We characterize the topology of the graph as a cycle matrix, and re-parameterize the problem using relative poses, which are further constrained by a cycle basis of the graph. We show that by using a minimum cycle basis, the cyclebased approach has superior convergence properties against its vertex-based counterpart, in terms of convergence speed and convergence to the global minimum. For sparse graphs, our cycle-based approach is also more time efficient than the vertexbased. As an additional contribution of this work we present an effective algorithm to compute the minimum cycle basis. Albeit known in computer science, we believe that this algorithm is not familiar to the robotics community. All the claims are validated by experiments on both standard benchmarks and simulated datasets. To foster the reproduction of the results, we provide a complete open-source C++ implementation 1 of our approach.

show abstract

Direct Relative Edge Optimization, A Robust Alternative for Pose Graph Optimization

Cited by 8 publications

References 19 publications

Sparse Pose Graph Optimization in Cycle Space

Sparse Pose Graph Optimization in Cycle Space

Research on Visual Positioning of a Roadheader and Construction of an Environment Map

Sparse Pose Graph Optimization in Cycle Space

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