Linear SLAM: Linearising the SLAM problems using submap joining

Zhao, Liang; Huang, Shoudong; Dissanayake, Gamini

doi:10.1016/j.automatica.2018.10.037

Cited by 13 publications

(8 citation statements)

References 41 publications

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“…The second mode addresses area coverage with uncertainty using an SQP method. In order to improve computational efficiency in both of these modes, Linear SLAM [16] is applied. Finally, simulations and experiments with an aerial robot are presented to verify the running-time efficiency of this framework.…”

Section: Introductionmentioning

confidence: 99%

Active SLAM for Mobile Robots With Area Coverage and Obstacle Avoidance

Chen

Huang

Fitch

2020

IEEE/ASME Trans. Mechatron.

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We present an active simultaneous localization and mapping (SLAM) framework for a mobile robot to obtain a collision-free trajectory with good performance in SLAM uncertainty reduction and in an area coverage task. Based on a model predictive control (MPC) framework, these two tasks are solved by the introduction of a control switching mechanism. For SLAM uncertainty reduction, graph topology is used to approximate the original problem as a constrained non-linear least-squares problem. A convex half-space representation is applied to relax non-convex spatial constraints that represent obstacle avoidance. Using convex relaxation, the problem is solved by a convex optimization method and a rounding procedure based on singular value decomposition (SVD). The area coverage task is addressed with a sequential quadratic programming (SQP) method. A submap joining approach, called Linear SLAM, is used to address the associated challenges of avoiding local minima, minimizing control switching, and potentially high computational cost. Finally, various simulations and experiments using an aerial robot are presented that verify the effectiveness of the proposed method, showing that our method produces a more accurate SLAM result and is more computationally efficient compared with multiple existing methods.

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Section: Introductionmentioning

confidence: 99%

Active SLAM for Mobile Robots With Area Coverage and Obstacle Avoidance

Chen

Huang

Fitch

2020

IEEE/ASME Trans. Mechatron.

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“…The basic idea is to divide the full PGO into several submaps (i.e., subgraphs), solve each one of them, and then join the submaps together to obtain an approximation to the full PGO. Zhao et al [35], [36] investigated the special case of joining two submaps, with a clever parameterization, which can be solved by a linear least squares, followed by a nonlinear transformation. For 2-D cases, Carlone et al [37] suggested a linear approximation framework to PGO, by computing first an orientation estimation, and then the position part using the given orientation.…”

Section: Related Workmentioning

confidence: 99%

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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“…For 3D feature-based SLAM, a simulated dataset is used with a trajectory of 870 poses and uniformly distributed features in the environment as used in [26]. Both Full-NLLS in (9) and the proposed Pose-Only algorithm (for 3D scenario) are performed.…”

Section: B 3d Feature-based Slammentioning

confidence: 99%

Feature-Based SLAM: Why Simultaneous Localisation and Mapping?

Zhao¹,

Mao²,

Huang³

2021

Robotics: Science and Systems XVII

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In this paper, we first prove an interesting result for point feature based SLAM. "When the covariance matrices of feature observation errors are isotropic, the robot poses and feature positions obtained in each Gauss-Newton iteration (when solving a reformulated least squares optimisation based SLAM) are independent of the feature positions in the previous step". That is, even if we reset the feature positions to different random values before each iteration, the results after the iteration never change. Building on this finding, we propose an algorithm to solve the robot poses only ("localisation") and show that the algorithm generates exactly the same robot poses in each iteration as the Gauss-Newton method (SLAM). The optimal feature positions can be easily recovered using a closed-form formula after the optimal robot poses are obtained.Similarly, when the covariance matrices of odometry translation errors are also isotropic, we can prove that the SLAM results are independent of both the feature positions and the robot positions. Thus, we can have an "rotation-only algorithm" which generates the same robot rotations as the full SLAM. Again, the optimal robot positions and the optimal feature positions can be computed from the obtained optimal robot rotations using a closed-form formula. We have used multiple 2D and 3D SLAM datasets to demonstrate our research findings. The video shows the interesting convergence results can be found at https://youtu.be/j1T8toqGtDE. We expect the findings in this paper can help SLAM researchers to further understand the special structure of the SLAM problems and to further develop more efficient and reliable SLAM algorithms.

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Linear SLAM: Linearising the SLAM problems using submap joining

Cited by 13 publications

References 41 publications

Active SLAM for Mobile Robots With Area Coverage and Obstacle Avoidance

Active SLAM for Mobile Robots With Area Coverage and Obstacle Avoidance

Sparse Pose Graph Optimization in Cycle Space

Feature-Based SLAM: Why Simultaneous Localisation and Mapping?

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