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Non-convex Pose Graph Optimization in SLAM via Proximal Linearized Riemannian ADMM

Author

Listed:
  • Xin Chen

    (Beihang University)

  • Chunfeng Cui

    (Beihang University)

  • Deren Han

    (Beihang University)

  • Liqun Qi

    (The Hong Kong Polytechnic University)

Abstract

Pose graph optimization is a well-known technique for solving the pose-based simultaneous localization and mapping (SLAM) problem. In this paper, we represent the rotation and translation by a unit quaternion and a three-dimensional vector, and propose a new model based on the von Mises-Fisher distribution. The constraints derived from the unit quaternions are spherical manifolds, and the projection onto the constraints can be calculated by normalization. Then a proximal linearized Riemannian alternating direction method of multipliers, denoted by PieADMM, is developed to solve the proposed model, which not only has low memory requirements, but also can update the poses in parallel. Furthermore, we establish the sublinear iteration complexity of PieADMM for finding the stationary point of our model. The efficiency of our proposed algorithm is demonstrated by numerical experiments on two synthetic and four 3D SLAM benchmark datasets.

Suggested Citation

  • Xin Chen & Chunfeng Cui & Deren Han & Liqun Qi, 2025. "Non-convex Pose Graph Optimization in SLAM via Proximal Linearized Riemannian ADMM," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-43, September.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:3:d:10.1007_s10957-025-02759-5
    DOI: 10.1007/s10957-025-02759-5
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    References listed on IDEAS

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    1. Xingju Cai & Deren Han & Xiaoming Yuan, 2017. "On the convergence of the direct extension of ADMM for three-block separable convex minimization models with one strongly convex function," Computational Optimization and Applications, Springer, vol. 66(1), pages 39-73, January.
    2. Suvrit Sra, 2012. "A short note on parameter approximation for von Mises-Fisher distributions: and a fast implementation of I s (x)," Computational Statistics, Springer, vol. 27(1), pages 177-190, March.
    3. Zhongming Chen & Chen Ling & Liqun Qi & Hong Yan, 2024. "A Regularization-Patching Dual Quaternion Optimization Method for Solving the Hand-Eye Calibration Problem," Journal of Optimization Theory and Applications, Springer, vol. 200(3), pages 1193-1215, March.
    4. Ying Cui & Xudong Li & Defeng Sun & Kim-Chuan Toh, 2016. "On the Convergence Properties of a Majorized Alternating Direction Method of Multipliers for Linearly Constrained Convex Optimization Problems with Coupled Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1013-1041, June.
    5. Kurt Hornik & Bettina Grün, 2014. "On maximum likelihood estimation of the concentration parameter of von Mises–Fisher distributions," Computational Statistics, Springer, vol. 29(5), pages 945-957, October.
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