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Pose graph optimization (PGO) 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…
In this paper, we first study the projections onto the set of unit dual quaternions, and the set of dual quaternion vectors with unit norms. Then we propose a power method for computing the dominant eigenvalue of a dual quaternion Hermitian…
It is common in pose graph optimization (PGO) algorithms to assume that noise in the translations and rotations of relative pose measurements is uncorrelated. However, existing work shows that in practice these measurements can be highly…
This paper discusses a class of two-block smooth large-scale optimization problems with both linear equality and linear inequality constraints, which have a wide range of applications, such as economic power dispatch, data mining, signal…
The hand-eye calibration problem is an important application problem in robot research. Based on the 2-norm of dual quaternion vectors, we propose a new dual quaternion optimization method for the hand-eye calibration problem. The dual…
Pose Graph Optimization (PGO) is the problem of estimating a set of poses from pairwise relative measurements. PGO is a nonconvex problem, and currently no known technique can guarantee the computation of an optimal solution. In this paper,…
Several common dual quaternion functions, such as the power function, the magnitude function, the $2$-norm function and the $k$th largest eigenvalue of a dual quaternion Hermitian matrix, are standard dual quaternion functions, i.e., the…
The objective of pose SLAM or pose-graph optimization (PGO) is to estimate the trajectory of a robot given odometric and loop closing constraints. State-of-the-art iterative approaches typically involve the linearization of a non-convex…
Pose graph optimization (PGO) is fundamental to robot perception and navigation systems, serving as the mathematical backbone for solving simultaneous localization and mapping (SLAM). Existing solvers suffer from polynomial growth in…
This paper introduces an efficient algorithm for computing the best approximation of a given matrix onto the intersection of linear equalities, inequalities and the doubly nonnegative cone (the cone of all positive semidefinite matrices…
Decentralized multi-robot LiDAR-SLAM is essential for collaborative missions but faces significant challenges in maintaining global consistency. Existing frameworks predominantly rely on local-search optimization or one-time coordinate…
Autonomous navigation requires an accurate model or map of the environment. While dramatic progress in the prior two decades has enabled large-scale SLAM, the majority of existing methods rely on non-linear optimization techniques to find…
Global registration is a fundamental task that estimates the relative pose between two viewpoints of 3D point clouds. However, there are two issues that degrade the performance of global registration in LiDAR SLAM: one is the sparsity issue…
This paper introduces a Moment-Quaternion-Sum-of-Squares (QSOS) hierarchy for solving a class of quaternion polynomial optimization problems. This hierarchy is formulated directly in the quaternion domain and consists of a sequence of…
Visual SLAM has regained attention due to its ability to provide perceptual capabilities and simulation test data for Embodied AI. However, traditional SLAM methods struggle to meet the demands of high-quality scene reconstruction, and…
This paper presents the first certifiably correct algorithm for distributed pose-graph optimization (PGO), the backbone of modern collaborative simultaneous localization and mapping (CSLAM) and camera network localization (CNL) systems. Our…
Graph matching, typically formulated as a Quadratic Assignment Problem (QAP), seeks to establish node correspondences between two graphs. To address the NP-hardness of QAP, some existing methods adopt projection-based relaxations that embed…
As a new color image representation tool, quaternion has achieved excellent results in color image processing problems. In this paper, we propose a novel low-rank quaternion matrix completion algorithm to recover missing data of color…
The back-end module of Distributed Collaborative Simultaneous Localization and Mapping (DCSLAM) requires solving a nonlinear Pose Graph Optimization (PGO) under a distributed setting, also known as SE(d)-synchronization. Most existing…
"Classical" First Order (FO) algorithms of convex optimization, such as Mirror Descent algorithm or Nesterov's optimal algorithm of smooth convex optimization, are well known to have optimal (theoretical) complexity estimates which do not…