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Accurate estimation of the environment structure simultaneously with the robot pose is a key capability of autonomous robotic vehicles. Classical simultaneous localization and mapping (SLAM) algorithms rely on the static world assumption to…

Robotics · Computer Science 2018-05-11 Mina Henein , Gerard Kennedy , Viorela Ila , Robert Mahony

The augmented Lagrangian method (ALM) is a benchmark for convex programming problems with linear constraints; ALM and its variants for linearly equality-constrained convex minimization models have been well studied in the literature.…

Optimization and Control · Mathematics 2022-06-22 Bingsheng He , Shengjie Xu , Jing Yuan

Simultaneous Localization and Mapping (SLAM) is pivotal in robotics, with photorealistic scene reconstruction emerging as a key challenge. To address this, we introduce Computational Alignment for Real-Time Gaussian Splatting SLAM (CaRtGS),…

Computer Vision and Pattern Recognition · Computer Science 2025-03-11 Dapeng Feng , Zhiqiang Chen , Yizhen Yin , Shipeng Zhong , Yuhua Qi , Hongbo Chen

Simultaneous Localization and Mapping (SLAM) algorithms perform visual-inertial estimation via filtering or batch optimization methods. Empirical evidence suggests that filtering algorithms are computationally faster, while optimization…

Systems and Control · Electrical Eng. & Systems 2022-08-05 Amay Saxena , Chih-Yuan Chiu , Joseph Menke , Ritika Shrivastava , Shankar Sastry

We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…

Optimization and Control · Mathematics 2023-06-21 Jong Gwang Kim

Based on the complete-lattice approach, a new Lagrangian duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions for the known scalar formulas involving infimum and supremum…

Optimization and Control · Mathematics 2024-01-26 Andreas H. Hamel , Andreas Löhne

This paper solves the classical problem of simultaneous localization and mapping (SLAM) in a fashion which avoids linearized approximations altogether. Based on creating virtual synthetic measurements, the algorithm uses a linear time-…

Robotics · Computer Science 2016-12-30 Feng Tan , Winfried Lohmiller , Jean-Jacques Slotine

Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…

Optimization and Control · Mathematics 2025-11-07 Venkat Chandrasekaran , Timothy Duff , Jose Israel Rodriguez , Kevin Shu

We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…

Theoretical Economics · Economics 2026-05-07 Chengfeng Shen , Felix Kübler , Yucheng Yang , Zhennan Zhou

Most recently, He and Yuan [arXiv:2108.08554, 2021] have proposed a balanced augmented Lagrangian method (ALM) for the canonical convex programming problem with linear constraints, which advances the original ALM by balancing its…

Optimization and Control · Mathematics 2021-12-30 Shengjie Xu

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,…

Robotics · Computer Science 2015-05-14 Giuseppe Calafiore , Luca Carlone , Frank Dellaert

3D Gaussian Splatting (3DGS) has shown promising results for 3D scene modeling using mixtures of Gaussians, yet its existing simultaneous localization and mapping (SLAM) variants typically rely on direct, deterministic pose optimization…

Computer Vision and Pattern Recognition · Computer Science 2026-04-06 Yuhan Zhu , Yanyu Zhang , Jie Xu , Wei Ren

This survey comprehensively reviews the evolving field of multi-robot collaborative Simultaneous Localization and Mapping (SLAM) using 3D Gaussian Splatting (3DGS). As an explicit scene representation, 3DGS has enabled unprecedented…

Robotics · Computer Science 2025-10-29 Phuc Nguyen Xuan , Thanh Nguyen Canh , Huu-Hung Nguyen , Nak Young Chong , Xiem HoangVan

Modern 3D laser-range scanners have a high data rate, making online simultaneous localization and mapping (SLAM) computationally challenging. Recursive state estimation techniques are efficient but commit to a state estimate immediately…

Robotics · Computer Science 2018-10-17 David Droeschel , Sven Behnke

The SLAM problem is known to have a special property that when robot orientation is known, estimating the history of robot poses and feature locations can be posed as a standard linear least squares problem. In this work, we develop a SLAM…

Robotics · Computer Science 2016-09-20 Saurav Agarwal , Vikram Shree , Suman Chakravorty

Building object-level maps can facilitate robot-environment interactions (e.g. planning and manipulation), but objects could often have multiple probable poses when viewed from a single vantage point, due to symmetry, occlusion or…

Robotics · Computer Science 2021-09-09 Ziqi Lu , Qiangqiang Huang , Kevin Doherty , John Leonard

A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…

Optimization and Control · Mathematics 2018-06-05 Chen Zhao , Ziyan Luo , Weiyue Li , Houduo Qi , Naihua Xiu

Deep visual Simultaneous Localization and Mapping (SLAM) techniques, e.g., DROID, have made significant advancements by leveraging deep visual odometry on dense flow fields. In general, they heavily rely on global visual similarity…

Computer Vision and Pattern Recognition · Computer Science 2024-10-31 Yucheng Huang , Luping Ji , Hudong Liu , Mao Ye

SLAM (Simultaneous Localization And Mapping) seeks to provide a moving agent with real-time self-localization. To achieve real-time speed, SLAM incrementally propagates position estimates. This makes SLAM fast but also makes it vulnerable…

Robotics · Computer Science 2020-09-24 Huajian Huang , Wen-Yan Lin , Siying Liu , Dong Zhang , Sai-Kit Yeung

Traditional SLAM algorithms are typically based on artificial features, which lack high-level information. By introducing semantic information, SLAM can own higher stability and robustness rather than purely hand-crafted features. However,…

Computer Vision and Pattern Recognition · Computer Science 2022-09-16 Xianwei Meng , Bonian Li