Related papers: Lagrangian Duality in 3D SLAM: Verification Techni…
An efficient hardware implementation for Simultaneous Localization and Mapping (SLAM) methods is of necessity for mobile autonomous robots with limited computational resources. In this paper, we propose a resource-efficient FPGA…
In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of…
We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…
Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…
Dynamic SLAM methods jointly estimate for the static and dynamic scene components, however existing approaches, while accurate, are computationally expensive and unsuitable for online applications. In this work, we present the first…
We propose to solve large instances of the non-convex optimization problems reformulated with canonical duality theory. To this aim we propose an interior point potential reduction algorithm based on the solution of the primal-dual total…
Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the…
Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
In this paper, we will demonstrate how Manhattan structure can be exploited to transform the Simultaneous Localization and Mapping (SLAM) problem, which is typically solved by a nonlinear optimization over feature positions, into a model…
The reliability of Simultaneous Localization and Mapping (SLAM) is severely constrained in environments where visual inputs suffer from noise and low illumination. Although recent 3D Gaussian Splatting (3DGS) based SLAM frameworks achieve…
Simultaneous Localization and Mapping (SLAM) in large-scale, unknown, and complex subterranean environments is a challenging problem. Sensors must operate in off-nominal conditions; uneven and slippery terrains make wheel odometry…
Simultaneous Localization and Mapping (SLAM) with 3D Gaussian Splatting (3DGS) enables fast, differentiable rendering and high-fidelity reconstruction across diverse real-world scenes. However, existing 3DGS-SLAM approaches handle…
Dense simultaneous localization and mapping (SLAM) is crucial for robotics and augmented reality applications. However, current methods are often hampered by the non-volumetric or implicit way they represent a scene. This work introduces…
Data association in SLAM is fundamentally challenging, and handling ambiguity well is crucial to achieve robust operation in real-world environments. When ambiguous measurements arise, conservatism often mandates that the measurement is…
Simultaneous Localization and Mapping (SLAM) presents a formidable challenge in robotics, involving the dynamic construction of a map while concurrently determining the precise location of the robotic agent within an unfamiliar environment.…
This paper proposes a new algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently…
Recent advancements in data science have significantly elevated the importance of orthogonally constrained optimization problems. The Riemannian approach has become a popular technique for addressing these problems due to the advantageous…
Dual decomposition, and more generally Lagrangian relaxation, is a classical method for combinatorial optimization; it has recently been applied to several inference problems in natural language processing (NLP). This tutorial gives an…
We present a novel Simultaneous Localization and Mapping (SLAM) method that employs Gaussian Process (GP) based landmark (object) representations. Instead of conventional grid maps or point cloud registration, we model the environment on a…