Related papers: Lagrangian Duality in 3D SLAM: Verification Techni…
SLAM (Simultaneous Localization and mapping) is one of the most challenging problems for mobile platforms and there is a huge amount of modern SLAM algorithms. The choice of the algorithm that might be used in every particular problem…
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…
Joint optimization of poses and features has been extensively studied and demonstrated to yield more accurate results in feature-based SLAM problems. However, research on jointly optimizing poses and non-feature-based maps remains limited.…
Simultaneous Localization and Mapping (SLAM) has wide robotic applications such as autonomous driving and unmanned aerial vehicles. Both computational efficiency and localization accuracy are of great importance towards a good SLAM system.…
Achieving real-time Simultaneous Localization and Mapping (SLAM) based on 3D Gaussian splatting (3DGS) in large-scale real-world environments remains challenging, as existing methods still struggle to jointly achieve low-latency pose…
In this paper, we propose an optimization based SLAM approach to simultaneously optimize the robot trajectory and the occupancy map using 2D laser scans (and odometry) information. The key novelty is that the robot poses and the occupancy…
Simultaneous localization and mapping (SLAM) is a foundational state estimation problem in robotics in which a robot accurately constructs a map of its environment while also localizing itself within this construction. We study the active…
We develop a methodology for closing duality gap and guaranteeing strong duality in infinite convex optimization. Specifically, we examine two new Lagrangian-type dual formulations involving infinitely many dual variables and infinite sums…
To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthonormalization procedure. However, such demand is…
Many algorithms in verification and automated reasoning leverage some form of duality between proofs and refutations or counterexamples. In most cases, duality is only used as an intuition that helps in understanding the algorithms and is…
In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…
Modern state estimation is often formulated as an optimization problem and solved using efficient local search methods. These methods at best guarantee convergence to local minima, but, in some cases, global optimality can also be…
Visual understanding of 3D environments in real-time, at low power, is a huge computational challenge. Often referred to as SLAM (Simultaneous Localisation and Mapping), it is central to applications spanning domestic and industrial…
The augmented Lagrangian method (ALM) is a classical optimization tool that solves a given "difficult" (constrained) problem via finding solutions of a sequence of "easier"(often unconstrained) sub-problems with respect to the original…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
Existence of symmetric objects, whose observation at different viewpoints can be identical, can deteriorate the performance of simultaneous localization and mapping(SLAM). This work proposes a system for robustly optimizing the pose of…
Simultaneous localization and mapping (SLAM) are essential in numerous robotics applications, such as autonomous navigation. Traditional SLAM approaches infer the metric state of the robot along with a metric map of the environment. While…
Traditional Simultaneous Localization and Mapping (SLAM) systems often face limitations including coarse rendering quality, insufficient recovery of scene details, and poor robustness in dynamic environments. 3D Gaussian Splatting (3DGS),…
SLAM is a fundamental component of modern autonomous systems, providing robots and their operators with a deeper understanding of their environment. SLAM systems often encounter challenges due to the dynamic nature of robotic motion,…
We analyze the convergence behaviour of a recently proposed algorithm for regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is based on a new interpretation of DAL as a proximal minimization algorithm. We…