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Exploration is a critical challenge in robotics, centered on understanding unknown environments. In this work, we focus on robots exploring structured indoor environments which are often predictable and composed of repeating patterns. Most…
By utilizing only depth information, the paper introduces a novel but efficient local planning approach that enhances not only computational efficiency but also planning performances for memoryless local planners. The sampling is first…
It is difficult to collect data on a large scale in a monocular depth estimation because the task requires the simultaneous acquisition of RGB images and depths. Data augmentation is thus important to this task. However, there has been…
We present a simple and efficient acceleration technique for an arbitrary method for computing the Euclidean projection of a point onto a convex polytope, defined as the convex hull of a finite number of points, in the case when the number…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
In this work, we present a novel iterative deep Ritz method (IDRM) for solving a general class of elliptic problems. It is inspired by the iterative procedure for minimizing the loss during the training of the neural network, but at each…
This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…
Depth sensing is a critical function for robotic tasks such as localization, mapping and obstacle detection. There has been a significant and growing interest in depth estimation from a single RGB image, due to the relatively low cost and…
Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional…
In this paper we will discuss two variants of an inexact feasible interior point algorithm for convex quadratic programming. We will consider two different neighbourhoods: a (small) one induced by the use of the Euclidean norm which yields…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
In robotic applications, a key requirement for safe and efficient motion planning is the ability to map obstacle-free space in unknown, cluttered 3D environments. However, commodity-grade RGB-D cameras commonly used for sensing fail to…
In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This…
Minimizing a convex risk function is the main step in many basic learning algorithms. We study protocols for convex optimization which provably leak very little about the individual data points that constitute the loss function.…
We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding…
In this work, we present a method for a probabilistic fusion of external depth and onboard proximity data to form a volumetric 3-D map of a robot's environment. We extend the Octomap framework to update a representation of the area around…
Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…
Using gradient descent (GD) with fixed or decaying step-size is a standard practice in unconstrained optimization problems. However, when the loss function is only locally convex, such a step-size schedule artificially slows GD down as it…
Region extraction is necessary in a wide range of applications, from object detection in autonomous driving to analysis of subcellular morphology in cell biology. There exist two main approaches: convex hull extraction, for which exact and…