Related papers: Towards Constructing Finer then Homotopy Path Clas…
Autonomous technology, which has become widespread today, appears in many different configurations such as mobile robots, manipulators, and drones. One of the most important tasks of these vehicles during autonomous operations is path…
Visual navigation is a core capability for mobile robots, yet end-to-end learning-based methods often struggle with generalization and safety in unseen, cluttered, or narrow environments. These limitations are especially pronounced in dense…
Modern navigation services often provide multiple paths connecting the same source and destination for users to select. Hence, ranking such paths becomes increasingly important, which directly affects the service quality. We present…
The scientific community is able to present a new set of solutions to practical problems that substantially improve the performance of modern technology in terms of efficiency and speed of computation due to the advancement in neural…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
In this paper we generalize the discrete r-homotopy to the discrete (s, r)-homotopy. Then by this notion, we introduce the discrete motion planning for robots which can move discreetly. Moreover, in this case the number of motion planning,…
With the increasing integration of robots into human life, their role in architectural spaces where people spend most of their time has become more prominent. While motion capabilities and accurate localization for automated robots have…
Task And Motion Planning (TAMP) is the problem of finding a solution to an automated planning problem that includes discrete actions executable by low-level continuous motions. This field is gaining increasing interest within the robotics…
In this paper, we propose a new mathematical optimization model for multiclass classification based on arrangements of hyperplanes. Our approach preserves the core support vector machine (SVM) paradigm of maximizing class separation while…
Binary classification is one of the most common problem in machine learning. It consists in predicting whether a given element belongs to a particular class. In this paper, a new algorithm for binary classification is proposed using a…
Place classification is a fundamental ability that a robot should possess to carry out effective human-robot interactions. It is a nontrivial classification problem which has attracted many research. In recent years, there is a high…
We introduce the notion of a "category with path objects", as a slight strengthening of Kenneth Brown's classic notion of a "category of fibrant objects". We develop the basic properties of such a category and its associated homotopy…
We consider the configuration formation problem in modular robotic systems where a set of singleton modules that are spatially distributed in an environment are required to assume appropriate positions so that they can configure into a new,…
We often wish to classify objects by their shapes. Indeed, the study of shapes is an important part of many scientific fields such as evolutionary biology, structural biology, image processing, and archaeology. The most widely-used method…
The Topological complexity a la Farber $\text{TC}(-)$ is a homotopy invariant which have interesting applications in Robotics, specifically, in the robot motion planning problem. In this work we calculate the topological complexity of the…
Path generation, the process of converting high-level mission specifications, such as sequences of waypoints from a path planner, into smooth, executable paths, is a fundamental challenge in mobile robotics. Most path following and…
Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…
Real-time motion planning is a vital function of robotic systems. Different from existing roadmap algorithms which first determine the free space and then determine the collision-free path, researchers recently proposed several convex…
Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and…
A topological hyperplane is a subspace of R^n (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R^n is a finite set H such that k topological…