Related papers: Maze solving Algorithm for line following robot an…
Given an orthogonal polygon $ P $ with $ n $ vertices, the goal of the watchman route problem is finding a path $ S $ of the minimum length in $ P $ such that every point of the polygon $ P $ is visible from at least one of the point of $ S…
Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: Distance Geometry Problem is about finding a Euclidean realization of an incomplete set of distances in a Euclidean space, whereas Nonlinear…
Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…
Multi-mobile robot systems show great advantages over one single robot in many applications. However, the robots are required to form desired task-specified formations, making feasible motions decrease significantly. Thus, it is challenging…
The reachability problem for timed automata asks if there exists a path from an initial state to a target state. The standard solution to this problem involves computing the zone graph of the automaton, which in principle could be infinite.…
This paper uses the smoothing and mapping framework to solve the SLAM problem in indoor environments; focusing on how some key issues such as feature extraction and data association can be handled by applying probabilistic techniques. For…
We describe a line-search algorithm which achieves the best-known worst-case complexity results for problems with a certain "strict saddle" property that has been observed to hold in low-rank matrix optimization problems. Our algorithm is…
Efficient motion planning algorithms are of central importance for deploying robots in the real world. Unfortunately, these algorithms often drastically reduce the dimensionality of the problem for the sake of feasibility, thereby foregoing…
We design a deterministic algorithm that, given $n$ points in a \emph{typical} constant degree regular~graph, queries $O(n)$ distances to output a constant factor approximation to the average distance among those points, thus answering a…
The Dijkstra algorithm is a classic path planning method, which in a discrete graph space, can start from a specified source node and find the shortest path between the source node and all other nodes in the graph. However, to the best of…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
We present a decoupled algorithm for motion planning for a collection of unit-balls moving among polyhedral obstacles in $\mathbb{R}^d$, for any $d \ge 2$. We assume that the robots have revolving areas in the vicinity of their start and…
We demonstrate that a graph-based search algorithm-relying on the construction of an approximate neighborhood graph-can directly work with challenging non-metric and/or non-symmetric distances without resorting to metric-space mapping…
To operate reactively in uncertain environments, robots need to be able to quickly estimate the risk that they will collide with their environment. This ability is important for both planning (to ensure that plans maintain acceptable levels…
In this paper, we propose a distributed algorithm to solve planar minimum time multi-vehicle rendezvous problem with non-identical velocity constraints on cyclic digraph (topology). Motivated by the cyclic alternating projection method that…
In this paper, we develop a \textcolor{black}{\emph{distributed}} algorithm to localize a network of robots moving arbitrarily in a bounded region. In the case of such mobile networks, the main challenge is that the robots may not be able…
Robot positioning accuracy is a key factory when performing high-precision manufacturing tasks. To effectively improve the accuracy of a manipulator, often up to a value close to its repeatability, calibration plays a crucial role. In the…
This paper presents a methodology for finding numerically, by means of curve-following, all real solutions of a general system of $n$ nonlinear equations in $n$ unknowns, within a given $n$-dimensional box. The main idea behind our method…
We consider nonconvex obstacle avoidance where a robot described by nonlinear dynamics and a nonconvex shape has to avoid nonconvex obstacles. Obstacle avoidance is a fundamental problem in robotics and well studied in control. However,…
This paper poses a question about a simple localization problem. The question is if an {\em oblivious} walker on a line-segment can localize the middle point of the line-segment in {\em finite} steps observing the direction (i.e., Left or…