Related papers: Coordinating the Motion of Labeled Discs with Opti…
Path planning in dynamic environments is essential to high-risk applications such as unmanned aerial vehicles, self-driving cars, and autonomous underwater vehicles. In this paper, we generate collision-free trajectories for a robot within…
Planning collision-free paths for multi-robot systems (MRS) is a challenging problem because of the safety and efficiency constraints required for real-world solutions. Even though coupled path planning approaches provide optimal…
We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach-- based on several approximations to predict the probability distribution…
Multi-robot systems have begun to permeate into a variety of different fields, but collision-free navigation in a decentralized manner is still an arduous task. Typically, the navigation of high speed multi-robot systems demands replanning…
Assume that two robots are located at the centre of a unit disk. Their goal is to evacuate from the disk through an exit at an unknown location on the boundary of the disk. At any time the robots can move anywhere they choose on the disk,…
Cuspidal robots are robots with at least two inverse kinematic solutions that can be connected by a singularity-free path. Deciding the cuspidality of generic 3R robots has been studied in the past, but extending the study to…
This paper studies an optimal control problem for a string of vehicles with safety requirements and finite-time specifications on the approach time to a target region. Our problem formulation is motivated by scenarios involving autonomous…
We present optimal motion planning algorithms which can be used in designing practical systems controlling objects moving in Euclidean space without collisions. Our algorithms are optimal in a very concrete sense, namely, they have the…
We study the problem of allocating many mobile robots for the execution of a pre-defined sweep schedule in a known two-dimensional environment, with applications toward search and rescue, coverage, surveillance, monitoring, pursuit-evasion,…
This paper studies a class of multi-robot coordination problems where a team of robots aim to reach their goal regions with minimum time and avoid collisions with obstacles and other robots. A novel numerical algorithm is proposed to…
We study active learning of homogeneous $s$-sparse halfspaces in $\mathbb{R}^d$ under the setting where the unlabeled data distribution is isotropic log-concave and each label is flipped with probability at most $\eta$ for a parameter $\eta…
In this work, we investigate how and to which extent a quantum system can be driven along a prescribed path in Hilbert space by a suitably shaped laser pulse. To calculate the optimal, i.e., the variationally best pulse, a properly defined…
Predicting theoretically the highest density, which a disordered packing of discs can achieve, has been a long-standing unresolved problem. Such predictions are hindered by two difficulties - the dependence of the density on the packing…
Location Routing is a fundamental planning problem in logistics, in which strategic location decisions on the placement of facilities (depots, distribution centers, warehouses etc.) are taken based on accurate estimates of operational…
Given a set of $n$ points in the plane, the Unit Disk Cover (UDC) problem asks to compute the minimum number of unit disks required to cover the points, along with a placement of the disks. The problem is NP-hard and several approximation…
We consider the problem of cooperative intersection management. It arises in automated transportation systems for people or goods but also in multi-robots environment. Therefore many solutions have been proposed to avoid collisions. The…
With the recent influx in demand for multi-robot systems throughout industry and academia, there is an increasing need for faster, robust, and generalizable path planning algorithms. Similarly, given the inherent connection between control…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
Coverage control has been widely used for constructing mobile sensor network such as for environmental monitoring, and one of the most commonly used methods is the Lloyd algorithm based on Voronoi partitions. However, when this method is…
Diversity maximization problem is a well-studied problem where the goal is to find $k$ diverse items. Fair diversity maximization aims to select a diverse subset of $k$ items from a large dataset, while requiring that each group of items be…