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The Sierpinski tetrahedron has a remarkable property: It is projected to squares in three orthogonal directions, and moreover, to sets with positive Lebesgue measures in numerous directions. This paper proposes a method for characterizing…
This paper introduces the correlated arc orienteering problem (CAOP), where the task is to find routes for a team of robots to maximize the collection of rewards associated with features in the environment. These features can be…
Previous works have been devoted to the study of two-dimensional noninvertible maps, obtained using a coupling between one-dimensional logistic maps. This paper is devoted to the study of a specific one, in order to complete previous…
Can an infinite-strength magnetic beacon always ``catch'' an iron ball, when the beacon is a point required to be remain nonstrictly outside a polygon, and the ball is a point always moving instantaneously and maximally toward the beacon…
The closure constraint is a central piece of the mathematics of loop quantum gravity. It encodes the gauge invariance of the spin network states of quantum geometry and provides them with a geometrical interpretation: each decorated vertex…
Rotation equivariance has recently become a strongly desired property in the 3D deep learning community. Yet most existing methods focus on equivariance regarding a global input rotation while ignoring the fact that rotation symmetry has…
In this paper we deal with an extension of the crossing postman problem to design Hamiltonian routes that have to visit different shapes of dimensional elements (neighborhoods or polygonal chains) rather than edges. This problem models…
This work presents a 3D multi-robot exploration framework for a team of UGVs moving on uneven terrains. The framework was designed by casting the two-level coordination strategy presented in [1] into the context of multi-robot exploration.…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
A new generation of cold atom experiments trapping atomic mixtures in species selective optical potentials opens up the intriguing possibility to create systems in which different atoms live in different spatial dimensions. Inspired by…
Modern perception systems in the field of autonomous driving rely on 3D data analysis. LiDAR sensors are frequently used to acquire such data due to their increased resilience to different lighting conditions. Although rotating LiDAR…
Colander are location aware entities that collaborate to determine approximate location of mobile or static objects when beacons from an object are received by all colanders that are within its distance $R$. This model, referred to as…
Echo-location is a broad approach to imaging and sensing that includes both man-made RADAR, LIDAR, SONAR and also animal navigation. However, full 3D information based on echo-location requires some form of scanning of the scene in order to…
Higher-dimensional spaces are ubiquitous in applications of mathematics. Yet, as we live in a three-dimensional space, visualizing, say, a four-dimensional space is challenging. We introduce a novel method of interactive visualization of…
Experiment shows that dumbbells, placed inside a tilted hollow cylindrical drum that rotates slowly around its axis, climb uphill by forming dynamically stable pairs, seemingly against the pull of gravity. Analysis of this experiment shows…
Anticipating the motion of all humans in dynamic environments such as homes and offices is critical to enable safe and effective robot navigation. Such spaces remain challenging as humans do not follow strict rules of motion and there are…
Motion planning for aerial manipulators in constrained environments has typically been limited to known environments or simplified to that of multi-rotors, which leads to poor adaptability and overly conservative trajectories. This paper…
This paper investigates the problem of communication relay establishment for multiple agent-based mobile units using a relay vehicle. The objective is to drive autonomously the relay vehicle to attain a position for communication relay…
As a continuation of a previous paper (arXiv:2303.05769 [nlin.CD]), we introduce examples of H\'enon-type mappings that exhibit new horseshoe topologies in three and four dimensional spaces that are otherwise impossible in two dimensions.
While 3D object bounding box (bbox) representation has been widely used in autonomous driving perception, it lacks the ability to capture the precise details of an object's intrinsic geometry. Recently, occupancy has emerged as a promising…