Related papers: Optimal Any-Angle Pathfinding on a Sphere
For high level path planning, environments are usually modeled as distance graphs, and path planning problems are reduced to computing the shortest path in distance graphs. One major drawback of this modeling is the inability to model…
In this work, we introduce SPADE, a path planning framework designed for autonomous navigation in dynamic environments using 3D scene graphs. SPADE combines hierarchical path planning with local geometric awareness to enable collision-free…
Path planning for wheeled mobile robots is a critical component in the field of automation and intelligent transportation systems. Car-like vehicles, which have non-holonomic constraints on their movement capability impose additional…
The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…
Let $V$ be a set of $n$ points in the plane. The unit-disk graph $G = (V, E)$ has vertex set $V$ and an edge $e_{uv} \in E$ between vertices $u, v \in V$ if the Euclidean distance between $u$ and $v$ is at most 1. The weight of each edge…
We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m…
Sphere fitting is a common problem in almost all science and engineering disciplines. Most of methods available are iterative in behavior. This involves fitting of the parameters in a least square sense or in a geometric sense. Here we…
Construction of the precise shape of an asteroid is critical for spacecraft operations as the gravitational potential is determined by spatial mass distribution. The typical approach to shape determination requires a prolonged mapping phase…
Let $s$ be a source point and $t$ be a destination point inside an $n$-vertex simple polygon $P$. Euclidean shortest paths and minimum-link paths between $s$ and $t$ inside $P$ have been well studied. Both these kinds of paths are simple…
This paper presents a novel and feasible path planning technique for a group of unmanned aerial vehicles (UAVs) conducting surface inspection of infrastructure. The ultimate goal is to minimise the travel distance of UAVs while…
Images conveniently capture the result of physical processes, representing rich source of information for data driven medicine, engineering, and science. The modeling of an image as a graph allows the application of graph-based algorithms…
Efficient comparison of spherical probability distributions becomes important in fields such as computer vision, geosciences, and medicine. Sliced optimal transport distances, such as spherical and stereographic spherical sliced Wasserstein…
In a seminal STOC'95 paper, titled "Euclidean spanners: short, thin and lanky", Arya et al. devised a construction of Euclidean $(1+\eps)$-spanners that achieves constant degree, diameter $O(\log n)$, and weight $O(\log^2 n) \cdot…
In this paper, we present a new algorithm that extends RRT* and RT-RRT* for online path planning in complex, dynamic environments. Sampling-based approaches often perform poorly in environments with narrow passages, a feature common to many…
Primal and dual algorithms are developed for solving the $n$-dimensional convex optimization problem of finding the Euclidean ball of minimum radius that covers $m$ given Euclidean balls, each with a given center and radius. Each algorithm…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
We propose a novel method for determining the radius of a spherical surface based on the distances measured between points on this surface. We consider the most general case of determining the radius when the distances are measured with…
In this paper, we present the geodesic-like algorithm for the computation of the shortest path between two objects on NURBS surfaces and periodic surfaces. This method can improve the distance problem not only on surfaces but in…
Navigation is one of the most widely used applications of the Location Based Services (LBS) which have become part of our digitally informed daily lives. Navigation services, however, have generally been designed for drivers rather than…
We give sufficient conditions on initial and target measures supported on the sphere $\S^n$ to ensure the solution to the optimal transport problem with the cost $|x-y|^2/2$ is a diffeomorphism.