Related papers: Optimal Any-Angle Pathfinding on a Sphere
In this paper, motion planning for a vehicle moving on a unit sphere with unit speed is considered, wherein the desired terminal location is fixed, but the terminal orientation is free. The motion of the vehicle is modeled to be constrained…
The radius and diameter are fundamental graph parameters. They are defined as the minimum and maximum of the eccentricities in a graph, respectively, where the eccentricity of a vertex is the largest distance from the vertex to another…
Given a set of celestial bodies, the problem of finding an optimal sequence of swing-bys, deep space manoeuvres (DSM) and transfer arcs connecting the elements of the set is combinatorial in nature. The number of possible paths grows…
We study the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…
We study the reverse shortest path problem on disk graphs in the plane. In this problem we consider the proximity graph of a set of $n$ disks in the plane of arbitrary radii: In this graph two disks are connected if the distance between…
In environments with scarce resources, adopting the right search strategy can make the difference between succeeding and failing, even between life and death. At different scales, this applies to molecular encounters in the cell cytoplasm,…
We consider the rooted orienteering problem in Euclidean space: Given $n$ points $P$ in $\mathbb R^d$, a root point $s\in P$ and a budget $\mathcal B>0$, find a path that starts from $s$, has total length at most $\mathcal B$, and visits as…
We present a deterministic local routing algorithm that is guaranteed to find a path between any pair of vertices in a half-$\theta_6$-graph (the half-$\theta_6$-graph is equivalent to the Delaunay triangulation where the empty region is an…
In this paper, we propose to study a new geometric optimization problem called "geometric prototype" in Euclidean space. Given a set of patterns, where each pattern is represented by a (weighted or unweighted) point set, the geometric…
There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…
Given in the plane a set $S$ of $n$ points and a set of disks centered at these points, the disk graph $G(S)$ induced by these disks has vertex set $S$ and an edge between two vertices if their disks intersect. Note that the disks may have…
In this paper, we propose a general graph optimization based framework for localization, which can accommodate different types of measurements with varying measurement time intervals. Special emphasis will be on range-based localization.…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
Large environments are challenging for path planning algorithms as the size of the configuration space increases. Furthermore, if the environment is mainly unexplored, large amounts of the path are planned through unknown areas. Hence, a…
This paper presents a new algorithm named spherical vector-based particle swarm optimization (SPSO) to deal with the problem of path planning for unmanned aerial vehicles (UAVs) in complicated environments subjected to multiple threats. A…
LiDAR odometry plays an important role in self-localization and mapping for autonomous navigation, which is usually treated as a scan registration problem. Although having achieved promising performance on KITTI odometry benchmark, the…
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…
Path planning in the presence of dynamic obstacles is a challenging problem due to the added time dimension in search space. In approaches that ignore the time dimension and treat dynamic obstacles as static, frequent re-planning is…
Essential tasks in autonomous driving includes environment perception, detection and tracking, path planning and action control. This paper focus on path planning, which is one of the challenging task as it needs to find optimal path in…
The complexity of nearest-neighbor search dominates the asymptotic running time of many sampling-based motion-planning algorithms. However, collision detection is often considered to be the computational bottleneck in practice. Examining…