Related papers: From Constrained Delaunay Triangulations to Roadma…
Safe UAV navigation is challenging due to the complex environment structures, dynamic obstacles, and uncertainties from measurement noises and unpredictable moving obstacle behaviors. Although plenty of recent works achieve safe navigation…
Mobile robots frequently navigate on roadmaps, i.e., graphs where edges represent safe motions, in applications such as healthcare, hospitality, and warehouse automation. Often the environment is quasi-static, i.e., it is sufficient to…
Effective path planning is a pivotal challenge across various domains, from robotics to logistics and beyond. This research is centred on the development and evaluation of the Dynamic Curvature-Constrained Path Planning Algorithm (DCCPPA)…
Factor graph, as a bipartite graphical model, offers a structured representation by revealing local connections among graph nodes. This study explores the utilization of factor graphs in modeling the autonomous racecar planning problem,…
In this report, we try to improve the performance of existing approaches for search operations in multi-robot context. We propose three novel algorithms that are using a triangular grid pattern, i.e., robots certainly go through the…
The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
In this paper, we propose a new method for path planning to a point for robot in environment with obstacles. The resulting algorithm is implemented as a simple variation of Dijkstra's algorithm. By adding a constraint to the shortest-path,…
Path planning is a classic problem for autonomous robots. To ensure safe and efficient point-to-point navigation an appropriate algorithm should be chosen keeping the robot's dimensions and its classification in mind. Autonomous robots use…
Recent advancements in self-driving car technologies have enabled them to navigate autonomously through various environments. However, one of the critical challenges in autonomous vehicle operation is trajectory planning, especially in…
We study the computational complexity of the map redistricting problem (gerrymandering). Mathematically, the electoral district designer (gerrymanderer) attempts to partition a weighted graph into $k$ connected components (districts) such…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
This paper describes a revision of the classic Lazy Probabilistic Roadmaps algorithm (Lazy PRM), that results from pairing PRM and a novel Branch-and-Cut (BC) algorithm. Cuts are dynamically generated constraints that are imposed on minimum…
This paper proposes a fast and accurate trajectory planning algorithm for autonomous parking. Nominally, an optimal control problem should be formulated to describe this scheme, but the dimensionality of the optimal control problem is…
In this paper, we present an innovative technique for the path planning of flying robots in a 3D environment in Rough Mereology terms. The main goal was to construct the algorithm that would generate the mereological potential fields in…
A roadmap for a semi-algebraic set $S$ is a curve which has a non-empty and connected intersection with all connected components of $S$. Hence, this kind of object, introduced by Canny, can be used to answer connectivity queries (with…
Path planning is a major problem in autonomous vehicles. In recent years, with the increase in applications of Unmanned Aerial Vehicles (UAVs), one of the main challenges is path planning, particularly in adversarial environments. In this…
This paper revives a four-decade-old problem concerning regularity theory for (continuous) constraint maps with free boundaries. Dividing the map into two parts, the distance part and the projected image to the constraint, one can prove…
Delaunay flip is an elegant, simple tool to convert a triangulation of a point set to its Delaunay triangulation. The technique has been researched extensively for full dimensional triangulations of point sets. However, an important case of…
In the constrained planarity setting, we ask whether a graph admits a planar drawing that additionally satisfies a given set of constraints. These constraints are often derived from very natural problems; prominent examples are Level…