Related papers: Does a robot path have clearance c?
We devise a data structure that can answer shortest path queries for two query points in a polygonal domain $P$ on $n$ vertices. For any $\varepsilon > 0$, the space complexity of the data structure is $O(n^{10+\varepsilon })$ and queries…
We consider the problem of finding minimum-link rectilinear paths in rectilinear polygonal domains in the plane. A path or a polygon is rectilinear if all its edges are axis-parallel. Given a set $\mathcal{P}$ of $h$ pairwise-disjoint…
This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be…
A constant-workspace algorithm has read-only access to an input array and may use only O(1) additional words of $O(\log n)$ bits, where $n$ is the size of the input. We assume that a simple $n$-gon is given by the ordered sequence of its…
The polygon retrieval problem on points is the problem of preprocessing a set of $n$ points on the plane, so that given a polygon query, the subset of points lying inside it can be reported efficiently. It is of great interest in areas such…
Motion planning seeks a collision-free path in a configuration space (C-space), representing all possible robot configurations in the environment. As it is challenging to construct a C-space explicitly for a high-dimensional robot, we…
Given a rectilinear domain $\mathcal{P}$ of $h$ pairwise-disjoint rectilinear obstacles with a total of $n$ vertices in the plane, we study the problem of computing bicriteria rectilinear shortest paths between two points $s$ and $t$ in…
Given a simple polygon $P$ consisting of $n$ vertices, we study the problem of designing space-efficient algorithms for computing (i) the visibility polygon of a point inside $P$, (ii) the weak visibility polygon of a line segment inside…
With the incremental development of robotic platforms to automate the manual processes, path planning has become a critical domain with or without the knowledge of the indoor and outdoor environment. The algorithms can be intelligent or…
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…
In this work, we present a workspace-based planning framework, which though using redundant workspace key-points to represent robot states, can take advantage of the interpretable geometric information to derive good quality collision-free…
Let $s$ be a point in a polygonal domain $\mathcal{P}$ of $h-1$ holes and $n$ vertices. We consider a quickest visibility query problem. Given a query point $q$ in $\mathcal{P}$, the goal is to find a shortest path in $\mathcal{P}$ to move…
The protection of pathways holds immense significance across various domains, including urban planning, transportation, surveillance, and security. This article introduces a groundbreaking approach to safeguarding pathways by employing…
The shortest secure path (routing) problem in communication networks has to deal with multiple attack layers e.g., man-in-the-middle, eavesdropping, packet injection, packet insertion, etc. Consider different probabilities for each such…
The determination of time-dependent collision-free shortest paths has received a fair amount of attention. Here, we study the problem of computing a time-dependent shortest path among growing discs which has been previously studied for the…
We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path.…
The determination of collision-free shortest paths among growing discs has previously been studied for discs with fixed growing rates. Here, we study a more general case of this problem, where: (1) the speeds at which the discs are growing…
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…
We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle…
We deal with the problem of planning collision-free trajectories for robots operating in a shared space. Given the start and destination position for each of the robots, the task is to find trajectories for all robots that reach their…