Related papers: Optimizing Visibility-based Search in Polygonal Do…
We consider the watchman route problem for multiple watchmen in staircase polygons, which are rectilinear $x$- and $y$-monotone polygons. For two watchmen, we propose an algorithm to find an optimal solution that takes quadratic time,…
We consider the problem of searching for an intruder in a geometric domain by utilizing multiple search robots. The domain is a simply connected orthogonal polygon with edges parallel to the cartesian coordinate axes. Each robot has a…
The problem of search by multiple agents to find and localize objects arises in many important applications. In this paper, we study a class of multi-agent search problems in which each agent can access only a subset of a discrete search…
We investigate the problem of optimally observing a finite set of targets using a mobile agent over an infinite time horizon. The agent is tasked to move in a network-constrained structure to gather information so as to minimize the…
Autonomous agents face the challenge of coordinating multiple tasks (perception, motion planning, controller) which are computationally expensive on a single onboard computer. To utilize the onboard processing capacity optimally, it is…
With the advent of autonomous robots with two- and three-dimensional scanning capabilities, classical visibility-based exploration methods from computational geometry have gained in practical importance. However, real-life laser scanning of…
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…
We consider the problem of finding patrol schedules for $k$ robots to visit a given set of $n$ sites in a metric space. Each robot has the same maximum speed and the goal is to minimize the weighted maximum latency of any site, where the…
We study the query version of constrained minimum link paths between two points inside a simple polygon $P$ with $n$ vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning…
In this paper we consider the problem of computing the weak visibility polygon of any query line segment $pq$ (or $WVP(pq)$) inside a given polygon $P$. Our first non-trivial algorithm runs in simple polygons and needs $O(n^3 \log n)$ time…
This article considers two variants of a shortest path problem for a car-like robot visiting a set of waypoints. The sequence of waypoints to be visited is specified in the first variant while the robot is allowed to visit the waypoints in…
Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in…
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…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
We study the problem of persistent monitoring of a finite number of inter-connected geographical nodes by a group of heterogeneous mobile agents. We assign to each geographical node a concave and increasing reward function that resets to…
We devise a polynomial-time approximation scheme for the classical geometric problem of finding an approximate short path amid weighted regions. In this problem, a triangulated region P comprising of n vertices, a positive weight associated…
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…
Given a simple polygon $ \mathcal {P} $ of $ n $ vertices in the Plane. We study the problem of computing the visibility area from a given viewpoint $ q $ inside $ \mathcal {P} $ where only sub-linear variables are allowed for working…
The subject of this work is the patrolling of an environment with the aid of a team of autonomous agents. We consider both the design of open-loop trajectories with optimal properties, and of distributed control laws converging to optimal…
Inspired by the diverse set of technologies used in underground object detection and imaging, we introduce a novel multimodal linear search problem whereby a single searcher starts at the origin and must find a target that can only be…