A (7/2)-Approximation Algorithm for Guarding Orthogonal Art Galleries with Sliding Cameras

Consider a sliding camera that travels back and forth along an orthogonal line segment $s$ inside an orthogonal polygon $P$ with $n$ vertices. The camera can see a point $p$ inside $P$ if and only if there exists a line segment containing $p$ that crosses $s$ at a right angle and is completely contained in $P$. In the minimum sliding cameras (MSC) problem, the objective is to guard $P$ with the minimum number of sliding cameras. In this paper, we give an $O(n^{5/2})$-time $(7/2)$-approximation algorithm to the MSC problem on any simple orthogonal polygon with $n$ vertices, answering a question posed by Katz and Morgenstern (2011). To the best of our knowledge, this is the first constant-factor approximation algorithm for this problem.Comment: 11 page

Guaranteed Road Network Search with Small Unmanned Aircraft

The use of teams of small unmanned aircraft in real-world rapid-response missions is fast becoming a reality. One such application is search and detection of an evader in urban areas. This paper draws on results in graph-based pursuit-evasion, developing mappings from these abstractions to primitive motions that may be performed by aircraft, to produce search strategies providing guaranteed capture of road-bound targets. The first such strategy is applicable to evaders of arbitrary speed and agility, offering a conservative solution that is insensitive to motion constraints pursuers may possess. This is built upon to generate two strategies for capture of targets having a known speed bound that require searcher teams of much smaller size. The efficacy of these algorithms is demonstrated by evaluation in extensive simulation using realistic vehicle models across a spectrum of environment classes

Placement and motion planning algorithms for robotic sensing systems

University of Minnesota Ph.D. dissertation. October 2014. Major: Computer Science. Advisor: Prof. Ibrahim Volkan Isler. I computer file (PDF); xxiii, 226 pages.Recent technological advances are making it possible to build teams of sensors and robots that can sense data from hard-to-reach places at unprecedented spatio-temporal scales. Robotic sensing systems hold the potential to revolutionize a diverse collection of applications such as agriculture, environmental monitoring, climate studies, security and surveillance in the near future. In order to make full use of this technology, it is crucial to complement it with efficient algorithms that plan for the sensing in these systems. In this dissertation, we develop new sensor planning algorithms and present prototype robotic sensing systems.In the first part of this dissertation, we study two problems on placing stationary sensors to cover an environment. Our objective is to place the fewest number of sensors required to ensure that every point in the environment is covered. In the first problem, we say a point is covered if it is seen by sensors from all orientations. The environment is represented as a polygon and the sensors are modeled as omnidirectional cameras. Our formulation, which builds on the well-known art gallery problem, is motivated by practical applications such as visual inspection and video-conferencing where seeing objects from all sides is crucial. In the second problem, we study how to deploy bearing sensors in order to localize a target in the environment. The sensors measure noisy bearings towards the target which can be combined to localize the target. The uncertainty in localization is a function of the placement of the sensors relative to the target. For both problems we present (i) lower bounds on the number of sensors required for an optimal algorithm, and (ii) algorithms to place at most a constant times the optimal number of sensors. In the second part of this dissertation, we study motion planning problems for mobile sensors. We start by investigating how to plan the motion of a team of aerial robots tasked with tracking targets that are moving on the ground. We then study various coverage problems that arise in two environmental monitoring applications: using robotic boats to monitor radio-tagged invasive fish in lakes, and using ground and aerial robots for data collection in precision agriculture. We formulate the coverage problems based on constraints observed in practice. We also present the design of prototype robotic systems for these applications. In the final problem, we investigate how to optimize the low-level motion of the robots to minimize their energy consumption and extend the system lifetime.This dissertation makes progress towards building robotic sensing systems along two directions. We present algorithms with strong theoretical performance guarantees, often by proving that our algorithms are optimal or that their costs are at most a constant factor away from the optimal values. We also demonstrate the feasibility and applicability of our results through system implementation and with results from simulations and extensive field experiments

Single-crossing orthogonal axial lines in orthogonal rectangles

The axial map of a town is one of the key components of the space syntax method – a tool for analysing urban layout. It is derived by placing the longest and fewest lines, called axial lines, to cross the adjacencies between convex polygons in a convex map of a town. Previous research has shown that placing axial lines to cross the adjacencies between a collection of convex polygons is NP-complete, even when the convex polygons are restricted to rectangles and the axial lines to have orthogonal orientation. In this document, we show that placing orthogonal axial lines in orthogonal rectangles where the adjacencies between the rectangles are restricted to be crossed only once (ALPSC- OLOR) is NP-complete. As a result, we infer the single adjacency crossing version of the general axial line placement problem is NP-complete. The transformation of NPcompleteness of ALP-SC-OLOR is from vertex cover for biconnected planar graphs. A heuristic is then presented that gives a reasonable approximate solution to ALP-SC-OLOR based on a greedy method

AUTOMATED 3D CAMERA PLACEMENT

This project aims to find the minimum number of cameras needed to observe given three-dimensional (3D) environment and the cameras placement. This report traces the structure of the algorithm used to find the optimal number and placement of the cameras, the deployment of the algorithm in camera placement system, and presents the results of testing done on the system. This study related to the well known Art Gallery Problem (AGP) that addressed the problem of finding minimum number of guards necessary to guard the art gallery. Since this problem was posed, much research has been done on solving the problem from two dimensional (2D) perspectives. Not much research is done from 3D perspective and only recently more researchers are interested to study this problem in 3D environment.

Efficient, collision-free multi-robot navigation in an environment abstraction framework

Industrial automation deploys a continuously increasing amount of mobile robots in favor of classical linear conveyor systems for material flow handling in manufacturing and intralogistics. This increases flexibility by handling a larger variety of goods, improves scalability by adapting the fleet size to varying system loads, and enhances fault tolerance by avoiding single points of failure. However, it also raises the need for efficient, collision-free multi-robot navigation. This core problem is first precisely modeled in a form that differs from existing approaches specifically in terms of application relevance and structured algorithmic treatability. Collision-free trajectories for the mobile robots between given start and goal locations are sought so that the number of goals reached per time is as high as possible. Based on this, a decoupled solution called the Collaborative Local Planning Framework (CLPF), is designed and implemented, which, in contrast to existing solutions, aims at avoiding deadlocks with the greatest possible concurrency. Moreover, this solution includes the handling of dynamic inputs consisting of both moving and non-moving robots. For testing, performance analysis, and optimization, due to the complexity of multi-robot systems, the use of simulation is common. However, this also creates a gap between real and simulated robots. These issues can be reduced by using several different simulators---albeit with the disadvantage of further increasing complexity. For this purpose, the Robot Experimentation Framework (REF) is introduced to write robotic experiments with a unified interface that can be run on multiple simulators and also on real hardware. It facilitates the creation of experiments for performance assessment, (parameter) optimization and runtime analysis. The framework has proven its effectiveness throughout this thesis. Lastly, experimental proof of the viability of the solution is provided based on a case study of a complete (simulated) assembly system of decentralized autonomous agents for the production of highly individualized automobiles. This integrates all developed concepts into a holistic application of industrial automation. Detailed evaluations of more than 800 000 solved scenarios with more than 5 700 000 processed goals have experimentally proven the robustness and reliability of the developed concepts. Robots have never crashed into each other in any of the conducted experiments, empirically proving the claimed safety guarantees. A fault-tolerance analysis of the decentralized assembly system has experimentally proven its resilience to failures at workstations and, thus, specifically revealed an advantage over linear conveyor systems