Meeting in a Polygon by Anonymous Oblivious Robots

The Meeting problem for $k\geq 2$ searchers in a polygon $P$ (possibly with holes) consists in making the searchers move within $P$, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of $P$, we minimize the number of searchers $k$ for which the Meeting problem is solvable. Specifically, if $P$ has a rotational symmetry of order $\sigma$ (where $\sigma=1$ corresponds to no rotational symmetry), we prove that $k=\sigma+1$ searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with $k=2$ searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look-Compute-Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations, and each searcher can geometrically construct its own destination point at each cycle using only a compass. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest.Comment: 37 pages, 9 figure

Positional Encoding by Robots with Non-Rigid Movements

Consider a set of autonomous computational entities, called \emph{robots}, operating inside a polygonal enclosure (possibly with holes), that have to perform some collaborative tasks. The boundary of the polygon obstructs both visibility and mobility of a robot. Since the polygon is initially unknown to the robots, the natural approach is to first explore and construct a map of the polygon. For this, the robots need an unlimited amount of persistent memory to store the snapshots taken from different points inside the polygon. However, it has been shown by Di Luna et al. [DISC 2017] that map construction can be done even by oblivious robots by employing a positional encoding strategy where a robot carefully positions itself inside the polygon to encode information in the binary representation of its distance from the closest polygon vertex. Of course, to execute this strategy, it is crucial for the robots to make accurate movements. In this paper, we address the question whether this technique can be implemented even when the movements of the robots are unpredictable in the sense that the robot can be stopped by the adversary during its movement before reaching its destination. However, there exists a constant $\delta > 0$, unknown to the robot, such that the robot can always reach its destination if it has to move by no more than $\delta$ amount. This model is known in literature as \emph{non-rigid} movement. We give a partial answer to the question in the affirmative by presenting a map construction algorithm for robots with non-rigid movement, but having $O(1)$ bits of persistent memory and ability to make circular moves

Meeting in a Polygon by Anonymous Oblivious Robots

The Meeting problem for k>=2 searchers in a polygon P (possibly with holes) consists in making the searchers move within P, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of P, we minimize the number of searchers k for which the Meeting problem is solvable. Specifically, if P has a rotational symmetry of order sigma (where sigma=1 corresponds to no rotational symmetry), we prove that k=sigma+1 searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with k=2 searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look-Compute-Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations (provided that the coordinates of the polygon\u27s vertices are algebraic real numbers in some global coordinate system), and each searcher can geometrically construct its own destination point at each cycle using only a compass. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest

Adaptive Path Planning for Depth Constrained Bathymetric Mapping with an Autonomous Surface Vessel

This paper describes the design, implementation and testing of a suite of algorithms to enable depth constrained autonomous bathymetric (underwater topography) mapping by an Autonomous Surface Vessel (ASV). Given a target depth and a bounding polygon, the ASV will find and follow the intersection of the bounding polygon and the depth contour as modeled online with a Gaussian Process (GP). This intersection, once mapped, will then be used as a boundary within which a path will be planned for coverage to build a map of the Bathymetry. Methods for sequential updates to GP's are described allowing online fitting, prediction and hyper-parameter optimisation on a small embedded PC. New algorithms are introduced for the partitioning of convex polygons to allow efficient path planning for coverage. These algorithms are tested both in simulation and in the field with a small twin hull differential thrust vessel built for the task.Comment: 21 pages, 9 Figures, 1 Table. Submitted to The Journal of Field Robotic

Vision-Based Localization Algorithm Based on Landmark Matching, Triangulation, Reconstruction, and Comparison

Many generic position-estimation algorithms are vulnerable to ambiguity introduced by nonunique landmarks. Also, the available high-dimensional image data is not fully used when these techniques are extended to vision-based localization. This paper presents the landmark matching, triangulation, reconstruction, and comparison (LTRC) global localization algorithm, which is reasonably immune to ambiguous landmark matches. It extracts natural landmarks for the (rough) matching stage before generating the list of possible position estimates through triangulation. Reconstruction and comparison then rank the possible estimates. The LTRC algorithm has been implemented using an interpreted language, onto a robot equipped with a panoramic vision system. Empirical data shows remarkable improvement in accuracy when compared with the established random sample consensus method. LTRC is also robust against inaccurate map data

Origami constraints on the initial-conditions arrangement of dark-matter caustics and streams

In a cold-dark-matter universe, cosmological structure formation proceeds in rough analogy to origami folding. Dark matter occupies a three-dimensional 'sheet' of free- fall observers, non-intersecting in six-dimensional velocity-position phase space. At early times, the sheet was flat like an origami sheet, i.e. velocities were essentially zero, but as time passes, the sheet folds up to form cosmic structure. The present paper further illustrates this analogy, and clarifies a Lagrangian definition of caustics and streams: caustics are two-dimensional surfaces in this initial sheet along which it folds, tessellating Lagrangian space into a set of three-dimensional regions, i.e. streams. The main scientific result of the paper is that streams may be colored by only two colors, with no two neighbouring streams (i.e. streams on either side of a caustic surface) colored the same. The two colors correspond to positive and negative parities of local Lagrangian volumes. This is a severe restriction on the connectivity and therefore arrangement of streams in Lagrangian space, since arbitrarily many colors can be necessary to color a general arrangement of three-dimensional regions. This stream two-colorability has consequences from graph theory, which we explain. Then, using N-body simulations, we test how these caustics correspond in Lagrangian space to the boundaries of haloes, filaments and walls. We also test how well outer caustics correspond to a Zel'dovich-approximation prediction.Comment: Clarifications and slight changes to match version accepted to MNRAS. 9 pages, 5 figure

Analysis of Elephant Movement in Sub-Saharan Africa: Ecological, Climatic, and Conservation Perspectives

The interaction between elephants and their environment has profound implications for both ecology and conservation strategies. This study presents an analytical approach to decipher the intricate patterns of elephant movement in Sub-Saharan Africa, concentrating on key ecological drivers such as seasonal variations and rainfall patterns. Despite the complexities surrounding these influential factors, our analysis provides a holistic view of elephant migratory behavior in the context of the dynamic African landscape. Our comprehensive approach enables us to predict the potential impact of these ecological determinants on elephant migration, a critical step in establishing informed conservation strategies. This projection is particularly crucial given the impacts of global climate change on seasonal and rainfall patterns, which could substantially influence elephant movements in the future. The findings of our work aim to not only advance the understanding of movement ecology but also foster a sustainable coexistence of humans and elephants in Sub-Saharan Africa. By predicting potential elephant routes, our work can inform strategies to minimize human-elephant conflict, effectively manage land use, and enhance anti-poaching efforts. This research underscores the importance of integrating movement ecology and climatic variables for effective wildlife management and conservation planning.Comment: 11 pages, 17 figures, Accepted in ACM SIGCAS SIGCHI Conference on Computing and Sustainable Societies (COMPASS 2023

Intelligent Ground Vehicle Competition

The Intelligent Ground Vehicle Competition (IGVC) draws teams from various universities to compete in the annual autonomous vehicle challenge at the Oakland University campus. To compete, a vehicle must be fully autonomous and can navigate a course designated by various obstacles and painted white lines. Some design challenges are motor control, navigation, environment sensing and safety. A complex navigation system will utilize several tools including a high-precision differential GPS. The vehicle’s surroundings will be mapped using a combination of Light Detection and Ranging (LiDAR) and computer-vision enabled imaging. To comply with IGVC rules, the vehicle must also follow several safety requirements such as physical and wireless emergency stop, safety lighting, and the ability to assume manual control. By fulfilling these design challenges, the design team is seeking to compete in the 2017 Intelligent Ground Vehicle Competition

Developing Android Mobile Map Application with standard navigation tools for pedestrians

Advanced features of modern mobile devices have made it possible to develop and use maps and map based applications for navigation purposes. Since most mobile map applications nowadays are developed for motor vehicles, there is a demand for portable pedestrian navigation applications. In this thesis the Android mobile map application with standard navigation tools for pedestrian navigation was developed, as a platform for facilitating the Lund Challenge location based demonstrator of the HaptiMap project. The pivotal aim of the Lund Challenge demonstrator is to make the sights of Lund city more accessible. The mobile phone application is being designed as a touristic, historical location based game which will also assist tourists to navigate themselves in the city. To enable exploration of historical and current sites of Lund the demonstrator should contain basic components of exploring and way finding. Prior to the development the OpenStreetMap (OSM) road network data and Swedish National Road Database (NVDB) were introduced. The main advantage of using the OSM data over the NVDB dataset is the completeness of the OSM data in terms of pedestrian paths. The datasets were imported to PostgreSQL spatially extended PostGIS database, where different routing algorithms provided by pgRouting were used for routing calculations. As the Lund Challenge demonstrator is intended not only for general users but also for visually impaired users, the problem of user navigation in the parks and open areas were also discussed and the feasibility study was performed. The limitation of the developed application was the problem of the user navigation in the parks and open areas. It is therefore necessary to upgrade the road database with possible path in the open areas and parks in order to implement this application.Advanced features of modern devices have made it possible to develop and use maps and map-based applications for navigation purposes. Since most mobile map applications are currently developed for motor vehicles, there is a demand for portable pedestrian navigation applications. In this thesis, a mobile map application was developed with standard navigation tools for pedestrians, which can be used with mobile phones running Android Operating System. The application will be used as a platform for facilitating the Lund Challenge location based demonstrator. Lund Challenge location based demonstrator is designed to make historical and actual maps of Lund more accessible and is a part of the HaptiMap project. This project aims to create maps and develop location-based services for all users, including elderly and visually impaired. The goal of the Lund Challenge location based demonstrator (also known as The Lund Time Machine) is to minimize the efforts of pedestrians, especially tourists, with finding interesting sites around the city. Initially, it is being designed as a historical location based game which will assist tourists to navigate themselves around the city. In order to further explore historical and current sites, the Lund Challenge should be enhanced with the basic features of exploration and navigation included in this thesis. The road network data was chosen from two available sources: 1) data from OpenStreetMap (OSM) project which provides free geographic data, and 2) The Swedish National Road Database (NVDB) authorized by the Swedish government, which includes all Swedish road network and selected cycle paths. For this thesis, analysis was performed on the datasets using different shortest path algorithms for routing calculations. A primary advantage of using OSM over NVDB is the completeness of data relating to pedestrian paths. As a result, the determination was made that the OSM option was more appropriate for the purpose of this thesis. Since the Lund Challenge location based demonstrator is intended for both general and visually impaired users, the problem of user navigation in parks and open areas was also discussed and a feasibility study was performed. This study revealed a limitation in the application with user navigation in parks and open areas. To resolve this, it is necessary to upgrade the road network with all possible pedestrian paths for parks and open areas