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 $k\geq 2$ 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

System Issues in Multi-agent Simulation of Large Crowds

Crowd simulation is a complex and challenging domain. Crowds demonstrate many complex behaviours and are consequently difficult to model for realistic simulation systems. Analyzing crowd dynamics has been an active area of research and efforts have been made to develop models to explain crowd behaviour. In this paper we describe an agent based simulation of crowds, based on a continuous field force model. Our simulation can handle movement of crowds over complex terrains and we have been able to simulate scenarios like clogging of exits during emergency evacuation situations. The focus of this paper, however, is on the scalability issues for such a multi-agent based crowd simulation system. We believe that scalability is an important criterion for rescue simulation systems. To realistically model a disaster scenario for a large city, the system should ideally scale up to accommodate hundreds of thousands of agents. We discuss the attempts made so far to meet this challenge, and try to identify the architectural and system constraints that limit scalability. Thereafter we propose a novel technique which could be used to richly simulate huge crowds

Interactive rendering of massive geometric models

Booklet2005-02Conference held in Pisa, ItalyTutorial notes, Eurographics Italy. Conference held in Pisa, Italy, February 17--18, CDROM Proceedings, February 200

A novel rapid method for viewshed computation on DEM through max-pooling and min-expected height

Viewshed computation of a digital elevation model (DEM) plays an important role in a geographic information system, but the required high computational time is a serious problem for a practical application. Hitherto, the mainstream methods of viewshed computing include line-of-sight method, reference planes method, etc. Based on these classical algorithms, a new algorithm for viewshed computation is proposed in this paper: the Matryoshka doll algorithm. Through a pooling operation, the minimum expected height of the DEM is introduced as max-pooling with minimum expected height in the viewshed computing optimization. This is to increase the efficiency and adaptability of the computation of the visibility range. The experimental results demonstrate that the algorithm has obvious advantages in computing speed, but with the accuracy only slightly reduced

Compact Modeling Technique for Outdoor Navigation

16 pages, 46 figures.In this paper, a new methodology to build compact local maps in real time for outdoor robot navigation is presented. The environment information is obtained from a 3-D scanner laser. The navigation model, which is called traversable region model, is based on a Voronoi diagram technique, but adapted to large outdoor environments. The model obtained with this methodology allows a definition of safe trajectories that depend on the robot's capabilities and the terrain properties, and it will represent, in a topogeometric way, the environment as local and global maps. The application presented is validated in real outdoor environments with the robot called GOLIAT.This work was supported by the Spanish Government through the MICYT project DPI2003-01170.Publicad