Polygon Exploration with Time-Discrete Vision

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 useful accuracy does not allow the robot to scan continuously while in motion; instead, it has to stop each time it surveys its environment. This requirement was studied by Fekete, Klein and Nuechter for the subproblem of looking around a corner, but until now has not been considered in an online setting for whole polygonal regions. We give the first algorithmic results for this important algorithmic problem that combines stationary art gallery-type aspects with watchman-type issues in an online scenario: We demonstrate that even for orthoconvex polygons, a competitive strategy can be achieved only for limited aspect ratio A (the ratio of the maximum and minimum edge length of the polygon), i.e., for a given lower bound on the size of an edge; we give a matching upper bound by providing an O(log A)-competitive strategy for simple rectilinear polygons, using the assumption that each edge of the polygon has to be fully visible from some scan point.Comment: 28 pages, 17 figures, 2 photographs, 3 tables, Latex. Updated some details (title, figures and text) for final journal revision, including explicit assumption of full edge visibilit

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

Istraživanje i modeliranje nepoznatog poligonalnog prostora zasnovano na nesigurnim podacima udaljenosti

We consider problem of exploration and mapping of unknown indoor environments using laser range finder. We assume a setup with a resolved localization problem and known uncertainty sensor models. Most exploration algorithms are based on detection of a boundary between explored and unexplored regions. They are, however, not efficient in practice due to uncertainties in measurement, localization and map building. The exploration and mapping algorithm is proposed that extends Ekman’s exploration algorithm by removing rigid constraints on the range sensor and robot localization. The proposed algorithm includes line extraction algorithm developed by Pfister, which incorporates noise models of the range sensor and robot’s pose uncertainty. A line representation of the range data is used for creating polygon that represents explored region from each measurement pose. The polygon edges that do not correspond to real environmental features are candidates for a new measurement pose. A general polygon clipping algorithm is used to obtain the total explored region as the union of polygons from different measurement poses. The proposed algorithm is tested and compared to the Ekman’s algorithm by simulations and experimentally on a Pioneer 3DX mobile robot equipped with SICK LMS-200 laser range finder.Razmatramo problem istraživanja i izgradnje karte nepoznatog unutarnjeg prostora koristeći laserski sensor udaljenosti. Pretpostavljamo riješenu lokalizaciju robota i poznati model nesigurnosti senzora. Većna se algoritama istraživanja zasniva na otkrivanju granica istraženog i neistraženog područja. Međutim, u praksi nisu učinkoviti zbog nesigurnosti mjerenja, lokalizacije i izgradnje karte. Razvijen je algoritam istraživanja i izgradnje karte koji proširuje Ekmanov algoritam uklanjanjem strogih ograničenja na senzor udaljenosti i lokalizaciju robota. Razvijeni algoritam uključuje algoritam izdvajanja linijskih segmenata prema Pfisteru, koji uzima u obzir utjecaje zašumljenosti senzora i nesigurnosti položaja mobilnog robota. Linijska reprezentacija podataka udaljenosti koristi se za stvaranje poligona koji predstavlja istraženo područje iz svakog mjernog položaja. Bridovi poligona koji se ne podudaraju sa stvarnim značajkama prostora su kandidati za novi mjerni položaj. Algoritam općenitog isijecanja poligona korišten je za dobivanje ukupnog istraženog područja kao unija poligona iz različitih mjernih položaja. Razvijeni algoritam testiran je i uspoređen s izvornim Ekmanovim algoritmom simulacijski i eksperimentalno na mobilnom robotu Pioneer 3DX opremljenim laserskim senzorom udaljenosti SICK LMS-200

Algorithms for Rapidly Dispersing Robot Swarms in Unknown Environments

We develop and analyze algorithms for dispersing a swarm of primitive robots in an unknown environment, R. The primary objective is to minimize the makespan, that is, the time to fill the entire region. An environment is composed of pixels that form a connected subset of the integer grid. There is at most one robot per pixel and robots move horizontally or vertically at unit speed. Robots enter R by means of k>=1 door pixels Robots are primitive finite automata, only having local communication, local sensors, and a constant-sized memory. We first give algorithms for the single-door case (i.e., k=1), analyzing the algorithms both theoretically and experimentally. We prove that our algorithms have optimal makespan 2A-1, where A is the area of R. We next give an algorithm for the multi-door case (k>1), based on a wall-following version of the leader-follower strategy. We prove that our strategy is O(log(k+1))-competitive, and that this bound is tight for our strategy and other related strategies.Comment: 17 pages, 4 figures, Latex, to appear in Workshop on Algorithmic Foundations of Robotics, 200

Online Algorithms with Discrete Visibility - Exploring Unknown Polygonal Environments

The context of this work is the exploration of unknown polygonal environments with obstacles. Both the outer boundary and the boundaries of obstacles are piecewise linear. The boundaries can be nonconvex. The exploration problem can be motivated by the following application. Imagine that a robot has to explore the interior of a collapsed building, which has crumbled due to an earthquake, to search for human survivors. It is clearly impossible to have a knowledge of the building's interior geometry prior to the exploration. Thus, the robot must be able to see, with its onboard vision sensors, all points in the building's interior while following its exploration path. In this way, no potential survivors will be missed by the exploring robot. The exploratory path must clearly reflect the topology of the free space, and, therefore, such exploratory paths can be used to guide future robot excursions (such as would arise in our example from a rescue operation)

Online Exploration of Polygons with Holes

We study online strategies for autonomous mobile robots with vision to explore unknown polygons with at most h holes. Our main contribution is an (h+c_0)!-competitive strategy for such polygons under the assumption that each hole is marked with a special color, where c_0 is a universal constant. The strategy is based on a new hybrid approach. Furthermore, we give a new lower bound construction for small h.Comment: 16 pages, 9 figures, submitted to WAOA 201