scholarly journals Time-Optimal Gathering under Limited Visibility with One-Axis Agreement

Information ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 448
Author(s):  
Pavan Poudel ◽  
Gokarna Sharma
Keyword(s):  
Euclidean Distance ◽  
Autonomous Robots ◽  
Fundamental Problem ◽  
Single Point ◽  
Time Algorithm ◽  
Initial Configuration ◽  
Autonomous Mobile Robots ◽  
Coordinate Axis ◽  
Time Optimal ◽  
Limited Visibility

We consider the distributed setting of N autonomous mobile robots that operate in Look-Compute-Move (LCM) cycles following the well-celebrated classic oblivious robots model. We study the fundamental problem of gathering N autonomous robots on a plane, which requires all robots to meet at a single point (or to position within a small area) that is not known beforehand. We consider limited visibility under which robots are only able to see other robots up to a constant Euclidean distance and focus on the time complexity of gathering by robots under limited visibility. There exists an O(DG) time algorithm for this problem in the fully synchronous setting, assuming that the robots agree on one coordinate axis (say north), where DG is the diameter of the visibility graph of the initial configuration. In this article, we provide the first O(DE) time algorithm for this problem in the asynchronous setting under the same assumption of robots’ agreement with one coordinate axis, where DE is the Euclidean distance between farthest-pair of robots in the initial configuration. The runtime of our algorithm is a significant improvement since for any initial configuration of N≥1 robots, DE≤DG, and there exist initial configurations for which DG can be quadratic on DE, i.e., DG=Θ(DE2). Moreover, our algorithm is asymptotically time-optimal since the trivial time lower bound for this problem is Ω(DE).

FINDING AN OPTIMAL BRIDGE BETWEEN TWO POLYGONS

2002 ◽  
Vol 12 (03) ◽  
pp. 249-261 ◽  
Author(s):  
XUEHOU TAN
Keyword(s):  
Hierarchical Structure ◽  
Shortest Path ◽  
Line Segment ◽  
Euclidean Distance ◽  
Geodesic Distance ◽  
Simple Polygon ◽  
Time Algorithm ◽  
Search Trees ◽  
Bridge Problem ◽  
Path Queries

Let π(a,b) denote the shortest path between two points a, b inside a simple polygon P, which totally lies in P. The geodesic distance between a and b in P is defined as the length of π(a,b), denoted by gd(a,b), in contrast with the Euclidean distance between a and b in the plane, denoted by d(a,b). Given two disjoint polygons P and Q in the plane, the bridge problem asks for a line segment (optimal bridge) that connects a point p on the boundary of P and a point q on the boundary of Q such that the sum of three distances gd(p′,p), d(p,q) and gd(q,q′), with any p′ ∈ P and any q′ ∈ Q, is minimized. We present an O(n log 3 n) time algorithm for finding an optimal bridge between two simple polygons. This significantly improves upon the previous O(n2) time bound. Our result is obtained by making substantial use of a hierarchical structure that consists of segment trees, range trees and persistent search trees, and a structure that supports dynamic ray shooting and shortest path queries as well.

scholarly journals Constant-Time Complete Visibility for Robots with Lights: The Asynchronous Case

Algorithms ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 56
Author(s):  
Gokarna Sharma ◽  
Ramachandran Vaidyanathan ◽  
Jerry L. Trahan
Keyword(s):  
Mobile Robots ◽  
Line Segment ◽  
Autonomous Robots ◽  
Straight Line Segment ◽  
Autonomous Mobile Robots ◽  
Asymptotically Optimal ◽  
Time Translation ◽  
Straight Line ◽  
A New Technique ◽  
Colored Lights

We consider the distributed setting of N autonomous mobile robots that operate in Look-Compute-Move (LCM) cycles and use colored lights (the robots with lights model). We assume obstructed visibility where a robot cannot see another robot if a third robot is positioned between them on the straight line segment connecting them. In this paper, we consider the problem of positioning N autonomous robots on a plane so that every robot is visible to all others (this is called the Complete Visibility problem). This problem is fundamental, as it provides a basis to solve many other problems under obstructed visibility. In this paper, we provide the first, asymptotically optimal, O(1) time, O(1) color algorithm for Complete Visibility in the asynchronous setting. This significantly improves on an O(N)-time translation of the existing O(1) time, O(1) color semi-synchronous algorithm to the asynchronous setting. The proposed algorithm is collision-free, i.e., robots do not share positions, and their paths do not cross. We also introduce a new technique for moving robots in an asynchronous setting that may be of independent interest, called Beacon-Directed Curve Positioning.

A Real-time Algorithm for Obstacle Avoidance of Autonomous Mobile Robots

Robotica ◽  
1992 ◽  
Vol 10 (3) ◽  
pp. 217-227 ◽  
Author(s):  
Huang Han-Pang ◽  
Lee Pei-Chien
Keyword(s):  
Mobile Robots ◽  
Real Time ◽  
Obstacle Avoidance ◽  
Time Algorithm ◽  
Autonomous Mobile Robots ◽  
Computational Time ◽  
Avoidance Problem

SUMMARYA real-time obstacle avoidance algorithm is proposed for autonomous mobile robots. The algorithm is sensor-based and consists of a H-mode and T-mode. The algorithm can deal with a complicated obstacle environment, such as multiple concave and convex obstacles. It will be shown that the algorithm is more efficient and more robust than other sensor-based algorithms. In addition, the algorithm will guarantee a solution for the obstacle avoidance problem. Since the algorithm only takes up a small computational time, it can be implemented in real time.

scholarly journals Comparing Adjoint- and Ensemble-Sensitivity Analysis with Applications to Observation Targeting

2007 ◽  
Vol 135 (12) ◽  
pp. 4117-4134 ◽  
Author(s):  
Brian Ancell ◽  
Gregory J. Hakim
Keyword(s):  
Variance Reduction ◽  
Initial Conditions ◽  
Sampling Error ◽  
Forecast Error ◽  
Single Point ◽  
Error Variance ◽  
Initial Time ◽  
Forecast Errors ◽  
Adjoint Sensitivity ◽  
Time Optimal

Abstract The sensitivity of numerical weather forecasts to small changes in initial conditions is estimated using ensemble samples of analysis and forecast errors. Ensemble sensitivity is defined here by linear regression of analysis errors onto a given forecast metric. It is shown that ensemble sensitivity is proportional to the projection of the analysis-error covariance onto the adjoint-sensitivity field. Furthermore, the ensemble-sensitivity approach proposed here involves a small calculation that is easy to implement. Ensemble- and adjoint-based sensitivity fields are compared for a representative wintertime flow pattern near the west coast of North America for a 90-member ensemble of independent initial conditions derived from an ensemble Kalman filter. The forecast metric is taken for simplicity to be the 24-h forecast of sea level pressure at a single point in western Washington State. Results show that adjoint and ensemble sensitivities are very different in terms of location, scale, and magnitude. Adjoint-sensitivity fields reveal mesoscale lower-tropospheric structures that tilt strongly upshear, whereas ensemble-sensitivity fields emphasize synoptic-scale features that tilt modestly throughout the troposphere and are associated with significant weather features at the initial time. Optimal locations for targeting can easily be determined from ensemble sensitivity, and results indicate that the primary targeting locations are located away from regions of greatest adjoint and ensemble sensitivity. It is shown that this method of targeting is similar to previous ensemble-based methods that estimate forecast-error variance reduction, but easily allows for the application of statistical confidence measures to deal with sampling error.

TIME-OPTIMAL DIGITAL GEOMETRY ALGORITHMS ON MESHES WITH MULTIPLE BROADCASTING

1995 ◽  
Vol 09 (04) ◽  
pp. 601-613
Author(s):  
V. BOKKA ◽  
H. GURLA ◽  
S. OLARIU ◽  
J.L. SCHWING ◽  
I. STOJMENOVIĆ
Keyword(s):  
Lower Bound ◽  
Convex Hull ◽  
Lower Bounds ◽  
Minimum Distance ◽  
Fundamental Problem ◽  
Optimal Solution ◽  
The Other ◽  
Digital Geometry ◽  
Black Pixel ◽  
Time Optimal

The main contribution of this work is to show that a number of digital geometry problems can be solved elegantly on meshes with multiple broadcasting by using a time-optimal solution to the leftmost one problem as a basic subroutine. Consider a binary image pretiled onto a mesh with multiple broadcasting of size [Formula: see text] one pixel per processor. Our first contribution is to prove an Ω(n1/6) time lower bound for the problem of deciding whether the image contains at least one black pixel. We then obtain time lower bounds for many other digital geometry problems by reducing this fundamental problem to all the other problems of interest. Specifically, the problems that we address are: detecting whether an image contains at least one black pixel, computing the convex hull of the image, computing the diameter of an image, deciding whether a set of digital points is a digital line, computing the minimum distance between two images, deciding whether two images are linearly separable, computing the perimeter, area and width of a given image. Our second contribution is to show that the time lower bounds obtained are tight by exhibiting simple O(n1/6) time algorithms for these problems. As previously mentioned, an interesting feature of these algorithms is that they use, directly or indirectly, an algorithm for the leftmost one problem recently developed by one of the authors.

LOCATING AN OBNOXIOUS LINE AMONG PLANAR OBJECTS

2012 ◽  
Vol 22 (05) ◽  
pp. 391-405
Author(s):  
DANNY Z. CHEN ◽  
HAITAO WANG
Keyword(s):  
Convex Hull ◽  
Euclidean Distance ◽  
Time Algorithm ◽  
Positive Weight ◽  
Time Solution ◽  
Previous Algorithm ◽  
Minimum Weighted Euclidean Distance ◽  
Improved Algorithm

Given a set P of n points in the plane such that each point has a positive weight, we study the problem of finding an obnoxious line that intersects the convex hull of P and maximizes the minimum weighted Euclidean distance to all points of P. We present an O(n2 log n) time algorithm for the problem, improving the previously best-known O(n2 log 3 n) time solution. We also consider a variant of this problem whose input is a set of m polygons with a total of n vertices in the plane such that each polygon has a positive weight and whose goal is to locate an obnoxious line with respect to the weighted polygons. An O(mn + n log 2 n log m + m2 log n log 2 m) time algorithm for this variant was known previously. We give an improved algorithm of O(mn + n log 2 n + m2 log n) time. Further, we reduce the time bound of a previous algorithm for the case of the problem with unweighted polygons from O((m2 + n log m) log n) to O(m2 + n log m).

scholarly journals Design of Charge-Balanced Time-Optimal Stimuli for Spiking Neuron Oscillators

2014 ◽  
Vol 26 (10) ◽  
pp. 2223-2246 ◽  
Author(s):  
Isuru S. Dasanayake ◽  
Jr-Shin Li
Keyword(s):  
Optimal Control ◽  
Neural Control ◽  
Phase Response Curve ◽  
Fundamental Problem ◽  
External Control ◽  
Control Input ◽  
Optimal Controls ◽  
Oscillatory Systems ◽  
Time Optimal ◽  
Phase Models

In this letter, we investigate the fundamental limits on how the interspike time of a neuron oscillator can be perturbed by the application of a bounded external control input (a current stimulus) with zero net electric charge accumulation. We use phase models to study the dynamics of neurons and derive charge-balanced controls that achieve the minimum and maximum interspike times for a given bound on the control amplitude. Our derivation is valid for any arbitrary shape of the phase response curve and for any value of the given control amplitude bound. In addition, we characterize the change in the structures of the charge-balanced time-optimal controls with the allowable control amplitude. We demonstrate the applicability of the derived optimal control laws by applying them to mathematically ideal and experimentally observed neuron phase models, including the widely studied Hodgkin-Huxley phase model, and by verifying them with the corresponding original full state-space models. This work addresses a fundamental problem in the field of neural control and provides a theoretical investigation to the optimal control of oscillatory systems.

Optimization-based formation of autonomous mobile robots

Robotica ◽  
2010 ◽  
Vol 29 (4) ◽  
pp. 515-525 ◽  
Author(s):  
Huan Zhang ◽  
Pubudu N. Pathirana
Keyword(s):  
Mobile Robots ◽  
Formation Control ◽  
Fundamental Problem ◽  
Optimization Techniques ◽  
Autonomous Mobile Robots ◽  
Coordinate Systems ◽  
Geometric Pattern ◽  
Difference Function ◽  
Movement Strategy ◽  
Robot Configuration

SUMMARYThe formation of autonomous mobile robots to an arbitrary geometric pattern in a distributed fashion is a fundamental problem in formation control. This paper presents a new asynchronous, memoryless (oblivious) algorithm to the formation problem via distributed optimization techniques. The optimization minimizes an appropriately defined difference function between the current robot distribution and the target geometric pattern. The optimization processes are performed independently by individual robots in their local coordinate systems. A movement strategy derived from the results of the distributed optimizations guarantees that every movement makes the current robot configuration approaches the target geometric pattern until the final pattern is reached.

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