Investigating feasible tools for swarm pattern transformation

Abstract-The work reported in this paper is motivated by the need for developing swarm pattern transformation methodologies. Two methods, namely a macroscopic method and a mathematical method are investigated for pattern transformation. The first method is based on macroscopic parameters while the second method is based on both microscopic and macroscopic parameters. A formal definition to pattern transformation considering four special cases of transformation is presented. Simulations on a physics simulation engine are used to confirm the feasibility of the proposed transformation methods. A brief comparison between the two methods is also presented.

Modeling and simulating a mathematical tool for multi-robot pattern transformation

The work reported in this paper is motivated by the need to investigate general methods for pattern transformation. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some agents in the pattern are introduced. The need for a mathematical tool and simulations for visualizing the behavior of a transformation method is highlighted. A mathematical method based on the Moebius transformation is proposed. The transformation method involves discretization of events for planning paths of individual robots in a pattern. Simulations on a particle physics simulator are used to validate the feasibility of the proposed method.

Information system evolvability, feedback and pattern languages

Information systems for business are frequently heavily reliant on software. Two important feedback-related effects of embedding software in a business process are identified. First, the system dynamics of the software maintenance process can become complex, particularly in the number and scope of the feedback loops. Secondly, responsiveness to feedback can have a big effect on the evolvability of the information system. Ways have been explored to provide an effective mechanism for improving the quality of feedback between stakeholders during software maintenance. Understanding can be improved by using representations of information systems that are both service-based and architectural in scope. The conflicting forces that encourage change or stability can be resolved using patterns and pattern languages. A morphology of information systems pattern languages has been described to facilitate the identification and reuse of patterns and pattern languages. The kind of planning process needed to achieve consensus on a system's evolution is also considered.

Computational complexity of weighted splitting schemes on parallel computers

In models of complicated physical-chemical processes operator splitting is very often applied in order to achieve sufficient accuracy as well as efficiency of the numerical solution. The recently rediscovered weighted splitting schemes have the great advantage of being parallelizable on operator level, which allows us to reduce the computational time if parallel computers are used. In this paper, the computational times needed for the weighted splitting methods are studied in comparison with the sequential (S) splitting and the Marchuk-Strang (MSt) splitting and are illustrated by numerical experiments performed by use of simplified versions of the Danish Eulerian model (DEM).

Different splitting techniques with application to air pollution models

Splitting techniques are commonly used when large-scale models, which appear in different fields of science and engineering, are treated numerically. Four types of splitting procedures are defined and discussed. The problem of the choice of a splitting procedure is investigated. Several numerical tests, by which the influence of the splitting errors on the accuracy of the results is studied, are given. It is shown that the splitting errors decrease linearly when (1) the splitting procedure is of first order and (2) the splitting errors are dominant. Three examples for splitting procedures used in all large-scale air pollution models are presented. Numerical results obtained by a particular air pollution model, Unified Danish Eulerian Model (UNI-DEM), are given and analysed.

A review and implementation of swarm pattern formation and transformation models

Purpose: The purpose of this paper is to address a classic problem – pattern formation identified by researchers in the area of swarm robotic systems – and is also motivated by the need for mathematical foundations in swarm systems. Design/methodology/approach: The work is separated out as inspirations, applications, definitions, challenges and classifications of pattern formation in swarm systems based on recent literature. Further, the work proposes a mathematical model for swarm pattern formation and transformation. Findings: A swarm pattern formation model based on mathematical foundations and macroscopic primitives is proposed. A formal definition for swarm pattern transformation and four special cases of transformation are introduced. Two general methods for transforming patterns are investigated and a comparison of the two methods is presented. The validity of the proposed models, and the feasibility of the methods investigated are confirmed on the Traer Physics and Processing environment. Originality/value: This paper helps in understanding the limitations of existing research in pattern formation and the lack of mathematical foundations for swarm systems. The mathematical model and transformation methods introduce two key concepts, namely macroscopic primitives and a mathematical model. The exercise of implementing the proposed models on physics simulator is novel.

Flux difference splitting for inviscid, real gases with non-equilibrium chemistry

A flux-difference splitting method is presented for the inviscid terms of the compressible flow equations for chemical non-equilibrium gases