Spatio-Temporal Patterns act as Computational Mechanisms governing Emergent behavior in Robotic Swarms

open access articleOur goal is to control a robotic swarm without removing its swarm-like nature. In other words, we aim to intrinsically control a robotic swarm emergent behavior. Past attempts at governing robotic swarms or their selfcoordinating emergent behavior, has proven ineffective, largely due to the swarm’s inherent randomness (making it difficult to predict) and utter simplicity (they lack a leader, any kind of centralized control, long-range communication, global knowledge, complex internal models and only operate on a couple of basic, reactive rules). The main problem is that emergent phenomena itself is not fully understood, despite being at the forefront of current research. Research into 1D and 2D Cellular Automata has uncovered a hidden computational layer which bridges the micromacro gap (i.e., how individual behaviors at the micro-level influence the global behaviors on the macro-level). We hypothesize that there also lie embedded computational mechanisms at the heart of a robotic swarm’s emergent behavior. To test this theory, we proceeded to simulate robotic swarms (represented as both particles and dynamic networks) and then designed local rules to induce various types of intelligent, emergent behaviors (as well as designing genetic algorithms to evolve robotic swarms with emergent behaviors). Finally, we analysed these robotic swarms and successfully confirmed our hypothesis; analyzing their developments and interactions over time revealed various forms of embedded spatiotemporal patterns which store, propagate and parallel process information across the swarm according to some internal, collision-based logic (solving the mystery of how simple robots are able to self-coordinate and allow global behaviors to emerge across the swarm)

The Quantification of Perception Based Uncertainty Using R-fuzzy Sets and Grey Analysis

The nature of uncertainty cannot be generically defined as it is domain and context specific. With that being the case, there have been several proposed models, all of which have their own associated benefits and shortcomings. From these models, it was decided that an R-fuzzy approach would provide for the most ideal foundation from which to enhance and expand upon. An R-fuzzy set can be seen as a relatively new model, one which itself is an extension to fuzzy set theory. It makes use of a lower and upper approximation bounding from rough set theory, which allows for the membership function of an R-fuzzy set to be that of a rough set. An R-fuzzy approach provides the means for one to encapsulate uncertain fuzzy membership values, based on a given abstract concept. If using the voting method, any fuzzy membership value contained within the lower approximation can be treated as an absolute truth. The fuzzy membership values which are contained within the upper approximation, may be the result of a singleton, or the vast majority, but absolutely not all. This thesis has brought about the creation of a significance measure, based on a variation of Bayes' theorem. One which enables the quantification of any contained fuzzy membership value within an R-fuzzy set. Such is the pairing of the significance measure and an R-fuzzy set, an intermediary bridge linking to that of a generalised type-2 fuzzy set can be achieved. Simply by inferencing from the returned degrees of significance, one is able to ascertain the true significance of any uncertain fuzzy membership value, relative to other encapsulated uncertain values. As an extension to this enhancement, the thesis has also brought about the novel introduction of grey analysis. By utilising the absolute degree of grey incidence, it provides one with the means to measure and quantify the metric spaces between sequences, generated based on the returned degrees of significance for any given R-fuzzy set. As it will be shown, this framework is ideally suited to domains where perceptions are being modelled, which may also contain several varying clusters of cohorts based on any number of correlations. These clusters can then be compared and contrasted to allow for a more detailed understanding of the abstractions being modelled

A commentary on some of the intrinsic differences between grey systems and fuzzy systems

The aim of this paper is to distinguish between some of the more intrinsic differences that exist between grey system theory (GST) and fuzzy system theory (FST). There are several aspects of both paradigms that are closely related, it is precisely these close relations that will often result in a misunderstanding or misinterpretation. The subtly of the differences in some cases are difficult to perceive, hence why a definitive explanation is needed. This paper discusses the divergences and similarities between the interval-valued fuzzy set and grey set, interval and grey number; for both the standard and the generalised interpretation. A preference based analysis example is also put forward to demonstrate the alternative in perspectives that each approach adopts. It is believed that a better understanding of the differences will ultimately allow for a greater understanding of the ideology and mantras that the concepts themselves are built upon. By proxy, describing the divergences will also put forward the similarities. We believe that by providing an overview of the facets that each approach employs where confusion may arise, a thorough and more detailed explanation is the result. This paper places particular emphasis on grey system theory, describing the more intrinsic differences that sets it apart from the more established paradigm of fuzzy system theory

An R-fuzzy and Grey Analysis Framework

This paper puts forward the notion of an R-fuzzy and grey analysis framework. This is based on our previous works which involved enhancing the R-fuzzy set and the research undertaken on grey analysis, we believe that this newly proposed framework - the R-fuzzy grey analysis framework (RfGAf), to be a viable methodology to adopt when considering uncertainty modelling. It will be shown that the framework is very well suited in application areas involving perception modelling, where group consensus and subjectivity are prevalent. In such domains a single observation can have a multitude of different perspectives, choosing a single fuzzy value as a representative becomes problematic. The fundamental concept of an R-fuzzy set is that it allows for the collective perception of a populous, and also individualised perspectives to be encapsulated within its membership set. The introduction of a significance measure allowed for the quantification of any membership value contained within any generated R-fuzzy set. This in addition provided one the means to infer from the conditional probability of each contained fuzzy membership value. Such is the pairing of the significance measure and the R-fuzzy concept, it replicates in part, the higher order of complex uncertainty which can be garnered using a type-2 fuzzy approach, with the computational ease and objectiveness of a typical type-1 fuzzy set. This paper utilises the use of grey analysis, in particular, the use of the absolute degree of grey incidence for the inspection of the sequence generated when using the significance measure, when quantifying the degree of significance for each contained fuzzy membership value. Using the absolute degree of grey incidence provides a means to measure the metric spaces between sequences, so that perception divergence can be quantified

Quantification of Perception Clusters Using R-Fuzzy Sets and Grey Analysis

This paper investigates the use of the R-fuzzy significance measure hybrid approach introduced by the authors in a previous work; used in conjunction with grey analysis to allow for further inferencing, providing a higher dimension of accuracy and understanding. As a single observation can have a multitude of different perspectives, choosing a single fuzzy value as a representative becomes problematic. The fundamental concept of an R-fuzzy set is that it allows for the collective perception of a populous, and also individualised perspectives to be encapsulated within its membership set. The introduction of the significance measure allowed for the quantification of any membership value contained within any generated R-fuzzy set. Such is the pairing of the significance measure and the R-fuzzy concept, it replicates in part, the higher order of complex uncertainty which can be garnered using a type-2 fuzzy approach, with the computational ease and objectiveness of a typical type-1 fuzzy set. This paper utilises the use of grey analysis, in particular, the use of the absolute degree of grey incidence for the inspection of the sequence generated when using the significance measure, when quantifying the degree of significance fore each contained fuzzy membership value. Using the absolute degree of grey incidence provides a means to measure the metric spaces between sequences. As the worked example will show, if the data contains perceptions from clusters of cohorts, these clusters can be compared and contrasted to allow for a more detailed understanding of the abstract concepts being modelled

A Significance Measure for R-Fuzzy Sets

This paper presents a newly created significance measure based on a variation of Bayes' theorem, one which quantifies the significance of any value contained within an R-fuzzy set. An R-fuzzy set is a relatively new concept and an extension to fuzzy sets. By utilising the lower and upper approximations from rough set theory, an R-fuzzy approach allows for uncertain fuzzy membership values to be encapsulated. The membership values associated with the lower approximation are regarded as absolute truths, whereas the values associated with the upper approximation maybe be the result of a single voter, or the vast majority, but definitely not all. By making use of the significance measure one can inspect each and every encapsulated membership value. The significance value itself is a coefficient, this value will indicate how strongly it was agreed upon by the populace for a specific R-fuzzy descriptor. There has been no recent effort made in order to make sense of the significance of any of the values contained within an R-fuzzy set, hence the motivation for this paper. Also presented is a worked example, demonstrating the coupling together of an R-fuzzy approach and the significance measure

R-fuzzy Sets and Grey System Theory

This paper investigates the use of grey theory to enhance the concept of an R-fuzzy set, with regards to the precision of the encapsulating set of returned significance values. The use of lower and upper approximations from rough set theory, allow for an R-fuzzy approach to encapsulate uncertain fuzzy membership values; both collectively generic and individually specific. The authors have previously created a significance measure, which when combined with an R-fuzzy set provides one with a refined approach for expressing complex uncertainty. This pairing of an R-fuzzy set and the significance measure, replicates in part, the high detail of uncertainty representation from a type-2 fuzzy approach, with the relative ease and objectiveness of a type-1 fuzzy approach. As a result, this new research method allows for a practical means for domains where ideally a generalised type-2 fuzzy set is more favourable, but ultimately unfeasible due to the subjectiveness of type-2 fuzzy membership values. This paper focuses on providing a more effective means for the creation of the set which encapsulates the returned degrees of significance. Using grey techniques, rather than the arbitrary configuration of the original work, the result is a high precision set for encapsulation, with the minimal configuration of parameter values. A worked example is used to demonstrate the effectiveness of using grey theory in conjunction with R-fuzzy sets and the significance measure

<i>Cis</i> P-tau is induced in clinical and preclinical brain injury and contributes to post-injury sequelae

Induction of the cis form of phosphorylated tau (cis P-tau) has previously been shown to occur in animal models of traumatic brain injury (TBI), and blocking this form of tau using antibody was beneficial in a rodent model of severe TBI. Here the authors show that cis P-tau induction is a feature of several different forms of TBI in humans, and that administration of cis P-tau targeting antibody to rodents reduces or delays pathological features of TBI