Bearing Rigidity and Almost Global Bearing-Only Formation Stabilization

A fundamental problem that the bearing rigidity theory studies is to determine when a framework can be uniquely determined up to a translation and a scaling factor by its inter-neighbor bearings. While many previous works focused on the bearing rigidity of two-dimensional frameworks, a first contribution of this paper is to extend these results to arbitrary dimensions. It is shown that a framework in an arbitrary dimension can be uniquely determined up to a translation and a scaling factor by the bearings if and only if the framework is infinitesimally bearing rigid. In this paper, the proposed bearing rigidity theory is further applied to the bearing-only formation stabilization problem where the target formation is defined by inter-neighbor bearings and the feedback control uses only bearing measurements. Nonlinear distributed bearing-only formation control laws are proposed for the cases with and without a global orientation. It is proved that the control laws can almost globally stabilize infinitesimally bearing rigid formations. Numerical simulations are provided to support the analysis

Translational and Scaling Formation Maneuver Control via a Bearing-Based Approach

This paper studies distributed maneuver control of multi-agent formations in arbitrary dimensions. The objective is to control the translation and scale of the formation while maintaining the desired formation pattern. Unlike conventional approaches where the target formation is defined by relative positions or distances, we propose a novel bearing-based approach where the target formation is defined by inter-neighbor bearings. Since the bearings are invariant to the translation and scale of the formation, the bearing-based approach provides a simple solution to the problem of translational and scaling formation maneuver control. Linear formation control laws for double-integrator dynamics are proposed and the global formation stability is analyzed. This paper also studies bearing-based formation control in the presence of practical problems including input disturbances, acceleration saturation, and collision avoidance. The theoretical results are illustrated with numerical simulations

Bearing rigidity theory and its applications for control and estimation of network systems: Life beyond distance rigidity

Distributed control and location estimation of multiagent systems have received tremendous research attention in recent years because of their potential across many application domains [1], [2]. The term agent can represent a sensor, autonomous vehicle, or any general dynamical system. Multiagent systems are attractive because of their robustness against system failure, ability to adapt to dynamic and uncertain environments, and economic advantages compared to the implementation of more expensive monolithic systems

Localizability and distributed protocols for bearing-based network localization in arbitrary dimensions

This paper addresses the problem of bearing-based network localization, which aims to localize all the nodes in a static network given the locations of a subset of nodes termed anchors and inter-node bearings measured in a common reference frame. The contributions of the paper are twofold. Firstly, we propose necessary and sufficient conditions for network localizability with both algebraic and rigidity theoretic interpretations. Secondly, we propose and analyze a linear distributed protocol for bearing-based network localization. One novelty of our work is that the localizability analysis and localization protocol are applicable to networks in arbitrary dimensional spaces

On the maximal number of real embeddings of spatial minimally rigid graphs

The number of embeddings of minimally rigid graphs in $\mathbb{R}^D$ is (by definition) finite, modulo rigid transformations, for every generic choice of edge lengths. Even though various approaches have been proposed to compute it, the gap between upper and lower bounds is still enormous. Specific values and its asymptotic behavior are major and fascinating open problems in rigidity theory. Our work considers the maximal number of real embeddings of minimally rigid graphs in $\mathbb{R}^3$. We modify a commonly used parametric semi-algebraic formulation that exploits the Cayley-Menger determinant to minimize the {\em a priori} number of complex embeddings, where the parameters correspond to edge lengths. To cope with the huge dimension of the parameter space and find specializations of the parameters that maximize the number of real embeddings, we introduce a method based on coupler curves that makes the sampling feasible for spatial minimally rigid graphs. Our methodology results in the first full classification of the number of real embeddings of graphs with 7 vertices in $\mathbb{R}^3$, which was the smallest open case. Building on this and certain 8-vertex graphs, we improve the previously known general lower bound on the maximum number of real embeddings in $\mathbb{R}^3$

Neurophysiological Correlates of Emotion Regulation in Children and Adolescents

& Psychologists consider emotion regulation a critical devel-opmental acquisition. Yet, there has been very little research on the neural underpinnings of emotion regulation across childhood and adolescence. We selected two ERP compo-nents associated with inhibitory control—the frontal N2 and frontal P3. We recorded these components before, during, and after a negative emotion induction, and compared their am-plitude, latency, and source localization over age. Fifty-eight children 5–16 years of age engaged in a simple go/no-go pro-cedure in which points for successful performance earned a valued prize. The temporary loss of all points triggered negative emotions, as confirmed by self-report scales. Both the frontal N2 and frontal P3 decreased in amplitude and la-tency with age, consistent with the hypothesis of increasing cortical efficiency. Amplitudes were also greater following the emotion induction, only for adolescents for the N2 but across the age span for the frontal P3, suggesting different but overlapping profiles of emotion-related control mechanisms. No-go N2 amplitudes were greater than go N2 amplitudes following the emotion induction at all ages, suggesting a consistent effect of negative emotion on mechanisms of re-sponse inhibition. No-go P3 amplitudes were also greater than go P3 amplitudes and they decreased with age, whereas go P3 amplitudes remained low. Finally, source modeling in-dicated a developmental decline in central-posterior midline activity paralleled by increasing activity in frontal midline re-gions suggestive of the anterior cingulate cortex. Negative emotion induction corresponded with an additional right ven-tral prefrontal or temporal generator beginning in middle childhood. &amp

Neurophysiological Correlates of Executive Function: A Comparison of European-Canadian and Chinese-Canadian 5-Year-Old Children

This study explored the neurophysiological correlates of executive function (EF) in young children from two different cultural backgrounds. Twenty European-Canadian and 17 Chinese-Canadian 5-year-olds participated in a go/no-go task, during which high-density electroencephalographic (EEG) data were recorded. No cultural group differences were observed in children's behavioral performance on the task, but marked differences were revealed by ERP analyses, which focused on the amplitude and latency of the N2 waveform. Chinese-Canadian children showed larger (i.e., more negative) N2 amplitudes than European-Canadian children on the right side of the scalp on no-go trials, as well as on the left side of the scalp on go trials, and for all children, larger N2 amplitudes were associated with faster median reaction times. Source analyses of the N2 were consistent with the hypothesis that compared to European-Canadian children, Chinese-Canadian children showed more activation in dorsomedial, ventromedial, and (bilateral) ventrolateral prefrontal cortex. These findings reveal that EEG can provide a measure of cultural differences in neurocognitive function that is more sensitive than behavioral data alone; that Chinese-Canadian children show a pattern of hemispheric differentiation in the context of this task than that is more pronounced than that of age-matched European-Canadian children; that the asymmetrically lateralized N2 may be a reliable marker of both effortful inhibition (on the right) and effortful approach (on the left); and that the neural correlates of EF may vary across samples of healthy participants, even in children

The opposites task: Using general rules to test cognitive flexibility in preschoolers

A brief narrative description of the journal article, document, or resource. Executive functions play an important role in cognitive development, and during the preschool years especially, children's performance is limited in tasks that demand flexibility in their behavior. We asked whether preschoolers would exhibit limitations when they are required to apply a general rule in the context of novel stimuli on every trial (the "opposites" task). Two types of inhibitory processing were measured: response interference (resistance to interference from a competing response) and proactive interference (resistance to interference from a previously relevant rule). Group data show 3-year-olds have difficulty inhibiting prepotent tendencies under these conditions, whereas 5-year-olds' accuracy is near ceiling in the task. (Contains 4 footnotes and 1 table.

Inhibition and young children's performance on the Tower of London task

Young children, when performing problem solving tasks, show a tendency to break task rules and produce incomplete solutions. We propose that this tendency can be explained by understanding problem solving within the context of the development of “executive functions” – general cognitive control functions, which serve to regulate the operation of the cognitive system. This proposal is supported by the construction of two computational models that simulate separately the performance of 3–4 year old and 5–6 year old children on the Tower of London planning task. We seek in particular to capture the emerging role of inhibition in the older group. The basic framework within which the models are developed is derived from Fox and Das’ Domino model [Fox, J., & Das, S. (2000). Safe and sound: Artificial intelligence in hazardous applications. Cambridge, MA: MIT Press] and Norman and Shallice’s [Norman, D.A., & Shallice, T. (1986). Attention to action: Willed and automatic control of behaviour. In R. Davidson, G. Schwartz, & D. Shapiro (Eds.), Consciousness and Self Regulation (Vol. 4). New York: Plenum] theory of willed and automatic action. Two strategies and a simple perceptual bias are implemented within the models and comparisons between model and child performance reveal a good fit for the key dependent measures (number of rule breaks and percentage of incomplete solutions) of the two groups