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A new identification of groups and clusters in the CfA1 Catalog of Huchra et al. is presented, using a percolation algorithm to identify density enhancements. It is shown that in the resulting catalog, contamination by interlopers is significantly reduced. The Schechter luminosity function is redetermined, including the Malmquist bias.
Through various specially designed numerical experiments with an aqua-planet general circulation model and theoretical arguments. Chao showed the existence of multiple quasi-equilibria of the intertropical convergence zone (ITCZ). He also showed that monsoon onset could be interpreted as an abrupt transition between the quasi-equilibria of the ITCZ. He further showed that the origin of these quasi-equilibria is related to two different types of attraction pulling the ITCZ in opposite directions. One type of attraction on the ITCZ is due to earth's rotation, which pulls the ITCZ toward the equator or two equatorial latitudes symmetric with respect to the equator depending on the choice of convection scheme, and the other due to the peak of the sea surface temperature (SST, which is given in the experiments a Gaussian profile in latitude and is uniform in longitude), which pulls the ITCZ toward a latitude just poleward of the SST peak. The strength of the attraction due to the earth's rotation has a highly nonlinear dependence on the latitude and that due to the SST peak has a linear (at least in a relative sense) dependence on the latitude.
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The results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. This paper is concerned with the asymptotic nonlinear dynamics at the dissipation parameter decreases and spatio-temporal chaos sets in. To this end the initial condition is taken to be the same for all numerical experiments (a single sine wave is used) and the large time evolution of the system is followed numerically. Numerous computations were performed to establish the existence of windows, in parameter space, in which the solution has the following characteristics as the viscosity is decreased: a steady fully modal attractor to a steady bimodal attractor to another steady fully modal attractor to a steady trimodal attractor to a periodic attractor, to another steady fully modal attractor, to another periodic attractor, to a steady tetramodal attractor, to another periodic attractor having a full sequence of period-doublings (in parameter space) to chaos. Numerous solutions are presented which provide conclusive evidence of the period-doubling cascades which precede chaos for this infinite-dimensional dynamical system. These results permit a computation of the length of subwindows which in turn provide an estimate for their successive ratios as the cascade develops. A calculation based on the numerical results is also presented to show that the period doubling sequences found here for the Kuramoto-Sivashinsky equation, are in complete agreement with Feigenbaum's universal constant of 4,669201609... . Some preliminary work shows several other windows following the first chaotic one including periodic, chaotic, and a steady octamodal window; however, the windows shrink significantly in size to enable concrete quantitative conclusions to be made.
The results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. This paper is concerned with the asymptotic nonlinear dynamics at the dissipation parameter decreases and spatio-temporal chaos sets in. To this end the initial condition is taken to be the same for all numerical experiments (a single sine wave is used) and the large time evolution of the system is followed numerically. Numerous computations were performed to establish the existence of windows, in parameter space, in which the solution has the following characteristics as the viscosity is decreased: a steady fully modal attractor to a steady bimodal attractor to another steady fully modal attractor to a steady trimodal attractor to a periodic attractor, to another steady fully modal attractor, to another periodic attractor, to a steady tetramodal attractor, to another periodic attractor having a full sequence of period-doublings (in parameter space) to chaos. Numerous solutions are presented which provide conclusive evidence of the period-doubling cascades which precede chaos for this infinite-dimensional dynamical system. These results permit a computation of the length of subwindows which in turn provide an estimate for their successive ratios as the cascade develops. A calculation based on the numerical results is also presented to show that the period doubling sequences found here for the Kuramoto-Sivashinsky equation, are in complete agreement with Feigenbaum's universal constant of 4,669201609 .... Some preliminary work shows several other windows following the first chaotic one including periodic, chaotic, and a steady octamodal window; however, the windows shrink significantly in size to enable concrete quantitative conclusions to be made.
Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.
Recently, system theorists have recognized that low order systems of nonlinear differential equations can give rise to solutions which are neither periodic, constant, nor predictable in steady state, but which are nonetheless bounded and deterministic. This behavior, which was first described in the study of weather systems, has been termed 'chaotic.' Much study of chaotic systems has concentrated on analysis of the systems' phase space attractors. It has been recognized that invariant measures of the attractor possess inherent information about the system. One such measure is the dimension of the attractors. The dimension of a chaotic attractor has been shown to be noninteger, leading to the term 'strange attractor;' the attractor is said to have a fractal structure. The correlation dimension has become one of the most popular measures of dimension. However, many problems have been identified in correlation dimension estimation from time sequences. The most common methods for obtaining the correlation dimension have been least squares curves fitting to find the slope of the correlation integral and the Takens Estimator. However, these estimates show unacceptable sensitivity to the upper limit on the distance chosen. Here, a new method is proposed which is shown to be rather insensitive to the upper limit and to perform in a very stable manner, at least in the absence of noise. The correlation dimension is also shown to be an effective discriminant in distinguishing between radar returns resulting from weather and those from the ground. The weather returns are shown to have a correlation dimension generally between 2.0 and 3.0, while ground returns have a correlation dimension exceeding 3.0.
A dynamical systems approach is used to quantify the instantaneous and time-averaged predictability of a low-order moist general circulation model. Specifically, the effects on predictability of incorporating an active ocean circulation, implementing annual solar forcing, and asynchronously coupling the ocean and atmosphere are evaluated. The predictability and structure of the model attractors is compared using the Lyapunov exponents, the local divergence rates, and the correlation, fractal, and Lyapunov dimensions. The Lyapunov exponents measure the average rate of growth of small perturbations on an attractor, while the local divergence rates quantify phase-spatial variations of predictability. These local rates are exploited to efficiently identify and distinguish subtle differences in predictability among attractors. In addition, the predictability of monthly averaged and yearly averaged states is investigated by using attractor reconstruction techniques.
As autonomous systems continue to grow both in use and complexity, the necessity for robust and extensible simulation-to-flight frameworks is paramount for establishing an effective architecture for autonomous systems. Hardware test flights are time-consuming and cost prohibitive during early system design and development. Simulation environments can be useful tools to accelerate algorithm development and testing. However, transitions from simulation to flight (sim-to-flight) can be challenging, unless systems are designed with this transition in mind and with the necessary capabilities built into the architecture and framework. One of the objectives of Autonomy Teaming and TRAjectories for Complex Trusted Operational Reliability (ATTRACTOR) was to design and develop a distributed mixed-reality simulation environment to begin establishing a basis for certification of autonomous systems via research into trust and trustworthiness. ATTRACTOR’s objective was to construct computational concepts of trustworthiness and justifiable trust in multi-agent autonomous teams, to inform future certification of safety-critical and time-critical autonomous systems in aviation. In this paper, we present an autonomous systems architecture and development framework paired with a persistent distributed modeling and simulation (ModSim) environment for test and evaluation of autonomous systems. They were designed under ATTRACTOR in order to measure and establish trustworthiness and trust in single-and multi-agent human-machine systems whether these machines are fixed-wing general aviation, rotary-wing Unmanned Aerial Vehicles (UAVs), ground rovers, or even spacecraft. The Autonomous Entity Operational Network (AEON) framework enables autonomous system development with an easily extensible collection of libraries and plug-n-play nodes facilitated by the Data Distribution Service (DDS) communication protocol standard. The Baseline Environment for Autonomous Modeling (BEAM) simulation environment is a distributed mixed-reality Unity™-based environment built around the same DDS communication paradigm allowing for easy integration with AEON-based autonomous applications, enabling sim-to-flight with minimal configuration changes. Using AEON and BEAM, source code that runs in simulation ports directly to hardware and has successfully flown in the National Airspace System (NAS) at NASA LaRC many times over the lifetime of ATTRACTOR.
This paper presents a dynamic study of the Wildwood Pendulum, a commercially available desktop system which exhibits a strange attractor. The purpose of studying this chaotic pendulum is twofold: to gain insight in the paradigmatic approach of modeling, simulating, and determining chaos in nonlinear systems; and to provide a desktop model of chaos as a visual tool. For this study, the nonlinear behavior of this chaotic pendulum is modeled, a computer simulation is performed, and an experimental performance is measured. An assessment of the pendulum in the phase plane shows the strange attractor. Through the use of a box-assisted correlation dimension methodology, the attractor dimension is determined for both the model and the experimental pendulum systems. Correlation dimension results indicate that the pendulum and the model are chaotic and their fractal dimensions are similar.
Solar flux F(sub 10.7) directly affects the atmospheric density, thereby changing the lifetime and prediction of satellite orbits. For this reason, accurate forecasting of F(sub 10.7) is crucial for orbit determination of spacecraft. Our attempts to model and forecast F(sub 10.7) uncovered highly entangled dynamics. We concluded that the general lack of predictability in solar activity arises from its nonlinear nature. Nonlinear dynamics allow us to predict F(sub 10.7) more accurately than is possible using stochastic methods for time scales shorter than a characteristic horizon, and with about the same accuracy as using stochastic techniques when the forecasted data exceed this horizon. The forecast horizon is a function of two dynamical invariants: the attractor dimension and the Lyapunov exponent. In recent years, estimation of the attractor dimension reconstructed from a time series has become an important tool in data analysis. In calculating the invariants of the system, the first necessary step is the reconstruction of the attractor for the system from the time-delayed values of the time series. The choice of the time delay is critical for this reconstruction. For an infinite amount of noise-free data, the time delay can, in principle, be chosen almost arbitrarily. However, the quality of the phase portraits produced using the time-delay technique is determined by the value chosen for the delay time. Fraser and Swinney have shown that a good choice for this time delay is the one suggested by Shaw, which uses the first local minimum of the mutual information rather than the autocorrelation function to determine the time delay. This paper presents a refinement of this criterion and applies the refined technique to solar flux data to produce a forecast of the solar activity.
This paper presents and discusses physical models for simulating some aspects of neural intelligence, and, in particular, the process of cognition. The main departure from the classical approach here is in utilization of a terminal version of classical dynamics introduced by the author earlier. Based upon violations of the Lipschitz condition at equilibrium points, terminal dynamics attains two new fundamental properties: it is spontaneous and nondeterministic. Special attention is focused on terminal neurodynamics as a particular architecture of terminal dynamics which is suitable for modeling of information flows. Terminal neurodynamics possesses a well-organized probabilistic structure which can be analytically predicted, prescribed, and controlled, and therefore which presents a powerful tool for modeling real-life uncertainties. Two basic phenomena associated with random behavior of neurodynamic solutions are exploited. The first one is a stochastic attractor ; a stable stationary stochastic process to which random solutions of a closed system converge. As a model of the cognition process, a stochastic attractor can be viewed as a universal tool for generalization and formation of classes of patterns. The concept of stochastic attractor is applied to model a collective brain paradigm explaining coordination between simple units of intelligence which perform a collective task without direct exchange of information. The second fundamental phenomenon discussed is terminal chaos which occurs in open systems. Applications of terminal chaos to information fusion as well as to explanation and modeling of coordination among neurons in biological systems are discussed. It should be emphasized that all the models of terminal neurodynamics are implementable in analog devices, which means that all the cognition processes discussed in the paper are reducible to the laws of Newtonian mechanics.
As autonomous systems continue to grow both in use and complexity, the necessity for robust and extensible simulation-to-flight methods is paramount for establishing an effective architecture for autonomous systems. A fundamental objective of the ATTRACTOR (Autonomy Teaming and TRAjectories for Complex Trusted Operational Reliability) project was to design and develop a distributed mixed-reality simulation environment to begin establishing a basis for certification of autonomous systems via research into trust and trustworthiness. In this paper, we present an autonomous systems architecture and development framework paired with a persistent distributed modeling and simulation environment for test and evaluation of autonomous systems. The Autonomous Entity Operations Network (AEON) framework enables autonomous system development with an easily extensible collection of libraries and plug-n-play nodes facilitated by the Data Distribution Service (DDS) communication protocol standard. The Baseline Environment for Autonomous Modeling (BEAM) simulation environment is a distributed mixed-reality Unity™-based environment built around the same DDS communication paradigm allowing for easy integration with AEON-based autonomous applications. They were designed under ATTRACTOR in order to measure and establish trustworthiness and trust in single- and multi-agent human-machine systems whether these machines are fixed-wing general aviation, rotary-wing Unmanned Aerial Vehicles (UAVs), ground rovers, or even spacecraft. Together AEON and BEAM enable sim-to-flight with minimal configuration changes. By using AEON and BEAM, source code that runs in simulation ports directly to hardware and has successfully flown in the lab and in the National Airspace System (NAS) at NASA LaRC many times over the lifetime of ATTRACTOR.
In support of the Autonomy Teaming and TRAjectories for Complex Trusted Operational Reliability (ATTRACTOR) project, a fleet of unmanned ground vehicles (UGVs) was developed as a test and evaluation (T\&E) platform to reduce system integration gaps between simulation and live flight hardware. While simulation and hardware-in-the-loop bench testing provide adequate environments for preliminary validation, differences in system deployment architecture, software interfaces, and hardware infrastructure increase the risks to safety, property, and the project. Given ATTRACTOR’s goal of establishing a basis of certification of trust and trustworthiness in multi-agent autonomous systems, bridging these gaps was critical to successful project execution and feasibility assessment. In this paper we present the UGV fleet and its role in speeding up system integration, smoothing the transition from simulation to flight, and providing researchers an easy-to-use hardware test bed. An overview of the hardware and software on-board the vehicles is provided along with supporting infrastructure. The system integration process is documented including results in supporting both the overarching design reference mission (DRM) of ATTRACTOR and individual research efforts conducted since the creation of the fleet. Finally, we discuss the practical lessons learned regarding the testing, deployment, and operation of multi-agent autonomous systems.
As autonomous systems continue to grow both in use and complexity, the necessity for robust and extensible simulation-to-flight methods is paramount for establishing an effective architecture for autonomous systems. A fundamental objective of the ATTRACTOR (Autonomy Teaming and TRAjectories for Complex Trusted Operational Reliability) project was to design and develop a distributed mixed-reality simulation environment to begin establishing a basis for certification of autonomous systems via research into trust and trustworthiness. In this paper, we present an autonomous systems architecture and development framework paired with a persistent distributed modeling and simulation environment for test and evaluation of autonomous systems. The Autonomous Entity Operations Network (AEON) framework enables autonomous system development with an easily extensible collection of libraries and plug-n-play nodes facilitated by the Data Distribution Service (DDS) communication protocol standard. The Baseline Environment for Autonomous Modeling (BEAM) simulation environment is a distributed mixed-reality Unity™-based environment built around the same DDS communication paradigm allowing for easy integration with AEON-based autonomous applications. They were designed under ATTRACTOR in order to measure and establish trustworthiness and trust in single- and multi-agent human-machine systems whether these machines are fixed-wing general aviation, rotary-wing Unmanned Aerial Vehicles (UAVs), ground rovers, or even spacecraft. Together AEON and BEAM enable sim-to-flight with minimal configuration changes. By using AEON and BEAM, source code that runs in simulation ports directly to hardware and has successfully flown in the lab and in the National Airspace System (NAS) at NASA LaRC many times over the lifetime of ATTRACTOR.
The demands of traditional industrial robotics differ significantly from those of remote, supervised operations in hostile environments, such as operations in space. While industry requires robots that can perform repetitive tasks with precision and speed, the space environment needs robots to cope with uncertainties, dynamics, and communication delays or interruptions, similar to human astronauts. These demands make a well-suited application for compliant robotics and behavior-based programming. Pose Target Wrench Limiting (PTWL) is a compliant behavior paradigm developed specifically to meet these demands. PTWL controls a robot by moving a virtual attractor to a target pose. The attractor applies virtual forces, based on stiffness and damping presets, to an underlying admittance controller. Guided by virtual forces, the robot will follow the attractor until safety conditions are violated or success criteria are met. PTWL was tested on a variety of quasi-static and dynamic tasks that may be useful for future space operations. Results demonstrate that PTWL is a powerful tool. It makes teleoperation easy and safe for a wide range of quasi-static tasks. It also facilitates the creation of semi-autonomous state machines that can reliably complete complex tasks with minimal human intervention.
The demands of traditional industrial robotics differ significantly from those of space robotics. While industry requires robots that can perform repetitive tasks with precision and speed, the space environment needs robots to cope with uncertainties, dynamics, and communication delays or interruptions, similar to human astronauts. These demands make a well-suited application for compliant robotics and behavior-based programming. Pose Target Wrench Limiting (PTWL) is a compliant behavior paradigm developed specifically to meet these demands. PTWL controls a robot by moving a virtual attractor to a target pose. The attractor applies virtual forces, based on stiffness and damping presets, to an underlying admittance controller. Guided by virtual forces, the robot will follow the attractor until safety conditions are violated or success criteria are met. We tested PTWL on a variety of quasi-static tasks that may be useful for future space operations. Our results demonstrate that PTWL is an extremely powerful tool. It makes teleoperation easy and safe for a wide range of quasi-static tasks. It also facilitates the creation of semi-autonomous state machines that can reliably complete complex tasks with minimal human intervention.
Establishing a basis for certification of autonomous systems using trust and trustworthiness is the focus of Autonomy Teaming and TRAjectories for Complex Trusted Operational Reliability (ATTRACTOR). The Human-Machine Interface (HMI) team is working to capture and utilize the multitude of ways in which humans are already comfortable communicating mission goals and translate that into an intuitive mission planning interface. Several input/output modalities (speech/audio, typing/text, touch, and gesture) are being considered and investigated in the context human-machine teaming for the ATTRACTOR design reference mission (DRM) of Search and Rescue or (more generally) intelligence, surveillance, and reconnaissance (ISR). The first of these investigations, the Human Informed Natural-language GANs Evaluation (HINGE) data collection effort, is aimed at building an image description database to train a Generative Adversarial Network (GAN). In addition to building an image description database, the HMI team was interested if, and how, modality (spoken vs. written) affects different aspects of the image description given. The results will be analyzed to better inform the designing of an interface for mission planning.