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Register a new userExtraction and Visualization of Poincare Map Topology for Spacecraft Trajectory Design
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Mission designers must study many dynamical models to plan a low-cost spacecraft trajectory that satisfies mission constraints. They routinely use Poincare maps to search for a suitable path through the interconnected web of periodic orbits and invariant manifolds found in multi-body gravitational systems. This paper is concerned with the extraction and interactive visual exploration of this structural landscape to assist spacecraft trajectory planning. We propose algorithmic solutions that address the specific challenges posed by the characterization of the topology in astrodynamics problems and allow for an effective visual analysis of the resulting information. This visualization framework is applied to the circular restricted three-body problem (CR3BP), where it reveals novel periodic orbits with their relevant invariant manifolds in a suitable format for interactive transfer selection. Representative design problems illustrate how spacecraft path planners can leverage our topology visualization to fully exploit the natural dynamics pathways for energy-efficient trajectory designs.
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We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed in [1,2]. The algorithms for computation of the time averages of observables on phase space are developed and used to provide an approximation of the ergodic partition of the phase space. We term the graphical representation of this approximation - based on time averages of observables - a Mesochronic Plot (from Greek: textit{meso} - mean, textit{chronos} - time}. The method is useful for identifying low-dimensional projections (e.g. two-dimensional slices) of invariant structures in phase spaces of dimensionality bigger than two. We also introduce the concept of the ergodic quotient space, obtained by assigning a point to every ergodic set, and provide an embedding method whose graphical representation we call the Mesochronic Scatter Plot (MSP). We use the Chirikov standard map as a well-known and dynamically rich example in order to illustrate the implementation of our methods. In addition, we expose applications to other higher dimensional maps such as the Froeschle map for which we utilize our methods to analyze merging of resonances and, the three-dimensional Extended standard map for which we study the conjecture on its ergodicity [3]. We extend the study in our next paper [4] by investigating the visualization of periodic sets using harmonic time averages. Both of these methods are related to eigenspace structure of the Koopman operator.
Among the mitigation measures introduced to cope with the space debris issue there is the de-orbiting of decommissioned satellites. Guidelines for re-entering objects call for a ground casualty risk no higher than 0.0001. To comply with this requirement, satellites can be designed through a design-for-demise philosophy. Still, a spacecraft designed to demise has to survive the debris-populated space environment for many years. The demisability and the survivability of a satellite can both be influenced by a set of common design choices such as the material selection, the geometry definition, and the position of the components. Within this context, two models have been developed to analyse the demise and the survivability of satellites. Given the competing nature of the demisability and the survivability, a multi-objective optimisation framework was developed, with the aim to identify trade-off solutions for the preliminary design of satellites. As the problem is nonlinear and involves the combination of continuous and discrete variables, classical derivative based approaches are unsuited and a genetic algorithm was selected instead. The genetic algorithm uses the developed demisability and survivability criteria as the fitness functions of the multi-objective algorithm. The paper presents a test case, which considers the preliminary optimisation of tanks in terms of material, geometry, location, and number of tanks for a representative Earth observation mission. The configuration of the external structure of the spacecraft is fixed. Tanks were selected because they are sensitive to both design requirements: they represent critical components in the demise process and impact damage can cause the loss of the mission because of leaking and ruptures. The results present the possible trade off solutions, constituting the Pareto front obtained from the multi-objective optimisation.
Visual representation of information is a fundamental tool for advancing our understanding of science. It enables the research community to extract new knowledge from complex datasets, and plays an equally vital role in communicating new results across a spectrum of public audiences. Visualizations which make research results accessible to the public have been popularized by the press, and are used in formal education, informal learning settings, and all aspects of lifelong learning. In particular, visualizations of astronomical data (hereafter astrovisualization or astroviz) have broadly captured the human imagination, and are in high demand. Astrovisualization practitioners need a wide variety of specialized skills and expertise spanning multiple disciplines (art, science, technology). As astrophysics research continues to evolve into a more data rich science, astroviz is also evolving from artists conceptions to data-driven visualizations, from two-dimensional images to three-dimensional prints, requiring new skills for development. Currently astroviz practitioners are spread throughout the country. Due to the specialized nature of the field there are seldom enough practitioners at one location to form an effective research group for the exchange of knowledge on best practices and new techniques. Because of the increasing importance of visualization in modern astrophysics, the fact that the astroviz community is small and spread out in disparate locations, and the rapidly evolving nature of this field, we argue for the creation and nurturing of an Astroviz Community of Practice. We first summarize our recommendations. We then describe the current make-up of astrovisualization practitioners, give an overview of the audiences they serve, and highlight technological considerations.
Background: It is possible to find many different visual representations of data values in visualizations, it is less common to see visual representations that include uncertainty, especially in visualizations intended for non-technical audiences. Objective: our aim is to rigorously define and evaluate the novel use of visual entropy as a measure of shape that allows us to construct an ordered scale of glyphs for use in representing both uncertainty and value in 2D and 3D environments. Method: We use sample entropy as a numerical measure of visual entropy to construct a set of glyphs using R and Blender which vary in their complexity. Results: A Bradley-Terry analysis of a pairwise comparison of the glyphs shows participants (n=19) ordered the glyphs as predicted by the visual entropy score (linear regression R2 >0.97, p<0.001). We also evaluate whether the glyphs can effectively represent uncertainty using a signal detection method, participants (n=15) were able to search for glyphs representing uncertainty with high sensitivity and low error rates. Conclusion: visual entropy is a novel cue for representing ordered data and provides a channel that allows the uncertainty of a measure to be presented alongside its mean value.
Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of supporting domain experts in handling, understanding, and trouble-shooting high-dimensional optimization with a large number of constraints. Leveraging visual analytics, users are supported in exploring the computation process of nonlinear constraint optimization. Our system was designed for robot motion planning problems and developed in tight collaboration with domain experts in nonlinear programming and robotics. We report on the experiences from this design study, illustrate the usefulness for relevant example cases, and discuss the extension to visual analytics for nonlinear programming in general.
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