New Worlds Observer Formation Control Design Based on the Dynamics of Relative Motion

The New Worlds Observer (NWO) mission is designed for the direct detection and characterization of extrasolar planets. The NWO mission concept employs a two spacecraft leader-follower formation on a trajectory around the Earth/Moon-Sun L(sub 2) Libration Point. The leader spacecraft is baselined as a 4 meter optical telescope. The follower, Starshade spacecraft, is designed to suppress light from a central body star permitting direct detection of a surrounding exoplanetary system. The current design requires a nominal leader-follower separation range of 72 Megameters. NWO poses many challenges including formation control. NWO cycles between three principal control modes during the nominal mission timeline: science (fine pointing), realignment and transition. This paper examines formation control strategies in the context of dynamics of relative motion for two spacecraft operating in the vicinity of the Earth/Moon-Sun L(sub 2)libration point. The paper presents an overview of the equations of relative motion followed by a discussion of each of the control modes. Discussion and analysis characterize control strategies for each of the mission control modes, including requirements, implementation challenges and project fuel budgets

Nature et rôle des inférences impliquées dans la résolution de problèmes mathématiques

La réalisation de ce projet a été rendue possible grâce à la bourse de maîtrise en recherche du Fonds de recherche du Québec – Société et culture (FQRSC), de même qu’à la bourse de doctorat du Programme de bourses d’études supérieures du Canada Joseph-Armand-Bombardier (CRSH).Dans le milieu des enseignants de mathématiques au secondaire, on entend souvent dire que les élèves ont de la difficulté à résoudre des problèmes « parce qu’ils ne savent pas lire ». Si l’on admet aisément l’existence d’un lien entre les habiletés en lecture et celles en résolution de problèmes, il importe d'examiner ce lien de façon systématique afin d’aller au-delà des idées reçues. Cette thèse s’intéresse donc au rôle de la lecture dans la résolution de problèmes mathématiques et, en particulier, à une composante-clé de la compréhension en lecture : les inférences. Différents modèles de la compréhension en lecture ont été explorés pour mieux discerner le rôle qu’y jouent les inférences. Il en ressort que, pour bien comprendre un texte, il faut s’en construire une représentation mentale appelée modèle de situation, dans la construction de laquelle les inférences jouent un rôle important. Plusieurs auteurs s’étant intéressés à la compréhension de problèmes mathématiques parlent également du modèle de situation – par opposition à une stratégie de traduction directe où l’élève ne fait que combiner, au fur et à mesure qu’ils apparaissent, les nombres et les mots-clés de l’énoncé – comme d’un facteur important dans la réussite en résolution de problèmes, sans toutefois aborder la question des inférences. Or, puisqu’elles interviennent dans la construction du modèle de situation, le fait de ne pas construire un tel modèle pourrait être lié à des lacunes dans les habiletés inférentielles ; c’est ce que nous avons voulu vérifier, de même que la nature des inférences impliquées dans la résolution de problèmes et le rôle qu’elles y jouent. Pour ce faire, différentes épreuves ont été administrées à 175 élèves québécois de 4e secondaire : habiletés inférentielles en lecture, résolution de problèmes mathématiques, tâche de rappel des énoncés desdits problèmes, et, pour certains élèves, une entrevue individuelle. Les données ainsi obtenues nous ont permis de tirer les conclusions suivantes. D’abord, il y a une corrélation positive entre le score obtenu en production d’inférences et celui en résolution de problèmes ; nous avons également déterminé quels types d’inférences étaient le plus fortement corrélés à la réussite en résolution de problèmes. Ensuite, puisque les inférences sont impliquées dans la construction d’un modèle de situation, nous avons voulu savoir si les élèves qui construisent un tel modèle réussissent mieux en production d’inférences que ceux utilisant une stratégie de traduction directe, ce qui fut le cas. Ces résultats nous permettaient de déceler des tendances générales en ce qui concerne la nature des inférences impliquées dans la résolution de problèmes mathématiques, mais nous avons voulu voir s’il était possible d’établir des profils d’élèves en combinant leurs habiletés inférentielles et leur stratégie privilégiée de résolution de problèmes. Nous avons ainsi pu identifier six profils ayant chacun des caractéristiques spécifiques. Finalement, nous avons analysé les données recueillies pour faire ressortir six rôles joués par les inférences dans la démarche de résolution d’un problème mathématique, de même que les moments auxquels des inférences étaient produites et le type d’inférence dans chacun des cas.Among high school mathematics teachers, it is a common conception that student have a hard time solving problems because « they don’t know how to read ». Although it seems common sense that a relation between reading abilities and problem solving abilities exists, it is nonetheless important to examine systematically this relation in order to go beyond popular belief. This thesis addresses this issue by exploring the role of reading comprehension in mathematical problem solving, focusing on inferences which are one of reading comprehension’s components. Various reading comprehension models have been explored in order to discern the role inferences play within this process. Most researchers agree that it is important, to understand a text properly, to build a situation model, which is a particular type of mental representation of the text, in the construction of which inferences play an important part. Many authors who studied mathematical problem comprehension also consider the construction of a situation model, as opposed to a direct translation strategy (which consists in combining numbers and keywords as they appear in the problem statement to get to a solution), as very important for succeeding in problem solving, although they don’t mention inferences. Since inferences play an important role in the situation model construction, the failure to construct the latter might be explained by a weakness in inference generation. That is what this research addresses, as well as the nature of the inferences that are involved in problem solving and their role in that process. To achieve this goal, we administered various tests to 175 secondary 4 students from the Province of Quebec: an inferential skills test, a problem solving test, a recall task about the problem statements, and, for some participants, an individual interview. The data thus obtained allowed us to draw the following conclusions. First of all, there is a positive correlation between the inference generation score and the problem solving score; we were even able to determine which types of inferences were more closely related to successful problem solving. Since inferences take part in the situation model construction, we wanted to know if the students who did build such a situation model got a better inference generation score than the students who mostly used a direct translation strategy, which they did. General conclusions on the nature of the inferences implied in mathematical problem solving were drawn from these results, but we also wanted to see if the data could lead to a more specific understanding of this relation. Therefore, we tried to establish student profiles by combining their inference generation abilities and their preferred problem solving strategy. We identified six different profiles, each with specific characteristics. Finally, we analyzed the problem solving and the interviews to highlight six different inference functions within the problem solving process, as well as the moments when inferences were used and the types of inferences involved, which let us to better understand and define these functions

Spacecraft Formation Control: Managing Line-of-Sight Drift Based on the Dynamics of Relative Motion

In a quest to improve space-based observational capability, an increasing number of investigators are proposing missions with precision formation flying architectures. Typical missions include the Micro- Arcsecond X-ray Imaging Mission (MAXIM), Stellar Imager (SI), and the New Worlds Observer (NWO). Missions designed to explore targets in deep-space generally require holding a formation configuration fixed in inertial space during science observation. Analysis in this paper is specifically aimed at the NWO architecture, characterizing the natural drift of the line-of-sight and the separation range for two spacecraft operating in the vicinity of the Earth/Moon-Sun L(sub 2) libration point. Analysis employs a linear form of the relative dynamics associated with an n-body gravity field. The study is designed to identify favorable observation directions, characterized by minimal line-of-sight drift, along the mission timeline

Recent Developments in Hardware-in-the-Loop Formation Navigation and Control

The Formation Flying Test-Bed (FFTB) at NASA Goddard Space Flight Center (GSFC) provides a hardware-in-the-loop test environment for formation navigation and control. The facility is evolving as a modular, hybrid, dynamic simulation facility for end-tc-end guidance, navigation, and control (GN&C) design and analysis of formation flying spacecraft. The core capabilities of the FFTB, as a platform for testing critical hardware and software algorithms in-the-loop, are reviewed with a focus on many recent improvements. Two significant upgrades to the FFTB are a message-oriented middleware (MOM) architecture, and a software crosslink for inter-spacecraft ranging. The MOM architecture provides a common messaging bus for software agents, easing integration, arid supporting the GSFC Mission Services Evolution Center (GMSEC) architecture via software bridge. Additionally, the FFTB s hardware capabilities are expanding. Recently, two Low-Power Transceivers (LPTs) with ranging capability have been introduced into the FFTB. The LPT crosslinks will be connected to a modified Crosslink Channel Simulator (CCS), which applies realistic space-environment effects to the Radio Frequency (RF) signals produced by the LPTs

Nonlinear Control Design Techniques For Precision Formation Flying At Lagrange Points

Precision spacecraft formation flying is an enabling technology for a variety of proposed space-based observatories, such as NASA's Terrestrial Planet Finder (TPF), the Micro-Arcsecond X-Ray Imaging Mission (MAXIM), and Stellar Imager (SI). This research specifically examines the precision formation flying control architecture, characterizing the relative performance of linear and nonlinear controllers. Controller design is based on a 6DOF control architecture, characteristic of precision formation flying control. In an effort to minimize the influence of design parameters in the comparison, analysis employs "equivalent" controller gains, and incorporates an integrator in the linear control design. Controller performance is evaluated through various simulations designed to reflect a realistic space environment. The simulation architecture includes a full gravitational model and solar pressure effects. Spacecraft model properties are based on realistic mission design parameters. Control actuators are modeled as a fixed set of thrusters for both translation and attitude control. Analysis includes impact on controller performance due to omitted dynamics in the model (gravitational sources and solar pressure) and model uncertainty (mass properties, thruster placement and thruster alignment). Linearized equations of relative motion are derived for spacecraft operating in the context of the Restricted Three Body Problem. Linearization is performed with respect to a reference spacecraft within the formation. Analysis demonstrates robust stability for the Linear Quadratic Regulator controller design based on the linearized dynamics. Nonlinear controllers are developed based on Lyapunov analysis, including both non-adaptive and adaptive designs. While the linear controller demonstrates greater robustness to model uncertainty, both nonlinear controllers exhibit superior performance. The adaptive controller provides the best performance. As a key feature, the adaptive controller design requires only relative navigation knowledge. Analysis demonstrates the ability of the nonlinear controller to compensate for unknown dynamics and model uncertainty. Results exhibit the potential of a nonlinear adaptive architecture for improving controller performance. Nonlinear adaptive control is a viable strategy for meeting the extreme control requirements associated with formation flying missions like MAXIM and Stellar Imager. Mission specific analysis from a systems perspective is required to determine the best controller design

Systems and methods for determining a spacecraft orientation

Disclosed are systems and methods of determining or estimating an orientation of a spacecraft. An exemplary system generates telemetry data, including star observations, in a satellite. A ground station processes the telemetry data with data from a star catalog, to generate display data which, in this example, includes observed stars overlaid with catalog stars. An operator views the display and generates an operator input signal using a mouse device, to pair up observed and catalog stars. Circuitry in the ground station then processes two pairs of observed and catalog stars, to determine an orientation of the spacecraft

BIC-seq: a fast algorithm for detection of copy number alterations based on high-throughput sequencing data

DNA copy number alterations (CNA), which are amplifications and deletions of certain regions in the genome, play an important role in the pathogenesis of cancer and have been shown to be associated with other diseases such as autism, schizophrenia and obesity

rSW-seq: Algorithm for detection of copy number alterations in deep sequencing data

Background Recent advances in sequencing technologies have enabled generation of large-scale genome sequencing data. These data can be used to characterize a variety of genomic features, including the DNA copy number profile of a cancer genome. A robust and reliable method for screening chromosomal alterations would allow a detailed characterization of the cancer genome with unprecedented accuracy. Results We develop a method for identification of copy number alterations in a tumor genome compared to its matched control, based on application of Smith-Waterman algorithm to single-end sequencing data. In a performance test with simulated data, our algorithm shows >90% sensitivity and >90% precision in detecting a single copy number change that contains approximately 500 reads for the normal sample. With 100-bp reads, this corresponds to a ~50 kb region for 1X genome coverage of the human genome. We further refine the algorithm to develop rSW-seq, (recursive Smith-Waterman-seq) to identify alterations in a complex configuration, which are commonly observed in the human cancer genome. To validate our approach, we compare our algorithm with an existing algorithm using simulated and publicly available datasets. We also compare the sequencing-based profiles to microarray-based results. Conclusion We propose rSW-seq as an efficient method for detecting copy number changes in the tumor genome.National Institute of General Medical Sciences (U.S.) (R01 GM082798

Formation Control for the MAXIM Mission

Over the next twenty years, a wave of change is occurring in the space-based scientific remote sensing community. While the fundamental limits in the spatial and angular resolution achievable in spacecraft have been reached, based on today s technology, an expansive new technology base has appeared over the past decade in the area of Distributed Space Systems (DSS). A key subset of the DSS technology area is that which covers precision formation flying of space vehicles. Through precision formation flying, the baselines, previously defined by the largest monolithic structure which could fit in the largest launch vehicle fairing, are now virtually unlimited. Several missions including the Micro-Arcsecond X-ray Imaging Mission (MAXIM), and the Stellar Imager will drive the formation flying challenges to achieve unprecedented baselines for high resolution, extended-scene, interferometry in the ultraviolet and X-ray regimes. This paper focuses on establishing the feasibility for the formation control of the MAXIM mission. MAXIM formation flying requirements are on the order of microns, while Stellar Imager mission requirements are on the order of nanometers. This paper specifically addresses: (1) high-level science requirements for these missions and how they evolve into engineering requirements; and (2) the development of linearized equations of relative motion for a formation operating in an n-body gravitational field. Linearized equations of motion provide the ground work for linear formation control designs

Estimating enrichment of repetitive elements from high-throughput sequence data

We describe computational methods for analysis of repetitive elements from short-read sequencing data, and apply them to study histone modifications associated with the repetitive elements in human and mouse cells. Our results demonstrate that while accurate enrichment estimates can be obtained for individual repeat types and small sets of repeat instances, there are distinct combinatorial patterns of chromatin marks associated with major annotated repeat families, including H3K27me3/H3K9me3 differences among the endogenous retroviral element classes