Process algebra can provide spacecraft designers with a mathematical formalism for specifying, understanding, analyzing, and verifying spacecraft system behavior. Although it is standard practice to mathematically model and analyze the subsystems of a spacecraft to ensure that they will function correctly when built, the system-level behavior of the spacecraft is generally understood in much less rigorous terms. This leaves the spacecraft system vulnerable to design errors which may not become apparent until the integration and test phase, when design changes are most expensive. In this dissertation, we develop a formal approach to engineering spacecraft behavior, based on mathematical models of behavior expressed using the process algebra Communicating Sequential Processes. This new approach to spacecraft behavior is intended to help spacecraft systems engineers to model and analyze proposed spacecraft system designs in a rigorous manner, and to detect subtle specification and design errors earlier in the design process than the errors would otherwise be found.

This thesis focuses on practical methods for constructing robust nonlinear control systems. In general, the development of such control systems is characterized by the solution to one or more Hamilton-Jacobi partial differential equations (HJE). However, no general analytical solution has yet been obtained to solve this optimization problem. Solutions have thus far only been obtained under certain conditions. Therefore, the first significant contribution of this thesis is a method for obtaining analytical expressions for approximate solutions to a common form of HJE (under certain assumptions regarding the class of nonlinear systems used). Additionally, modern state space controller synthesis techniques typically result in state estimators of equal or greater dimension than the plant model. However, it is often desirable, or even necessary, to approximate these controllers by models of lower state dimension. Presently, methods for developing nonlinear state balancing transformations are not very well understood. Therefore, the second significant contribution of this thesis is a proper algorithm for the application of state balancing techniques to nonlinear control systems and the subsequent reduction of the number of control states. The method to be developed for state balancing is based on the above framework for constructing analytical solutions to the HJE. In this thesis we will make use of three existing robust nonlinear control methods from the literature. These three methods have the advantage that they can all be constructed from solutions to a single form of HJE. Thus, by developing a method for obtaining analytical expressions for the solution to a single form of HJE, we are able to develop explicit polynomial solutions for each of these three control methods. Due to the difficulties associated with quantifying robustness and performance properties for nonlinear systems, the effectiveness of the three control methods considered shall be demonstrated via numerical simulations. The particular applications of interest to us here are space systems. First, we will consider the attitude control of a single spacecraft. Second, we examine the problem of formation flying control for a pair of spacecraft. The third and final problem we consider is the control of a nonlinear mass-spring chain.

This thesis explores the problems associated with an individual's interpretation of historical events; especially through a question such as "Where were you when you heard the news of the Challenger explosion?" Remembering an event in this manner implies that both a physical and temporal distance exists between an individual watching from afar and the event in question. This distance indicates that the event is never transparent nor is its meaning self-evident; it unfolds over time and is rendered almost incomprehensible through the proliferation of language and discourse surrounding the event, the fragmentary nature of its remnants, and the fallibility of both individual memory and the historical record. But instead of making the event meaningless, notions of 'distance' and 'incomprehensibility' provide a space where an event's meaning is most understandable for an individual. Beginning with Wittgenstein's Tractatus and ending with Barthes' A Lover's Discourse, I would like to show how little separates the philosopher attempting to understand the world, the historian interpreting the historical record, the amorous subject deciphering the signs and gestures of an absent or unattainable lover, and the individual remembering a historical event.

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Tensegrity is the name given to a system of interconnected bars and tendons that can form a flexible self-standing structure. Its flexibility is due to the ability of the bars to move near-independent to each other, movement that can be caused by controlled tension forces in the tendons or external forces such as gravity. However, a balance of sorts must be maintained - if a tendon were to go slack, the entire structure could become unstable and collapse on itself. This thesis looks at placing a tensegrity structure in orbit around the Earth. As a spacecraft's orbit is moved further away from the Earth, the strength of the Earth's gravity field lessens. Ideally, such a flexible structure would be placed far enough away from the Earth so that the gravity field would have too weak an impact on its individual elements to cause major distortions. However, the author recognizes that altitudes below 2,000 km, where the Earth's gravity field is still very prevalent, are the most common altitudes used by orbiting spacecraft today. The goal of this thesis is to analyze the distortions of the tensegrity structure at these lower altitudes, and also look at methods for controlling these distortions. / Ph. D.

In this dissertation the linearized dynamics and stability of a two-craft Coulomb tether formation are investigated. With a Coulomb tether the relative distance between two satellites is controlled using electrostatic Coulomb forces. A charge feedback law is introduced to stabilize the relative distance between the satellites to a constant value. Compared to previous Coulomb thrusting research, this is the first feedback control law that stabilizes a particular formation shape. The two craft are connected by an electrostatic virtual tether that essentially acts as a long, slender near-rigid body. Inter-spacecraft Coulomb forces cannot influence the inertial angular momentum of this formation. However, the differential gravitational attraction can be exploited to stabilize the attitude of this Coulomb tether formation about an orbit nadir direction. Stabilizing the separation distance will also stabilize the in-plane rotation angle, while the out-of-plane rotational motion remains unaffected. The other two relative equilibriums of the charged 2-craft problem are along the orbit-normal and the along-track direction. Unlike the charged 2-craft formation scenario aligned along the orbit radial direction, a feedback control law using inter-spacecraft electrostatic Coulomb forces and the differential gravitational accelerations is not sufficient to stabilize the Coulomb tether length and the formation attitude. Therefore, hybrid feedback control laws are presented which combine conventional thrusters and Coulomb forces. The Coulomb force feedback requires measurements of separation distance error and error rate, while the thruster feedback is in terms of Euler angles and their rates. This hybrid feedback control is designed to asymptotically stabilize the satellite formation shape and attitude while avoiding plume impingement issues. The relative distance between the two satellites can be increased or decreased using electrostatic Coulomb forces. The linear dynamics and stability analysis of such reconfiguration are studied for all the three equilibrium. The Coulomb tether expansion and contraction rates affect the stability of the structure and limits on these rates are discussed using the linearized time-varying dynamical models. These limits allow the reference length time histories to be designed while ensuring linear stability of the virtual structure. Throughout this dissertation the Coulomb tether is modeled as a massless, elastic component and, a point charge model is used to describe the charged craft. / Ph. D.

<div> <div> <div> <p>A control methodology to design and establish spacecraft formations is presented. The intuitive design of complex spacecraft formation geometry is achieved by utilizing two different sets of relative orbital elements derived from a linearization of the dynamics. These sets provide strong insights into the shape, size, and orientation of the relative trajectory and facilitate the design of relative orbits in addition to relative positions. An artificial potential function (APF) composed of an attractive potential for goal seeking and a repulsive potential for obstacle avoidance is constructed. The derivation of a control law from this APF results in a computationally efficient algorithm able to fully control the relative position and velocity of the spacecraft and therefore to establish spacecraft formations. The autonomous selection of some of the design parameters of the model based on fuel minimization considerations is described. An assessment of the formation establishment accuracy is conducted for different orbital perturbation as well as various degrees of thrust errors and state uncertainties. Then, the performance of the control algorithm is demonstrated with the numerical simulation of four different scenarios. The first scenario is the design and establishment of a 10-spacecraft triangular lattice, followed by the establishment of a 37-spacecraft formation composed of two hexagonal lattices on two different relative planes. The control method is used to illustrate proximity operations with the visual inspection of an on-orbit structure in the third scenario. Finally, a formation composed of four spacecraft arranged in a tetrahedron is presented.<br></p> </div> </div> </div>

International Telemetering Conference Proceedings / October 20-23, 2003 / Riviera Hotel and Convention Center, Las Vegas, Nevada / The Consultative Committee for Space Data Systems (CCSDS) is an international organization of national space agencies that is branching out to provide new standards to enhanced reuse of spacecraft equipment and software. These Spacecraft Onboard Interface (SOIF) standards will be directed towards a spacecraft architecture, as a distributed system of processors and busses. This paper will review the services that are being proposed for SOIF. These services include a Command and Data Acquisition Service, a Time Distribution Service, a Message Transfer Service, a File Transfer Service, and a CCSDS Packet Service. An Instrument & Subsystem “Plug & Play Service is currently under study, but is included in this paper for completeness.

The problem of system identification for dynamic effects on spacecraft has become increasingly relevant with the surge of agile spacecraft, which must perform large amplitude maneuvers at high rates. Precise knowledge of the state of the spacecraft, as well as of the parameters characterizing its motion, is vital for the design of control algorithms enabling stabilization and pointing accuracy. Traditional rigid body models and estimation methods are no longer sufficient to provide this knowledge. This thesis focuses on estimation of flexibility effects and spacecraft parameters through methods based on the unscented Kalman filter, an estimator for nonlinear dynamic systems. A spacecraft model consisting of a rigid central body and a flexible appendage described as an Euler-Bernoulli beam in pure bending is built, and equations for its translational and rotational motion, as well as the deflection of the beam, are derived in the Newton-Euler framework considering the first bending mode of the flexible deformation. Observability tests are successfully conducted to ensure that estimation of the relevant states and parameters can be performed exclusively from linear and angular velocity measurements. A total of eight filters, estimating the spacecraft’s state along with different combinations of parameters, are developed, implemented, and tested on simulated data. Grouped under the common denomination “UFFE” (Unscented Filter for Flexibility Effects), they are made available as Simulink library blocks. State estimation is performed for the linear and angular velocities of the spacecraft and the modal coordinate and velocity of the appendage, with estimates following closely the truth model of the state variables and estimation errors at least an order of magnitude lower than true state values. Simultaneous state and parameter estimation is implemented from two approaches, joint estimation and dual estimation, whose performance and applications are compared. Estimated parameters include the moments of inertia of the system and natural frequency, damping ratio, and modal participation factors of the flexible appendage. Convergence to true parameter values is reached in the first 100s of the estimation for inertia terms and natural frequency, while the estimation for modal participation factors is conditioned to precise tuning of the filter. Estimates of the damping ratio are biased, most likely due to the control input not being optimal for observation of this parameter. The dual approach to parameter estimation is found to be advantageous when proper filter tuning is possible, as it enables the continuous operation of a state filter combined with short runs of the parameter filter activated at will; this configuration could be employed to track the variation of spacecraft parameters along space missions.  The causes of estimation error are identified and methods for automatic tuning of the process noise and process noise covariance are researched. Five such tuning techniques are implemented and tested, with promising results found for online sampling of the process noise covariance through Monte Carlo methods. A discussion on the limitations of the chosen dynamic model and estimator, along with recommendations for extensions and future applications, concludes this work.

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