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. / 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 nearindependent 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.

The problem of reorienting a spacecraft to acquire a moving target is investigated. The spacecraft is modeled as a rigid body with N axisymmetric wheels controlled by axial torques, and the kinematics are represented by Modified Rodriques Parameters. The trajectory, denoted the reference trajectory, is one generated by a virtual spacecraft that is identical to the actual spacecraft. The open-loop reference attitude, angular velocity, and angular acceleration tracking commands are constructed so that the solar panel vector is perpendicular to the sun vector during the tracking maneuver. We develop a nonlinear feedback tracking control law, derived from Lyapunov stability and control theory, to provide the control torques for target tracking. The controller makes the body frame asymptotically track the reference motion when there are initial errors in the attitude and angular velocity. A spacecraft model, based on the X-ray Timing Explorer spacecraft, is used to demonstrate the effectiveness of the Lyapunov controller in tracking a given target. / Master of Science

Attitude determination and estimation algorithms are developed and implemented in simulation for the Exocube satellite currently under development by PolySat at Cal Poly. A mission requirement of ±5˚ of attitude knowledge has been flowed down from the NASA Goddard developed payload, and this requirement is to be met with a basic sensor suite and the appropriate algorithms. The algorithms selected in this work are TRIAD and an Extended Kalman Filter, both of which are placed in a simulation structure along with models for orbit propagation, spacecraft kinematics and dynamics, and sensor and reference vector models. Errors inherent from sensors, orbit position knowledge, and reference vector generation are modeled as well. Simulations are then run for anticipated dynamic states of Exocube while varying parameters for the spacecraft, attitude algorithms, and level of error. The nominal case shows steady state convergence to within 1˚ of attitude knowledge, with sensor errors set to 3.5˚ and reference vector errors set to 2˚. The algorithms employed have their functionality confirmed with the use of STK, and the simulations have been structured to be used as tools to help evaluate attitude knowledge capabilities for the Exocube mission and future PolySat missions.

In the present work, two numerical tools are under scrutiny. Both were made to study the atmospheric re-entry of a spacecraft: DEBRISK computes the trajectory and the survivability of the spacecraft as well as its fragments, and ELECTRA calculates the trajectory of the spacecraft and its fragments, as well as the associated on-ground risk of human casualty. However, they differ in some of their functionalities and their physical models, leading to a difference in the trajectories, thus in the impact points locations for the same spacecraft. This work has multiple purposes. First, the influence of several simulation parameters are studied in both tools in order to determine a correction law for the trajectory of the spacecraft in ELECTRA, making it imitate the DEBRISK trajectory. To do so, a large dataset is built then manipulated, and a verification process is realised to quantify the accuracy of the correction law. Successive iterations of the method show a decent improvement in the ELECTRA trajectory, yet uncertainties around the correction and the low applicability of the law lead to try a new promising method based on a live data reading of the flight parameters from DEBRISK to ELECTRA. Finally, the influence of the shielding of the buildings on the human casualty risk computation, symbolised by a protection coefficient in ELECTRA is studied. Results show that considering this, protection coefficients can multiply up by five the risk of casualty. A technical documentation was written for potential future works on the same subject. / I detta arbete studeras två numeriska verktyg som utformats för att studera det atmosfäriska återinträdet av en rymdfarkost: DEBRISK beräknar rymdfarkostens bana och överlevnadsförmåga såväl som dess fragment, och ELECTRA beräknar rymdfarkostens bana och dess fragment, samt tillhörande risk för olycksfall på marken. De skiljer sig åt i vissa av sina funktioner och sina fysiska modeller, vilket leder till skillnader i banorna, alltså i nedslagspunkterna för samma rymdfarkost. Detta arbete har flera syften. Först studeras påverkan av flera simuleringsparametrar i båda verktygen för att bestämma en korrigeringslag för rymdfarkostens bana i ELECTRA, vilket gör att den imiterar DEBRISK-banan. För att göra detta byggs en stor datamängd som sedan manipuleras, och en verifieringsprocess realiseras för att kvantifiera korrigeringslagens korrekthet. Successiva iterationer av metoden visar en viss förbättring av ELECTRA-banan, men osäkerhet kring korrigeringen och den låga tillämpligheten av lagen leder till att en ny lovande metod, baserad på en direkt dataavläsning av flygparametrarna från DEBRISK till ELECTRA, provats. Slutligen studeras inverkan av avskärmningen av byggnaderna på riskberäkningen av mänskliga olyckor, symboliserad med en skyddskoefficient i ELECTRA. Resultaten visar att med tanke på detta kan skyddskoefficienter multiplicera upp med en faktor fem risken för olyckor. En teknisk dokumentation skrevs för potentiella framtida arbeten om samma ämne.

This dissertation investigates attitude transition maneuvers of a gyrosat-satellite between relative equilibria. The primary challenge in transitioning between relative equilibria is the proper adjustment of the system angular momentum so that upon completing the transition maneuver the gyrostat-satellite will satisfy all the requirements for a relative equilibrium. The system angular momentum is a function of the attitude trajectory taken during the transition maneuver. A new concept, the constant orbital momentum equilibrium trajectory or COMET, is introduced as a means to a straight-forward solution to a subset of the possible transitions between relative equilbria. COMETs are a class of paths in SO(3) that a gyrostat-satellite may travel along that maintain a constant system angular momentum. The primary contributions of this dissertation are the introduction and analysis of COMETs and their application to the problem of transitioning a gyrostat-satellite between two relative equilibria. The current work introduces, defines, and analyzes COMETs in detail. The requirements for a path in SO(3) to be a COMET are defined. It is shown via example that COMETs are closed-curves in SO(3). Visualizations of families of COMETs are presented and discussed in detail. A subset of COMETs are shown to contain critical points that represent isolated relative equilibrium attitudes or furcations of the COMET. The problem of transitioning between two relative equilibria is split into the sub-problems of transitioning between relative equilibria on the same COMET and transitioning between relative equilibria on different COMETs. For transitions between relative equilibria on the same COMET, an open-loop control law is developed that drives a gyrostat-satellite along the COMET until the target relative equilibrium is reached. For transitions between relative equilibria on different COMETs, an open-loop control law is developed that transfers a gyrostat-satellite from the initial relative equilibrium to a relative equilibrium that resides on the same COMET as the target relative equilbrium. Acquisition of the target relative equilibrium is then accomplished via the application of the open-loop control law for transitions between relative equilibria on the same COMET. The results of numeric simulations of gyrostat-satellites executing these transitions are presented. / Ph. D.

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.

abstract: It remains unquestionable that space-based technology is an indispensable component of modern daily lives. Success or failure of space missions is largely contingent upon the complex system analysis and design methodologies exerted in converting the initial idea into an elaborate functioning enterprise. It is for this reason that this dissertation seeks to contribute towards the search for simpler, efficacious and more reliable methodologies and tools that accurately model and analyze space systems dynamics. Inopportunely, despite the inimical physical hazards, space systems must endure a perturbing dynamical environment that persistently disorients spacecraft attitude, dislodges spacecraft from their designated orbital locations and compels spacecraft to follow undesired orbital trajectories. The ensuing dynamics’ analytical models are complexly structured, consisting of parametrically excited nonlinear systems with external periodic excitations–whose analysis and control is not a trivial task. Therefore, this dissertation’s objective is to overcome the limitations of traditional approaches (averaging and perturbation, linearization) commonly used to analyze and control such dynamics; and, further obtain more accurate closed-form analytical solutions in a lucid and broadly applicable manner. This dissertation hence implements a multi-faceted methodology that relies on Floquet theory, invariant center manifold reduction and normal forms simplification. At the heart of this approach is an intuitive system state augmentation technique that transforms non-autonomous nonlinear systems into autonomous ones. Two fitting representative types of space systems dynamics are investigated; i) attitude motion of a gravity gradient stabilized spacecraft in an eccentric orbit, ii) spacecraft motion in the vicinity of irregularly shaped small bodies. This investigation demonstrates how to analyze the motion stability, chaos, periodicity and resonance. Further, versal deformation of the normal forms scrutinizes the bifurcation behavior of the gravity gradient stabilized attitude motion. Control laws developed on transformed, more tractable analytical models show that; unlike linear control laws, nonlinear control strategies such as sliding mode control and bifurcation control stabilize the intricate, unwieldy astrodynamics. The pitch attitude dynamics are stabilized; and, a regular periodic orbit realized in the vicinity of small irregularly shaped bodies. Importantly, the outcomes obtained are unconventionally realized as closed-form analytical solutions obtained via the comprehensive approach introduced by this dissertation. / Dissertation/Thesis / Doctoral Dissertation Systems Engineering 2019

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.