This dissertation addresses three diverse research problems pertaining to rigid body attitude stabilization and control. The problems addressed result in theoretical development for the topics of cooperative control, delayed feedback, and state estimation, through the formulation of a novel class of switching observers. In the area of consensus management for cooperative control, the problem of designing torque control laws that synchronize the attitude of a team of rigid bodies under constant, unknown communication time delays is addressed. Directed communication graphs are considered, which encompass both leader-follower and leaderless architectures. A feedback linearization result involving the Modified Rodrigues parameter (MRP) representation of attitude kinematics reduces the attitude dynamics equations to double integrator agents and the remainder of the control effort achieves position consensus. New necessary and sufficient delay dependent stability conditions for the system of double integrator agents are presented. This dissertation also considers the problem of stabilizing attitude dynamics with unknown piecewise-constant delayed feedback. The problem is addressed through stability analysis of switched linear time-invariant and nonlinear timedelay systems. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. Finally, this dissertation provides a new switching angular velocity observer formulation to the classical problem of rigid body attitude tracking in the absence of angular rate measurements. Exponential convergence of the angular velocity state estimation errors is proven independent of control design by using a novel error signal definition through this switching-type observer. The switching ensures C0 continuity for all the estimated states. Further, the maximum number of switches required by the observer is shown to be finite and that zeno-type behavior cannot occur. A “separation property” type result in the absence of actual angular rate measurements is established, wherein a linear and nonlinear controller utilizes angular velocity estimates from the proposed observer to achieve attitude tracking. / text

The problem of magnetic control for three-axis stability of a spacecraft is examined. Two controllers, a proportional-derivative controller and a constant coefficient linear quadratic regulator, are applied to the system of equations describing the motion of the spacecraft. The stability of each is checked for different spacecraft configurations through simulations, and the results for gravity-gradient stable and non gravity-gradient stable spacecraft are compared. An optimization technique is implemented in an attempt to obtain the best performance from the controller. For every spacecraft configuration, a set of gains can be chosen for implementation in the controller that stabilizes the linear and nonlinear equations of motion for the spacecraft. / Master of Science

This work addresses the problem of stabilizing attitude dynamics with an unknown delay in feedback. Two cases are considered: 1) constant time-delay 2) time-varying time-delay. This is to our best knowledge the first result that provides asymptotically stable closed-loop control design for the attitude dynamics problem with an unknown delay in feedback. Strict upper bounds on the unknown delay are assumed to be known. The time-varying delay is assumed to be made of the constant unknown delay with a time-varying perturbation. Upper bounds on the magnitude and rate of the time-varying part of the delay are assumed to be known. A novel modification to the concept of the complete type Lyapunov-Krasovskii (L-K) functional plays a crucial role in this analysis towards ensuring stability robustness to time-delay in the control design. The governing attitude dynamic equations are partitioned to form a nominal system with a perturbation term. Frequency domain analysis is employed in order to construct necessary and sufficient stability conditions for the nominal system. Consequently, a complete type L-K functional is constructed for stability analysis that includes the perturbation term. As an intermediate step, an analytical solution for the underlying Lyapunov matrix is obtained. Departing from previous approaches, where controller parameter values are arbitrarily chosen to satisfy the sufficient conditions obtained from robustness analysis, a systematic numerical optimization process is employed here to choose control parameters so that the region of attraction is maximized. The estimate of the region of attraction is directly related to the initial angular velocity norm and the closed-loop system is shown to be stable for a large set of initial attitude orientations. / text

This dissertation addresses the problem of rigid-body attitude tracking control under three scenarios of high relevance to many aerospace guidance and control applications: adaptive attitude-tracking control law development for a spacecraft with time-varying inertia parameters, velocity-free attitude stabilization using only vector measurements for feedback, and smooth angular velocity observer design for attitude tracking in the absence of angular velocity measurements. Inertia matrix changes in spacecraft applications often occur due to fuel depletion or mass displacement in a flexible or deployable spacecraft. As such, an adaptive attitude control algorithm that delivers consistent performance when faced with uncertain time-varying inertia parameters is of significant interest. This dissertation presents a novel adaptive control algorithm that directly compensates for inertia variations that occur as either pure functions of the control input, or as functions of time and/or the state. Another important problem considered in this dissertation pertains to rigid-body attitude stabilization of a spacecraft when only a set of inertial sensor measurements are available for feedback. A novel gyro-free attitude stabilization solution is presented that directly utilizes unit vector measurements obtained from inertial sensors without relying on observers to reconstruct the spacecraft's attitude or angular velocity. As the third major contribution of this dissertation, the problem of attitude tracking control in the absence of angular velocity measurements is investigated through angular velocity observer (estimator) design. A new angular velocity observer is presented which is smoothed and ensures asymptotic convergence of the estimation errors irrespective of the initial true states of the spacecraft. The combined implementation of a separately designed proportional-derivative type controller using estimates generated by the observer results in global asymptotic stability of the overall closed-loop tracking error dynamics. Accordingly, a separation-type property is established for the rigid-body attitude dynamics, the first such result to the author's best knowledge, using a smooth (switching-free) observer formulation. / text

This thesis deals with the scheduling problem for a constellation of Earth observation satellites, focusing on modelling the attitude dynamics to assess the tasking capabilities. A target selection algorithm is developed considering the time dependent manoeuvres between targets and the time-dependent value of the observed targets. Further, a closed-loop dynamics simulation is carried out to assess the agility of the 6U platform and verify the results of the algorithm. The work does not intend to present definitive numerical results, rather the goal is to develop a holistic framework that allows appraising the performance of a platform and the fulfilment of the mission objectives, aiming to maximise the collective value of the observed targets. Given the inputs in terms of platform, sensor, orbit and list of targets, this work serves to simulate the target selection and imaging at an arbitrary day and time for a chosen observation window. / Denna studie behandlar problemet med schemaläggning för en konstellation av jordobservationssatelliter och fokuserar på att modellera attityddynamiken för autonomt utförda uppgifter med beaktande av satellitens kapacitet. En målvalsalgoritm utvecklades med hänsyn till både tidsberoende manövrar mellan målen och tidsberoende värden för de observerade målen. Dessutom utfördes en simulering av styrdynamik i ett slutet system för en 6U-plattform för att bedöma och verifiera målvalsalgoritmen. Arbetet avser inte att presentera definitiva numeriska resultat, utan syftet var att utveckla ett helhetsramverk för möjlig bedömning av plattformens prestanda och att studera plattformens förmåga att välja mål som maximerar det samlade värdet av de observerade målen. Med givna ingångsvärden i form av plattform, sensor, omloppsbana samt lista over mål, ger detta arbete möjlighet att simulera satellitens val av mål i en avbildning vid en godtycklig dag och tid för ett valt observationsfönster.

SEAM (Small Explorer for Advanced Missions) is a 3U CubeSat developedat KTH Royal Institute of Technology which will provide highqualityDC and AC magnetic field measurements of Earth’s magneticfield. The measurement system requires extended periods of timeup to 1000 seconds without active attitude control. The satellite willuse passive gravity gradient stabilization and dipole cancellation via aseparate set of magnetorquers to satisfy LVLH pointing requirementsduring the coasting phases. In this thesis a detailed model of satellitemagnetic moment is presented which includes dipole moment sourcesfrom on-board current loops. The attitude dynamics of the satelliteis characterized with simulations and a strategy is proposed to estimateand compensate the time-dependent magnetic dipole momentusing the dipole compensation magnetorquers and an offline estimationalgorithm. The algorithm is tested with simulated error sourcesand noise and was found to be able to robustly identify and cancel outthe satellite dipole to satisfy mission requirements. / SEAM (Small Explorer for Advanced Missions) är en 3U CubeSat utveckladpå KTH Kungliga tekniska högskolan för DC och AC magnetiskfältmätningarav Jordens magnetfält. Mätningar kräver längretidperioder upp till 1000 sekunder utan aktiv attitydstyrning. Satellitenkommer använda passiv tyngdkraftsgradientstabilisering samtmagnetisk dipolmomentkompensation med hjälp av ett separat setav magnetiska spolar för att upprätthålla orienteringskrav under perioderutan attitydstyrning. Denna rapport presenterar en detaljeradmodell av satellitens magnetiskt dipolmoment som inkluderar dipolmomentkällorfrån strömslingor ombord satelliten. Satellitens attityddynamikär karaktäriserad med simulationer och en strategi tas framför att estimera och kompensera det tidsberoende magnetiska dipolmomentetgenom att använda dipolkompensations magnetiska spolaroch en offline estimeringsalgoritm. Algoritmen är testad med simuleradefelkällor och brus och har funnits pålitlig för uppskattning avdipolmomentet och dess kompensation för att uppfylla missionskrav.

The CalPoly Spacecraft Attitude Dynamics Simulator mimics the rotational dynamics of a spacecraft in orbit and acts as a testbed for spacecraft attitude control system development and demonstration. Prior to this thesis, the simulator platform and several subsystems had been designed and manufactured, but the total simulator system was not yet capable of closed-loop attitude control. Previous attempts to make the system controllable were primarily mired by data transport performance. Rather than exporting data to an external command computer, the strategy implemented in this thesis relies on a compact computer onboard the simulator platform to handle both attitude control processing and data acquisition responsibilities. Software drivers were created to interface the computer’s data acquisition boards with Matlab, and a Simulink library was developed to handle hardware interface functions and simplify the composition of attitude control schemes. To improve the usability of the system, a variety of actuator control, hardware testing, and data visualization utilities were also created. A closedloop attitude control strategy was adapted to facilitate future sensor installations, and was tested in numerical simulation. The control model was then updated to interface with the simulator hardware, and for the first time in the project history, attitude control was performed onboard the CalPoly spacecraft attitude dynamics simulator. The demonstration served to validate the numerical model and to verify the functionality of the entire simulator system.