Drag-free and attitude control for the GOCE satellite

The paper concerns Drag-Free and Attitude Control of the European satellite Gravity field and steady-state Ocean Circulation Explorer (GOCE) during the science phase. Design has followed Embedded Model Control, where a spacecraft/environment discrete-time model becomes the realtime control core and is interfaced to actuators and sensors via tuneable feedback laws. Drag-free control implies cancelling non-gravitational forces and all torques, leaving the satellite to free fall subject only to gravity. In addition, for reasons of science, the spacecraft must be carefully aligned to the local orbital frame, retrieved from range and rate of a Global Positioning System receiver. Accurate drag-free and attitude control requires proportional and low-noise thrusting, which in turn raises the problem of propellant saving. Six-axis drag-free control is driven by accurate acceleration measurements provided by the mission payload. Their angular components must be combined with the star-tracker attitude so as to compensate accelerometer drift. Simulated results are presented and discusse

NONLINEAR OBSERVER/CONTROLLER DESIGNS FOR SPACECRAFT ATTITUDE CONTROL SYSTEMS WITH UNCALIBRATED GYROS

Gyroscopes, or gyros, are vital sensors in spacecraft onboard attitude control systems. Gyro measurements are corrupted, though, due to errors in alignment and scale factor, biases, and noise. This work proposes a class of adaptive nonlinear observers for calibration of spacecraft gyros. Observers for each of the calibration parameters are separately developed, then combined. Lyapunov stability analysis is used to demonstrate the stability and convergence properties of each design. First, an observer to estimate gyro bias is developed, both with and without added noise effects. The observer is shown to be exponentially stable without any additional conditions. Next a scale factor observer is developed, followed by an alignment observer. The scale factor and alignment observers are both shown to be Lyapunov stable. Additionally, if the angular velocity meets a persistency of excitation (PE) condition, the scale factor and alignment observers are exponentially stable. Finally, the three observers are combined, and the combination is shown to be stable, with exponential stability if the angular velocity is persistently exciting. The specific PE condition for each observer is given in detail. Next, the adaptive observers are combined with a class of nonlinear control algorithms designed to asymptotically track a general time-varying reference attitude. This algorithm requires feedback from rate sensors, such as gyros. The miscalibration discussed above will seriously degrade the performance of these controllers. While the adaptive observers can eliminate this miscalibration, it is not immediately clear that the observers can be safely combined with the controller in this case. There is, in general, no "separation principle" for nonlinear systems, as there is for linear systems. However, Lyapunov analysis of the coupled controller-observer dynamics shows that the closed-loop system will be stable for the class of observers proposed. With only gyro bias miscalibration, the closed-loop system is in fact asymptotically stable. For more general combinations of miscalibration, closed-loop stability is ensured with modest constraints on the observer/controller design parameters. These constraints are identified in detail. It is also shown that the constraints are not required if the angular velocity can be a priori guaranteed to be persistently exciting

Learning-based attitude tracking control with high-performance parameter estimation

This paper aims to handle the optimal attitude tracking control tasks for rigid bodies via a reinforcement learning-based control scheme, in which a constrained parameter estimator is designed to compensate system uncertainties accurately. This estimator guarantees the exponential convergence of estimation errors and can strictly keep all instant estimates always within pre-determined bounds. Based on it, a critic-only adaptive dynamic programming (ADP) control strategy is proposed to learn the optimal control policy with respect to a user-defined cost function. The matching condition on reference control signals, which is commonly employed in relevant ADP design, is not required in the proposed control scheme. We prove the uniform ultimate boundedness of the tracking errors and critic weight's estimation errors under finite excitation conditions by Lyapunov-based analysis. Moreover, an easy-to-implement initial control policy is designed to trigger the real-time learning process. The effectiveness and advantages of the proposed method are verified by both numerical simulations and hardware-in-loop experimental tests

Line-of-sight-stabilization and tracking control for inertial platforms

Nowadays, line of sight stabilization and tracking using inertially stabilized platforms (ISPs) are still challenging engineering problems. With a growing demand for high-precision applications, more involved control techniques are necessary to achieve better performance. In this work, kinematic and dynamic models for a three degrees-of-freedom ISP are presented. These models are based in the vehicle-manipulator system (VMS) framework for modeling of robot manipulators operating in a mobile base (vehicles). The dynamic model follows the Euler-Lagrange formulation and is implemented by numeric simulations using the iterative Newton-Euler method. Two distinct control strategies for both stabilization and tracking are proposed: (i) computed torque control and (ii) sliding mode control using the recent SuperTwisting Algorithm (STA) combined with a High-Order Sliding Mode Observer (HOSMO). Simulations using data from a simulated vessel allow us to compare the performance of the computed torque controllers with respect to the commonly used P-PI controller. Besides, the results obtained for the sliding mode controllers indicate that the Super-Twisting algorithm offers ideal robustness to the vehicle motion disturbances and also to parametric uncertainties, resulting in a stabilization precision of approximately 0,8 mrad.Hoje em dia, a estabilização e o rastreamento da linha de visada utilizando plataformas inerciais continuam a constituir desafiadores problemas de engenharia. Com a crescente demanda por aplicações de alta precisão, técnicas de controle complexas são necessárias para atingir melhor desempenho. Neste trabalho, modelos cinemáticos e dinâmicos para uma plataforma mecânica de estabilização inercial são apresentados. Tais modelos se baseiam no formalismo para sistemas veículo-manipulator para a modelagem de manipuladores robóticos operando em uma base móvel (veículo). O modelo dinâmico apresentado segue a formulação analítica de Euler-Lagrange e é implementado em simulações numéricas através do método iterativo de Newton-Euler. Duas estratégias de controle distintas para estabilização e rastreamento são propostas: (i) controle por torque-computado e (ii) controle por modos deslizantes utilizando o recente algoritmo Super-Twisting combinado com um observador baseado em modos deslizantes de alta ordem. Simulações utilizando dados de movimentação de um navio simulado permitem comparar o desempenho dos controladores por torque computado em relação a um tipo comum de controlador linear utilizado na literatura: o P-PI. Além disso, os resultados obtidos para o controle por modos deslizantes permitem concluir que o algoritmo Super-Twisting apresenta rejeição ideal a perturbações provenientes do movimento do veículo e também a incertezas paramétricas, resultando em precisão de estabilização de aproximadamente 0,8 mrad

Adaptive Estimation and Heuristic Optimization of Nonlinear Spacecraft Attitude Dynamics

For spacecraft conducting on-orbit operations, changes to the structure of the spacecraft are not uncommon. These planned or unanticipated changes in inertia properties couple with the spacecraft\u27s attitude dynamics and typically require estimation. For systems with time-varying inertia parameters, multiple model adaptive estimation (MMAE) routines can be utilized for parameter and state estimates. MMAE algorithms involve constructing a bank of recursive estimators, each assuming a different hypothesis for the systems dynamics. This research has three distinct, but related, contributions to satellite attitude dynamics and estimation. In the first part of this research, MMAE routines employing parallel banks of unscented attitude filters are applied to analytical models of spacecraft with time-varying mass moments of inertia (MOI), with the objective of estimating the MOI and classifying the spacecraft\u27s behavior. New adaptive estimation techniques were either modified or developed that can detect discontinuities in MOI up to 98 of the time in the specific problem scenario.Second, heuristic optimization techniques and numerical methods are applied to Wahba\u27s single-frame attitude estimation problem,decreasing computation time by an average of nearly 67 . Finally, this research poses MOI estimation as an ODE parameter identification problem, achieving successful numerical estimates through shooting methods and exploiting the polhodes of rigid body motion with results, on average, to be within 1 to 5 of the true MOI values

Solving the nearest rotation matrix problem in three and four dimensions with applications in robotics

Aplicat embargament des de la data de defensa fins ei 31/5/2022Since the map from quaternions to rotation matrices is a 2-to-1 covering map, this map cannot be smoothly inverted. As a consequence, it is sometimes erroneously assumed that all inversions should necessarily contain singularities that arise in the form of quotients where the divisor can be arbitrarily small. This misconception was clarified when we found a new division-free conversion method. This result triggered the research work presented in this thesis. At first glance, the matrix to quaternion conversion does not seem to be a relevant problem. Actually, most researchers consider it as a well-solved problem whose revision is not likely to provide any new insight in any area of practical interest. Nevertheless, we show in this thesis how solving the nearest rotation matrix problem in Frobenius norm can be reduced to a matrix to quaternion conversion. Many problems, such as hand-eye calibration, camera pose estimation, location recognition, image stitching etc. require finding the nearest proper orthogonal matrix to a given matrix. Thus, the matrix to quaternion conversion becomes of paramount importance. While a rotation in 3D can be represented using a quaternion, a rotation in 4D can be represented using a double quaternion. As a consequence, the computation of the nearest rotation matrix in 4D, using our approach, essentially follow the same steps as in the 3D case. Although the 4D case might seem of theoretical interest only, we show in this thesis its practical relevance thanks to a little known mapping between 3D displacements and 4D rotations. In this thesis we focus our attention in obtaining closed-form solutions, in particular those that only require the four basic arithmetic operations because they can easily be implemented on microcomputers with limited computational resources. Moreover, closed-form methods are preferable for at least two reasons: they provide the most meaningful answer because they permit analyzing the influence of each variable on the result; and their computational cost, in terms of arithmetic operations, is fixed and assessable beforehand. We have actually derived closed-form methods specifically tailored for solving the hand-eye calibration and the pointcloud registration problems which outperform all previous approaches.Dado que la función que aplica a cada cuaternión su matrix de rotación correspondiente es 2 a 1, la inversa de esta función no es diferenciable en todo su dominio. Por consiguiente, a veces se asume erróneamente que todas las inversiones deben contener necesariamente singularidades que surgen en forma de cocientes donde el divisor puede ser arbitrariamente pequeño. Esta idea errónea se aclaró cuando encontramos un nuevo método de conversión sin división. Este resultado desencadenó el trabajo de investigación presentado en esta tesis. A primera vista, la conversión de matriz a cuaternión no parece un problema relevante. En realidad, la mayoría de los investigadores lo consideran un problema bien resuelto cuya revisión no es probable que proporcione nuevos resultados en ningún área de interés práctico. Sin embargo, mostramos en esta tesis cómo la resolución del problema de la matriz de rotación más cercana según la norma de Frobenius se puede reducir a una conversión de matriz a cuaternión. Muchos problemas, como el de la calibración mano-cámara, el de la estimación de la pose de una cámara, el de la identificación de una ubicación, el del solapamiento de imágenes, etc. requieren encontrar la matriz de rotación más cercana a una matriz dada. Por lo tanto, la conversión de matriz a cuaternión se vuelve de suma importancia. Mientras que una rotación en 3D se puede representar mediante un cuaternión, una rotación en 4D se puede representar mediante un cuaternión doble. Como consecuencia, el cálculo de la matriz de rotación más cercana en 4D, utilizando nuestro enfoque, sigue esencialmente los mismos pasos que en el caso 3D. Aunque el caso 4D pueda parecer de interés teórico únicamente, mostramos en esta tesis su relevancia práctica gracias a una función poco conocida que relaciona desplazamientos en 3D con rotaciones en 4D. En esta tesis nos centramos en la obtención de soluciones de forma cerrada, en particular aquellas que solo requieren las cuatro operaciones aritméticas básicas porque se pueden implementar fácilmente en microcomputadores con recursos computacionales limitados. Además, los métodos de forma cerrada son preferibles por al menos dos razones: proporcionan la respuesta más significativa porque permiten analizar la influencia de cada variable en el resultado; y su costo computacional, en términos de operaciones aritméticas, es fijo y evaluable de antemano. De hecho, hemos derivado nuevos métodos de forma cerrada diseñados específicamente para resolver el problema de la calibración mano-cámara y el del registro de nubes de puntos cuya eficiencia supera la de todos los métodos anteriores.Postprint (published version

Motion planning under uncertainty: application to an unmanned helicopter

A methodology is presented in this work for intelligent motion planning in an uncertain environment using a non-local sensor, like a radar sensor, that allows the sensing of the environment non-locally. This methodology is applied to an unmanned helicopter navigating a cluttered urban environment. It is shown that the problem of motion planning in a uncertain environment, under certain assumptions, can be posed as the adaptive optimal control of an uncertain Markov Decision Process, characterized by a known, control dependent system, and an unknown, control independent environment. The strategy for motion planning then reduces to computing the control policy based on the current estimate of the environment, also known as the "certainty equivalence principle" in the adaptive control literature. The methodology allows the inclusion of a non-local sensor into the problem formulation, which significantly accelerates the convergence of the estimation and planning algorithms. Further, the motion planning and estimation problems possess special structure which can be exploited to reduce the computational burden of the associated algorithms significately. As a result of the methodology developed for motion planning in this thesis, an unmanned helicopter is able to navigate through a partially known model of the Texas A&M campus

ACS Without an Attitude

The book (ACS without an Attitude) is an introduction to spacecraft attitude control systems. It is based on a series of lectures that Dr. Hallock presented in the early 2000s to members of the GSFC flight software branch, the target audience being flight software engineers (developers and testers), fairly new to the field that desire an introductory understanding of spacecraft attitude determination and control