Attitude control of rigid bodies with time-delayed measurements

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2016.Desenvolver condições de estabilidade e projeto de controladores para controle de atitude de corpos rígidos sujeitos a atrasos no tempo é o objetivo desta dissertação. O modelo utilizado, escrito na forma de equação diferencial atrasada, advém das equações cinemática e dinâmica do corpo rígido modificadas considerando atrasos temporais. Estes atrasos podem representar latências dos sensores e atuadores, além de tempo de processamento de dados (e.g., cômputo dos sinais de controle) e de transmissão de dados quando os elementos do sistema de controle estão conectados por redes comunicação. Em particular, são supostos atrasos desconhecidos e variantes no tempo, o que lhes confere generalidade maior do que os casos abordados até então na literatura, onde os poucos trabalhos que abordaram o problema aprensentam resultados dependentes do valor exato do atraso ou o assumem constante, o que na prática dificilmente é verificado. As condições obtidas, escritas na forma de teoremas, são baseadas em sua maioria na teoria de Lyapunov-Krasovskii. Outro aspecto que diferencia este trabalho em relação aos demais é que os teoremas são formulados como desigualdades matriciais lineares (LMIs, em inglês). A formulação por LMIs é vantajosa não só pelas excelentes propriedades computacionais das LMIs (resolução em tempo polinomial), mas também porque as condições são escritas com variáveis, reduzindo o conservadorismo dos resultados e permitindo a automação do processo de verificação de estabilidade e projeto de controladores, o que também é uma contribuição desta dissertação. Além disso, os controladores possuem performance garantida segundo o critério H∞ , isto é, além de estabilidade, este tipo de controlador tem um nível mínimo de atenuação de perturbações assegurado.Developing stability and controller design conditions for rigid body attitude control subjected to time delays is the goal of this dissertation. The rigid body model, written in form of functional differential equation, stems from the kinematic and dynamic rigid body equations, modified to take time delays into account. Such time delays may represent sensor and actuator latency, processing time (e.g., computing control signals) and transmission lags when the control system elements are connected by communication networks. In particular, time delays are considered unknown and time-varying, which makes them generalizations of previous results in literature, where the scarce works to tackle the problem present results dependent on the exact time delay value, which is hardly verified in practice. The proposed conditions, written as theorems, are mostly based on Lyapunov-Krasovskii theory. Another aspect that sets this work apart is that theorems are formulated as linear matrix inequalities (LMIs). LMI formulation is advantageous not only for its excellent computational properties (polynomial time solving), but also for the conditions are written with variables, which reduces results' conservatism e enables automating stability verification and controller design, which is a contribution of this work as well. In addition, controllers attain guaranteed performance according to H∞ criterion, that is, besides stability, this kind of controller presents a known minimum level of perturbation attenuation

Quaternion-based H∞ attitude tracking control of rigid bodies with time-varying delay in attitude measurements

The problem of attitude and angular velocity tracking in the presence of exogenous disturbances and where feedback measurements are subjected to unknown time-varying delays is addressed. Sufficient conditions which guarantee stability and disturbance attenuation performance in the H∞ sense are provided. Results are presented in the form of LMIs, which allow the conditions to be simply and efficiently computed. Using a simple quaternion-based linear state feedback controller and a feedforward term to compensate the nonlinearities of the system dynamics, simulation results illustrate that the control law is able to effectively track desired trajectories and reject disturbances even in the presence of large time-varying delays

Robust Controller Design for Attitude Dynamics Subjected to Time-Delayed State Measurements

Attitude control and time-delay systems are well-developed fields in the control theory, but only a modicum of papers have explored control systems that fall within the intersection of the two. Indeed, combining kinematics and dynamics nonlinearities with sensor and actuator delays reinvigorates the original attitude control problem, typically leading to involved stability arguments based on nonlinear analysis techniques. This paper instead proposes solving the attitude stabilizer design problem by formulating it as a linear matrix inequality feasibility problem. The proposed approach simplifies the stability arguments, without loosing generality; the obtained conditions cope with the general case of rigid bodies that suffer from unknown, heterogeneous, time-varying state measurement delays, and have inertia uncertainties. This methodology is particularly well suited to resource-limited applications, because controllers can be designed offline using computationally efficient tools. Although simple, numerical evidence shows the stability criterion derived in this paper largely outperforms previous results

Development of Innovative GNC Algorithms for Aerospace Applications

The main context of the present dissertation is the SAPERE STRONG (Space Advanced Project for Excellence in Research and Enterprise – Sistemi, Tecnologie e Ricerche per l’Operatività Nazionale Globale) project, founded by Italian Ministry of University and Research (MIUR) with the goal to improve Italian access to Space and Space Exploration. For this purpose, extension of the launch capability of the Vega launcher is included in the project, realized with a Space-Tug which is used to deploy in the nominal orbit a payload spacecraft. This thesis has the objective to develop an advanced orbital simulator as a tool which makes the designer able to develop and test the Guidance, Navigation and Control (GNC) software for the Space-Tug spacecraft. The GNC software is developed in collaboration with the leader industrial company of the project, Thales Alenia Space. Thales Alenia Space (TAS) is in charge of developing the Navigation and Control Function and the main structure of flight software, while Politecnico di Torino collaborates with the development of the Guidance function and the orbital simulator. During the whole project has been planned an internship of 1500 hours inside the offices of TAS in Torino. The project includes also a visiting period of international institution. In the specific frame of this Ph. D. thesis, has been spent three months at the University of Sevilla, with the purpose of study and design of a Galileo receiver as an additional input for determination of position in advanced navigation systems, since the Galileo constellation is near to be fully operative in the next future. Details related to all the activities executed during this internship will be presented in Appendix B. The main objective of this dissertation is the development of innovative GNC algorithms, focusing mainly on the Guidance problem, for aerospace application. An extensive literature review of existing guidance law, control techniques, actuators for attitude and trajectory control, sensors and docking mechanism and techniques has been performed. The Guidance topic has been analyzed focusing on the missile-derived Proportional Navigation Guidance (PNG) algorithm, Zero-Effort-Miss/Zero-Effort-Velocity (ZEM/ZEV) algorithm and Lambert guidance. Feasibility, performance, pros and cons have been extensively studied in this work, especially in an experimental fashion, and new solutions and implementation strategies have been proposed. The literature review has been completed for Control and Navigation issues, as well. Control strategies, actuation systems and algorithm have been investigated, starting from the classical proportional/Integrative/Derivative (PID) controllers, to more recent and innovative control law, such as Linear Quadratic Regulator (LQR). As for the Control function, the Navigation topic, intended as navigation filters and algorithms, has been studied in the last period of this work, while the navigation problem form the hardware side (i.e. sensors) has been deeply analyzed in the present work. In addition to the GNC investigation, the simulation topic has been studied as well, since one of the goals of this dissertation is the realization of an orbital simulator. The orbital simulator is a complete 6 degrees-of-freedom simulator, based on the relative equation of motion (Hill’s equations) for the trajectory computation and based on the classical rigid body equation, including the quaternion notation, for the computation of the attitude dynamics. The orbital environment is well defined, including all common disturbances found in Low Earth Orbits (LEO) and affecting the dynamics of an orbiting body. A complete set of sensors is implemented, including an accurate model of common measurement errors affecting the sensors included in the spacecraft configuration (Inertial Measurement Unit, Star Tracker, GPS, Radio Finder, Lidar and Camera). Actuators are carefully modeled, including a reaction wheels system and a reaction control thrusters system. Errors derived for misalignment of the wheels system and non-nominal inertia and shooting and misalignment errors for the thrusters systems are modeled as well

Design and Test of an Attitude Determination and Control System for a 6U CubeSat using AFIT\u27s CubeSat Testbed

The design and test of a 6U CubeSat Attitude Determination and Control System (ADCS) are explored to establish single-axis control using AFIT\u27s CubeSat testbed consisting of a Helmholtz cage and hemi-spherical air bearing. The Helmholtz cage produces a near-uniform magnetic field inside the cage while the air bearing provides a near-frictionless surface for ADCS testing. The ADCS testbed includes a four wheel pyramid reaction wheel array (RWA) for actuation and an inertial measurement unit (IMU) for attitude determination. Along with the ADCS hardware, the ADCS testbed also includes an Electrical Power System (EPS) and Command and Data Handling (CDH) for power and wireless telemetry, respectively. Attitude estimation is performed using the QUEST algorithm with magnetometer and accelerometer sensor data to estimate a current quaternion. A Proportional-Integral-Derivative (PID) controller is used for control of the ADCS testbed while each reaction wheel motor is controlled by a proportional gain. ..

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 filtering applications to satellite navigation

PhDDifferential Global Navigation Satellite Systems employ the extended Kalman filter to estimate the reference position error. High accuracy integrated navigation systems have the ability to mix traditional inertial sensor outputs with navigation satellite based position information and can be used to develop high accuracy landing systems for aircraft. This thesis considers a host of estimation problems associated with aircraft navigation systems that currently rely on the extended Kalman filter and proposes to use a nonlinear estimation algorithm, the unscented Kalman filter (UKF) that does not rely on Jacobian linearisation. The objective is to develop high accuracy positioning algorithms to facilitate the use of GNSS or DGNSS for aircraft landing. Firstly, the position error in a typical satellite navigation problem depends on the accuracy of the orbital ephemeris. The thesis presents results for the prediction of the orbital ephemeris from a customised navigation satellite receiver's data message. The SDP4/SDP8 algorithms and suitable noise models are used to establish the measured data. Secondly, the differential station common mode position error not including the contribution due to errors in the ephemeris is usually estimated by employing an EKF. The thesis then considers the application of the UKF to the mixing problem, so as to facilitate the mixing of measurements made by either a GNSS or a DGNSS and a variety of low cost or high-precision INS sensors. Precise, adaptive UKFs and a suitable nonlinear propagation method are used to estimate the orbit ephemeris and the differential position and the navigation filter mixing errors. The results indicate the method is particularly suitable for estimating the orbit ephemeris of navigation satellites and the differential position and navigation filter mixing errors, thus facilitating interoperable DGNSS operation for aircraft landing

Health Management and Adaptive Control of Distributed Spacecraft Systems

As the development of challenging missions like on-orbit construction and collaborative inspection that involve multi-spacecraft systems increases, the requirements needed to improve post-failure safety to maintain the mission performance also increases, especially when operating under uncertain conditions. In particular, space missions that involve Distributed Spacecraft Systems (e.g, inspection, repairing, assembling, or deployment of space assets) are susceptible to failures and threats that are detrimental to the overall mission performance. This research applies a distributed Health Management System that uses a bio-inspired mechanism based on the Artificial Immune System coupled with a Support Vector Machine to obtain an optimized health monitoring system capable of detecting nominal and off-nominal system conditions. A simulation environment is developed for a fleet of spacecraft performing a low-Earth orbit inspection within close proximity of a target space asset, where the spacecraft observers follow stable relative orbits with respect to the target asset, allowing dynamics to be expressed using the Clohessy-Wiltshire-Hill equations. Additionally, based on desired points of inspection, the observers have specific attitude requirements that are achieved using Reaction Wheels as the control moment device. An adaptive control based on Deep Reinforcement Learning using an Actor-Critic-Adverse architecture is implemented to achieve high levels of mission protection, especially under disturbances that might lead to performance degradation. Numerical simulations to evaluate the capabilities of the health management architecture when the spacecraft network is subjected to failures are performed. A comparison of different attitude controllers such as Nonlinear Dynamic Inversion and Pole Placement against Deep Reinforcement Learning based controller is presented. The Dynamic Inversion controller showed better tracking performance but large control effort, while the Deep Reinforcement controller showed satisfactory tracking performance with minimal control effort. Numerical simulations successfully demonstrated the potential of both the bioinspired Health Monitoring System architecture and the controller, to detect and identify failures and overcome bounded disturbances, respectively

Advances in Spacecraft Attitude Control

Spacecraft attitude maneuvers comply with Euler's moment equations, a set of three nonlinear, coupled differential equations. Nonlinearities complicate the mathematical treatment of the seemingly simple action of rotating, and these complications lead to a robust lineage of research. This book is meant for basic scientifically inclined readers, and commences with a chapter on the basics of spaceflight and leverages this remediation to reveal very advanced topics to new spaceflight enthusiasts. The topics learned from reading this text will prepare students and faculties to investigate interesting spaceflight problems in an era where cube satellites have made such investigations attainable by even small universities. It is the fondest hope of the editor and authors that readers enjoy this book

Attitude Determination & Control System Design and Implementation for a 6U CubeSat Proximity Operations Mission

The purpose of this work is to discuss the attitude determination and control system (ADCS) design process and implementation for a 12 kg, 6U (36.6 cm x 23.9 cm x 27.97 cm) CubeSat class nano-satellite. The design is based on the requirements and capabilities of the Application for Resident Space Object Proximity Analysis and IMAging (ARAPAIMA) proximity operations mission. The satellite is equipped with a cold gas propulsion system capable of exerting 2.5 mN m torques in both directions about each body axis. The attitude sensors include an angular rate gyro and star tracker (STR), supplemented by the payload optical array cameras. The dynamic simulation of the satellite includes extensive environmental models and analyses that show how the satellite attitude is affected by aerodynamic drag, solar radiation pressure, gravity gradient torques, and residual magnetic moments. A mechanical propellant slosh model and a reaction torque analysis of the deployable solar panel hinges approximate the internal dynamics of the satellite. A trade study is presented to justify the use of a reaction control thruster actuated system over the more traditional reaction wheel configuration. Both actuation systems are modeled to hardware specifications and their propellant and energy requirements are examined alongside pointing performance. Two methods of accounting for sensor noise and sampling rates are presented. The first is an extended Kalman filter based on the nonlinear model of a rate gyro coupled with quaternion attitude kinematics. The second presents a gyro-less angular rate observer capable of extrapolating STR measurements to the desired frequency. An additional method uses images from the payload cameras to perform [camera] frame centering maneuvers and to address the possibility of bias in the controller reference signal. Four different controllers are described to reflect the chronological progression of the ADCS design. The first controller, designed to perform long angle maneuvers and target tracking, utilizes fixed gain eigenaxis control. The same controller is then augmented with a parallel proportional-integral-derivative (PID) type control law using scheduled gains. This configuration is designed to switch between eigenaxis and PID control during imaging procedures to take advantage of the integral control introduced by the PID algorithm. To reduce system complexity, a modified eigenaxis control law, which incorporates scheduled integral control but does not require a switch to PID control, is introduced. A discrete time equivalent of the modified eigenaxis control law is also developed. Additionally, a brief description of a detumbling control law is presented. Each of the four control laws is paired and tested with the different feedback and estimation methods discussed. An extensive showcase of numerical simulation results outlines the pointing performance of each system configuration and evaluates their capabilities of meeting a 1 arcmin pointing requirement. A comparison of the different properties and performance of each control system configuration precedes the selection of the discrete modified eigenaxis control law as the best alternative