Analytical attitude propagation with non-singular variables and gravity gradient torque for spin stabilized satellite

An analytical approach for the spin stabilized satellite attitude propagation is presented using the non-singular canonical variables to describe the rotational motion. Two sets of variables were introduced for Fukushima in 1994 by a canonical transformation and they are useful when the angle between z-satellite axis of a coordinate system fixed in artificial satellite and the rotational angular momentum vector is zero or when the angle between Z-equatorial axis and rotation angular momentum vector is zero. Analytical solutions for rotational motion equations and torque-free motion are discussed in terms of the elliptic functions and by the application of some simplification to get an approximated solution. These solutions are compared with a numerical solution and the results show a good agreement for many rotation periods. When the mean Hamiltonian associated with the gravity gradient torque is included, an analytical solution is obtained by the application of the successive approximations' method for the satellite in an elliptical orbit. These solutions show that the magnitude of the rotation angular moment is not affected by the gravity gradient torque but this torque causes linear and periodic variations in the angular variables, long and short periodic variations in Z-equatorial component of the rotation angular moment and short periodic variations in x-satellite component of the rotation angular moment. The goal of this analysis is to emphasize the geometrical and physical meaning of the non-singular variables and to validate the approximated analytical solution for the rotational motion without elliptic functions for a non-symmetrical satellite. The analysis can be applied for spin stabilized satellite and in this case the general solution and the approximated solution are coincidence. Then the results can be used in analysis of the space mission of the Brazilian Satellites. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Analysis of WCET in an experimental satellite software development.

This paper describes a case study in WCET analysis of an on-board spacecraft software system. The attitude control system of UPMSat-2, an experimental micro-satellite which is scheduled to be launched in 2013, is used for an experiment on analysing the worst-case execution time of code automatically generated from a Simulink model. In order to properly test the code, a hardware-in-the-loop configuration with a simulation model of the spacecraft environment has been used as a test bench. The code has been analysed with RapiTime, with some modifications to the original instrumentation routines, in order to take into account the particularities of the test configuration. Results from the experiment are described and commented in the paper.

Mixed-criticality design of a satellite software system

The continuous increment of processors computational power and the requirements on additional functionality and services are motivating a change in the way embedded systems are built. Components with different criticality level are allocated in the same processor, which give rise to mixed-criticality systems. The use of partitioned systems is a way of preventing undesirable interferences between components with different criticality level. An hypervisor provides these partitions or virtual machines, ensuring spatial, temporal and fault isolation between them. The purpose of this paper is to illustrate the development of a mixed-critical system. The attitude control subsystem is used for showing the different steps, which are supported by a toolset developed in the context of the MultiPARTES research project.

System identification, estimation and control for a cost effective open-source quadcopter

This paper describes system identification, estimation and control of translational motion and heading angle for a cost effective open-source quadcopter — the MikroKopter. The dynamics of its built-in sensors, roll and pitch attitude controller, and system latencies are determined and used to design a computationally inexpensive multi-rate velocity estimator that fuses data from the built-in inertial sensors and a low-rate onboard laser range finder. Control is performed using a nested loop structure that is also computationally inexpensive and incorporates different sensors. Experimental results for the estimator and closed-loop positioning are presented and compared with ground truth from a motion capture system.

Sensing and control for a small-size helicopter

This paper details the progress to date, toward developing a small autonomous helicopter. We describe system architecture, avionics, visual state estimation, custom IMU design, aircraft modelling, as well as various linear and neuro/fuzzy control algorithms. Experimental results are presented for state estimation using fused stereo vision and IMU data, heading control, and attitude control. FAM attitude and velocity controllers have been shown to be effective in simulation.

Non-linear model predictive control for UAVs with slung/swung load

Suspended loads on UAVs can provide significant benefits to several applications in agriculture, law enforcement and construction. The load impact on the underlying system dynamics should not be neglected as significant feedback forces may be induced on the vehicle during certain flight manoeuvres. Much research has focused on standard multi-rotor position and attitude control with and without a slung load. However, predictive control schemes, such as Nonlinear Model Predictive Control (NMPC), have not yet been fully explored. To this end, we present software and flight system architecture to test controller for safe and precise operation of multi-rotors with heavy slung load in three dimensions.

Multi-rotor with suspended load: System dynamics and control toolbox

There is an increasing demand for Unmanned Aerial Systems (UAS) to carry suspended loads as this can provide significant benefits to several applications in agriculture, law enforcement and construction. The load impact on the underlying system dynamics should not be neglected as significant feedback forces may be induced on the vehicle during certain flight manoeuvres. The constant variation in operating point induced by the slung load also causes conventional controllers to demand increased control effort. Much research has focused on standard multi-rotor position and attitude control with and without a slung load. However, predictive control schemes, such as Nonlinear Model Predictive Control (NMPC), have not yet been fully explored. To this end, we present a novel controller for safe and precise operation of multi-rotors with heavy slung load in three dimensions. The paper describes a System Dynamics and Control Simulation Toolbox for use with MATLAB/SIMULINK which includes a detailed simulation of the multi-rotor and slung load as well as a predictive controller to manage the nonlinear dynamics whilst accounting for system constraints. It is demonstrated that the controller simultaneously tracks specified waypoints and actively damps large slung load oscillations. A linear-quadratic regulator (LQR) is derived and control performance is compared. Results show the improved performance of the predictive controller for a larger flight envelope, including aggressive manoeuvres and large slung load displacements. The computational cost remains relatively small, amenable to practical implementations.

Attitude estimation using moment invariants

The problem of estimating the three-dimensional rotational parameters of a rigid body from its monocular image data has been considered using the method of moment invariants. Second- and third-order moment invariants are used to construct the feature vector for the scale and orientation independent identification of the camera view axis direction in the body-fixed reference frame. The camera rotation angle about the view axis is derived from second-order central moments. The relative attitude of the rigid body is then expressed in terms of quaternion parameters to model the outputs of a video sensor in attitude control simulations. Experimental results and simulation outputs are presented using the mathematical model of a spacecraft.

Autonomous Star Camera Calibration and Spacecraft Attitude Determination

This paper presents two methods of star camera calibration to determine camera calibrating parameters (like principal point, focal length etc) along with lens distortions (radial and decentering). First method works autonomously utilizing star coordinates in three consecutive image frames thus independent of star identification or biased attitude information. The parameters obtained in autonomous self-calibration technique helps to identify the imaged stars with the cataloged stars. Least Square based second method utilizes inertial star coordinates to determine satellite attitude and star camera parameters with lens radial distortion, both independent of each other. Camera parameters determined by the second method are more accurate than the first method of camera self calibration. Moreover, unlike most of the attitude determination algorithms where attitude of the satellite depend on the camera calibrating parameters, the second method has the advantage of computing spacecraft attitude independent of camera calibrating parameters except lens distortions (radial). Finally Kalman filter based sequential estimation scheme is employed to filter out the noise of the LS based estimation.

Autonomous rigid body attitude synchronization

Control laws to synchronize attitudes in a swarm of fully actuated rigid bodies, in the absence of a common reference attitude or hierarchy in the swarm, are proposed in [Smith, T. R., Hanssmann, H., & Leonard, N.E. (2001). Orientation control of multiple underwater vehicles with symmetry-breaking potentials. In Proc. 40th IEEE conf. decision and control (pp. 4598-4603); Nair, S., Leonard, N. E. (2007). Stable synchronization of rigid body networks. Networks and Heterogeneous Media, 2(4), 595-624]. The present paper studies two separate extensions with the same energy shaping approach: (i) locally synchronizing the rigid bodies' attitudes, but without restricting their final motion and (ii) relaxing the communication topology from undirected, fixed and connected to directed, varying and uniformly connected. The specific strategies that must be developed for these extensions illustrate the limitations of attitude control with reduced information. © 2008 Elsevier Ltd.

Problem of precision missile guidance: LQR and H‡ control frameworks

Addressed here is the precision missile guidance problem where the successful intercept criterion has been defined in terms of both minimizing the miss distance and controlling the missile body attitude with respect to the target at the terminal point. We show that the H∞ control theory, when suitably modified, provides an effective framework for the precision missile guidance problem. The existence of feedback controllers (guidance laws) is investigated for the case of finite horizon and non-zero initial conditions. Both state feedback and output feedback implementations are explored.

Spacecraft's attitude prediction: solar radiation torque and the Earth's shadow

A semi-analytical approach is proposed to study the rotational motion of an artificial satellite, under the influence of torque due to the solar radiation pressure, and taking into account the influence of Earth's shadow. Using Andoyer variables the equations for the rotational motion are presented in extended Hamiltonian form. In order to get a solution for the state variables close to an actual motion, the considered model for the shadow function takes into account physical and geometric factors and three specific regions: shadow, penumbra and full light. A mapping for the shadow function is proposed and a semi-analytical process is applied. When the satellite is totally illuminated or it is inside the penumbra, a known analytical solution is used to compute the satellite's attitude. A numerical simulation shows, when the penumbra region is included, the attenuation of the rotational motion during the transition from the shadow to the illuminate region and vice versa. (c) 2005 Published by Elsevier Ltd on behalf of COSPAR.

Nonlinear Control of Magnetically Actuated Spacecraft

The topic of this thesis is the feedback stabilization of the attitude of magnetically actuated spacecraft. The use of magnetic coils is an attractive solution for the generation of control torques on small satellites flying inclined low Earth orbits, since magnetic control systems are characterized by reduced weight and cost, higher reliability, and require less power with respect to other kinds of actuators. At the same time, the possibility of smooth modulation of control torques reduces coupling of the attitude control system with flexible modes, thus preserving pointing precision with respect to the case when pulse-modulated thrusters are used. The principle based on the interaction between the Earth's magnetic field and the magnetic field generated by the set of coils introduces an inherent nonlinearity, because control torques can be delivered only in a plane that is orthogonal to the direction of the geomagnetic field vector. In other words, the system is underactuated, because the rotational degrees of freedom of the spacecraft, modeled as a rigid body, exceed the number of independent control actions. The solution of the control issue for underactuated spacecraft is also interesting in the case of actuator failure, e.g. after the loss of a reaction-wheel in a three-axes stabilized spacecraft with no redundancy. The application of well known control strategies is no longer possible in this case for both regulation and tracking, so that new methods have been suggested for tackling this particular problem. The main contribution of this thesis is to propose continuous time-varying controllers that globally stabilize the attitude of a spacecraft, when magneto-torquers alone are used and when a momentum-wheel supports magnetic control in order to overcome the inherent underactuation. A kinematic maneuver planning scheme, stability analyses, and detailed simulation results are also provided, with new theoretical developments and particular attention toward application considerations.

Conception d’un mécanisme déployable à grand ratio d’expansion et de son système d’actionnement par roues d’inertie pour applications spatiales

Cette thèse propose de développer des mécanismes déployables pour applications spatiales ainsi que des modes d’actionnement permettant leur déploiement et le contrôle de l’orientation en orbite de l’engin spatial les supportant. L’objectif étant de permettre le déploiement de surfaces larges pour des panneaux solaires, coupoles de télécommunication ou sections de station spatiale, une géométrie plane simple en triangle est retenue afin de pouvoir être assemblée en différents types de surfaces. Les configurations à membrures rigides proposées dans la littérature pour le déploiement de solides symétriques sont optimisées et adaptées à l’expansion d’une géométrie ouverte, telle une coupole. L’optimisation permet d’atteindre un ratio d’expansion plan pour une seule unité de plus de 5, mais présente des instabilités lors de l’actionnement d’un prototype. Le principe de transmission du mouvement d’un étage à l’autre du mécanisme est revu afin de diminuer la sensibilité des performances du mécanisme à la géométrie de ses membrures internes. Le nouveau modèle, basé sur des courroies crantées, permet d’atteindre des ratios d’expansion plans supérieurs à 20 dans certaines configurations. L’effet des principaux facteurs géométriques de conception est étudié afin d’obtenir une relation simple d’optimisation du mécanisme plan pour adapter ce dernier à différents contextes d’applications. La géométrie identique des faces triangulaires de chaque surface déployée permet aussi l’empilement de ces faces pour augmenter la compacité du mécanisme. Une articulation spécialisée est conçue afin de permettre le dépliage des faces puis leur déploiement successivement. Le déploiement de grandes surfaces ne se fait pas sans influencer lourdement l’orientation et potentiellement la trajectoire de l’engin spatial, aussi, différentes stratégies de contrôle de l’orientation novatrices sont proposées. Afin de tirer profit d’une grande surface, l’actionnement par masses ponctuelles en périphérie du mécanisme est présentée, ses équations dynamiques sont dérivées et simulées pour en observer les performances. Celles-ci démontrent le potentiel de cette stratégie de réorientation, sans obstruction de l’espace central du satellite de base, mais les performances restent en deçà de l’effet d’une roue d’inertie de masse équivalente. Une stratégie d’actionnement redondant par roue d’inertie est alors présentée pour différents niveaux de complexité de mécanismes dont toutes les articulations sont passives, c’est-à-dire non actionnées. Un mécanisme à quatre barres plan est simulé en boucle fermée avec un contrôleur simple pour valider le contrôle d’un mécanisme ciseau commun. Ces résultats sont étendus à la dérivation des équations dynamiques d’un mécanisme sphérique à quatre barres, qui démontre le potentiel de l’actionnement par roue d’inertie pour le contrôle de la configuration et de l’orientation spatiale d’un tel mécanisme. Un prototype à deux corps ayant chacun une roue d’inertie et une seule articulation passive les reliant est réalisé et contrôlé grâce à un suivi par caméra des modules. Le banc d’essai est détaillé, ainsi que les défis que l’élimination des forces externes ont représenté dans sa conception. Les résultats montrent que le système est contrôlable en orientation et en configuration. La thèse se termine par une étude de cas pour l’application des principaux systèmes développés dans cette recherche. La collecte de débris orbitaux de petite et moyenne taille est présentée comme un problème n’ayant pas encore eu de solution adéquate et posant un réel danger aux missions spatiales à venir. L’unité déployable triangulaire entraînée par courroies est dupliquée de manière à former une coupole de plusieurs centaines de mètres de diamètre et est proposée comme solution pour capturer et ralentir ces catégories de débris. Les paramètres d’une mission à cette fin sont détaillés, ainsi que le potentiel de réorientation que les roues d’inertie permettent en plus du contrôle de son déploiement. Près de 2000 débris pourraient être retirés en moins d’un an en orbite basse à 819 km d’altitude.

Social influences and the physical activity intentions of parents of young-children families: An extended Theory of Planned Behavior Approach

Evidence within Australia and internationally suggests parenthood as a risk factor for inactivity; however, research into understanding parental physical activity is scarce. Given that active parents can create active families and social factors are important for parents’ decision making, the authors investigated a range of social influences on parents’ intentions to be physically active. Parents (N = 580; 288 mothers and 292 fathers) of children younger than 5 years completed an extended Theory of Planned Behavior questionnaire either online or paper based. For both genders, attitude, control factors, group norms, friend general support, and an active parent identity predicted intentions, with social pressure and family support further predicting mothers’ intentions and active others further predicting fathers’ intentions. Attention to these factors and those specific to the genders may improve parents’ intentions to be physically active, thus maximizing the benefits to their own health and the healthy lifestyle practices for other family members.