High Performance Simulation of Attitude and Translation Dynamics Ivanka Pelivan, Stefanie Grotjan, Michel S. Guilherme, Silvia Scheithauer, Stephan Theil ZARM / University of Bremen 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 1 2006 Outline • Motivation • Objectives • Simulator Target Missions • Simulator – Architecture – Core Features – Dynamics – Disturbance Models – Verification • Summary and Outlook 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 2 2006 Motivation (1/2) Future scientific space missions (LISA/LISA Pathfinder, Gaia, MICROSCOPE, STEP, etc.) are scientifically and technically a new generation. Reasons: – expected improvement of measurement accuracy by several orders of magnitude – utilisation of new key technologies – very close link between spacecraft dynamics and scientific measurements 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 3 2006 Motivation (2/2) • S/C developers and engineers need a tool for: – Analysis and engineering of AOCS – Performance validation of S/C systems • Scientific users need a tool for: – Error analysis and budgets – Development of the scientific data reduction – Development of scientific in-flight monitoring tools Development of a high-fidelity S/C dynamics simulator: ! Very accurate dynamics modelling ! Enhanced models of environment and disturbances 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 4 2006 Simulator Objectives • Provide comprehensive simulation of the real system including science signal and error sources • Provide simulation environment for control system performance validation • Generate data needed to test data reduction methods • Provide capability for identification of the satellite and instrument 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 5 2006 The Force and Torque Free Satellite Drag-free concept: Shield satellite payload (proof mass) from all external non-gravitational disturbances ! payload follows a purely gravitational orbit Disturbance Force Satellite Body Satellite is forced to follow the proof mass ! Distance between satellite and proof TM mass is controlled Disturbance Force Control Force ! Introduction of coupling forces and torques Control Force • First suggested and analyzed by B. Lange (1964) • First generation: TRIAD I (1971), TIP II (1974) • Second generation: Gravity Probe-B (2004), GOCE, LISA, MICROSCOPE, STEP, LISA Pathfinder 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 6 2006 Target Missions • Intended application to: – Drag-Free Missions: • Gravity Probe B – as a reference and for validation • MICROSCOPE – satellite dynamics model for independent scientific data reduction • LISA – simulator elements for the scientific data reduction • STEP – analysis and engineering tool – Astronomy missions: • Hipparcos – as a reference and for validation • Gaia – simulator elements for the scientific data reduction – Other missions: • Pioneer 10/11 – utilization of disturbance models for the re- analysis of the Doppler data 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 7 2006 General Simulator Structure 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 8 2006 Simulator Architecture • Modular Design in Matlab/Simulink and C/Fortran – Matlab/Simulink is wrapper for development and analysis. – Major blocks shall be coded in C/Fortran. – Modules are available as library. – Simulator for each mission is assembled from modules. – Initialisation and set-up through data files • Possibility to integrate into data reduction process – A transition to pure C/Fortran code necessary – Interfaces for estimation algorithms 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 9 2006 Simulator Architecture • Modules: Dynamics Core, Environment and Disturbance, Sensor, Controller, Actuator, Transformations • User Interface: Matlab/Simulink • Core and most Environment/Disturbance modules: s-function blocks 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 10 2006 Satellite and Test Mass Dynamics " Objects are treated as rigid bodies " 6 satellite degrees of freedom " 3 for translation FDist " 3 for rotation " GTM1 GTM2 6 degrees of freedom per test mass FControl " Driving force: GSat " Gravitation • Satellite dynamics described in inertial and satellite body-fixed frame • Test mass dynamics described in sensor and test mass frame 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 11 2006 Coordinate Frames inertial frame (ECI, i), body/satellite frame (b), mechanical/structural frame (m), accelerometer frame (a), sensitive axis frames for test masses 1 and 2 (sens1, sens2), test mass body frames for test masses 1 and 2 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 12 2006 Satellite Equations of Motion • Translation of Satellite: – Motion of a rigid body in a gravity field – Additional force = coupling force • Rotation of Satellite: 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 13 2006 Test Mass Equations of Motion • Definition in sensor coordinate frame: satellite-fixed, non inertial Considers accelerations and rotations of system • Translation: • Rotation: - Approach: Conservation of angular momentum 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 14 2006 Simulator Core Features • Simulation of full satellite and test mass dynamics in six degrees of freedom by numerical integration of the equations of motion (13 states: attitude rate, quaternion, position, velocity) • Up to four differential accelerometers utilizing two test masses each (8 (TMs) + 1 (Satellite) = 9x13 states = 117 states) • Consideration of linear and nonlinear coupling forces and torques between satellite and test masses as well as between test masses • Modelling of cross-coupling interaction • Earth gravity model up to 360th degree and order, influence of Sun, Moon and planets can be included • Gravity-gradient forces and torques • 5th order Runge-Kutta numerical integration • 128 bit numerical precision (`quad precision') on an ALPHA processor Several error sources are considered in the model: + misalignment and attitude errors + coupling biases + displacement errors 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 15 2006 Force & Torque Modeling (1/2) • Modeling of forces and torques acting on the satellite and test masses because of: – Gravitation and Gravity Gradients – Control (forces and torques applied by the control system) – Interaction with the upper layers of the Earth atmosphere – Electromagnetic radiation • heat, radio communication emission • Absorption and reflection of radiation incident (sun, Albedo, etc.) – Interaction with the magnetic field – Interaction (coupling) between satellite and test masses • Test mass sensing and actuation systems • Gravitational coupling 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 16 2006 Force & Torque Modeling (2/2) • Modeling approaches: 1. Utilization AND extension of standard models 2. Derivation of parametric models from detailed FEM analysis of specific effects • Standard models used: – International Geomagnetic Reference Field (IGRF, IAGA) – Earth Gravity Model (EGM, NASA) – Mass Spectrometer Incoherent Scatter Model (MSIS, NRL) • Short-term variations of Earth atmospheric density (analysis of CHAMP mission data) 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 17 2006 Attitude Dependency of Gravitational Acceleration • Origin: Gradient of gravity field • Center of Mass and Center of Gravity do not coincide. • Effects: – Gravity gradient torque – Attitude dependent gravity force CoM CoM CoG CoG Earth g g CoM CoG 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 18 2006 Gravity-Gradient Forces and Torques • Force from Earth potential field dF = dm!dF F = Fmono + FGG • Gravity-gradient Torque: T = r dF 1) T = r Gr 2) 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 19 2006 Modeling of Density Variations (1/3) • Processing of data from CHAMP mission: – Orbit data: position, velocity – Sensor data: star tracker, accelerometers – Further data: geometry, area, mass • Computation of density: • Analysis of the frequency spectrum • Design of a form filter in order to create the difference spectrum from white noise 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 20 2006 Modeling of Density Variations (2/3) 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 21 2006 Modeling of Density Variations (3/3) 3rd Internationall Workshop on Astrodynamiics tools and Techniiques, Noordwiijk, 2 - 5 October 22 2006 Modeling of Forces from Electromagnetic Radiation (1/2) • Effects: – EM radiation incident: • Sun light • Albedo light • Infrared (thermal) radiation of Earth – EM radiation emission: • Thermal radiation emission • Radio frequency emission • Basic equations: 3rd Internationall Workshop