The thesis focus on: study and proposal of an attitude methods by fusion of measurements from gyroscope sensor and star tracker for small Earth observation satellite which can meet the on-board contraints and space environments.
MINISTRY OF EDUCATION AND TRAINING VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY - NGO DUY TAN ATTITUDE ESTIMATION FOR SMALL EARTH OBSERVATION SATELLITE BY FUSION OF GYROSCOPE SENSOR AND STAR TRACKER Major: Control and Automation Engineering Code: 62 52 02 16 SUMMARY OF DOCTORAL THESIS ON CONTROL AND AUTOMATION ENGINEERING Hanoi – 2018 The thesis was completed at Graduate University of Science and Technology, Vietnam Academy of Science and Technology Supervisor 1: Assoc.Prof.Dr Thai Quang Vinh Supervisor 2: Dr Bui Trong Tuyen Reviewer 1: … Reviewer 2: … Reviewer 3: … The thesis is defended to the thesis committee for the Doctoral Degree, at Graduate University of Science and Technology – Vietnam Academy of Science and Technology, on Date Month Year 2018 Hardcopy of the thesis can be found at: - Library of Graduate University of Science and Technology - National Library of Vietnam LIST OF AUTHOR’S WORKS Dự đoán tư vệ tinh quan sát Trái đất phương pháp hợp liệu đa cảm biến, Kỷ yếu Hội thảo khoa học “Nghiên cứu phát triển ứng dụng công nghệ vũ trụ - 2011”, Viện Công nghệ vũ trụ, 2011 Hợp liệu cảm biến tốc độ quay cảm biến để dự đoán tư vệ tinh nhỏ, Kỷ yếu Hội thảo quốc gia lần thứ XV: Một số vấn đề chọn lọc Công nghệ thông tin truyền thông- Hà Nội, 03-04/12/2012 Xác định tư kết hợp cảm biến quay hồi chuyển vệ tinh VNREDSat-1, Kỷ yếu Hội thảo Công nghệ vũ trụ Ứng dụng – Hà Nội, 19/12/2014 Hiệu chỉnh quỹ đạo cho vệ tinh nhỏ quan sát Trái đất quỹ đạo đồng Mặt trời, Kỷ yếu Hội thảo Công nghệ vũ trụ Ứng dụng – Hà Nội, 19/12/2014 Small satellite attitude determination by gyroscope and star tracker fusion, International Conference on Information and Convergence Technology for Smart Society - Ho Chi Minh, 1/2016 A New Approach for Small Satellite Gyroscope and Star Tracker Fusion, Indian Journal of Science and Technology, Volume 9, Issue 17, 5/2016 (tạp chí thuộc danh mục SCOPUS) Xác định quỹ đạo vệ tinh viễn thám phù hợp với điều kiện Việt Nam, Tạp chí Khoa học đo đạc đồ, số 34-12/2017 Proposed design of a fault-tolerance attitude estimator for small earth observation satellite, International Journal of Mechanical Engineering & Technology (IJMET), Volume 9, Issue 1, 1/2018 (tạp chí thuộc danh mục SCOPUS) Study on the needs and proposal for high and very high resolution satellite remote sensing systems in Viet Nam, International Journal of Civil Engineering & Technology (IJCIET), Volume 9, Issue 1, 1/2018 (tạp chí thuộc danh mục SCOPUS) FOREWORD Data from satellite attitude sensors (orientation sensors, angular rate sensors) needs to be merged together to produce a reliable output provided to the controller This is the key task of the satellite attitude estimator Some challenges and contraints are: - Contraint in power supply - Processing capability: on-board tasks are mainly implemented on FPGA (Field Gate programmable array) or SoC (System on Chip) - Impacts by space environment and radiation: these are typical charateristcs which determine the design and on-board part selections - Ground-satellite communication period: limited duration for contact between satellite and ground control stations - Real-time - Complexity in transformation of coordinate systems Algorithms for attitude estimation are normally hardware implemented So this is the key consideration to select compact and reliable solutions Solutions for attitude estimation shall meet the following requirements: - Stability - Reliabilty - Responsibility against unexpected on-board circumstances such as faulty sensors - Optimality in performance and on-board resources (power supply, memory and processing capability) Therefore, study and proposal of adaptive estimation algorithms are major fields of research in satellite technology The implementation of the algorithms shall consider the stability and compactness in order to keep optimal with on-board limited resources So adaptive mechanism shall be simple but optimal in computation And fuzzy logic is of suitable for adaptive approaches Based on the above analysys, the author chose the topic of the thesis “Attitude estimation for small Earth observation satellite by fusion of gyroscope sensor and star tracker” OBJECTIVE OF THE THESIS The thesis focus on: study and proposal of an attitude methods by fusion of measurements from gyroscope sensor and star tracker for small Earth observation satellite which can meet the on-board contraints and space environments CHAPTER I - INTRODUCTION 1.1 Satellite attitude The term “satellite attitude” refers to the orientaiton of a satellite in a fixed coordiate system and its angular rates around the corresponding axis A satellite operation on-board shall meet the requirements in its orientation such as antenna pointing to ground station, solar panel orientation and earth pointing for imaging In order to be able to estimate and control the attitude of the satellite with programmed tasks, the attitude determination and control subsystem (ADCS) must be provided with accurate and reliable data from a various types of sensors such as: sun sensor, star tracker, angular rate sensor, magnetic field sensor It should be noted that each type of sensor has many different features such as sampling rate, accuracy, reliability and dependency on current position of the satellite Therefore: Multi-sensor data fusion is the process of combining measurements from different sensors to produce better results than using individual ones 1.2 Coordianate systems in investigation of satellite motion In order to analyze satellite motion, coordinate system shall be specified The coordinate systems include inertial i , orbital o and satellite body b coordinates In the scope of this dissertation, it is assumed that the satellite is a circular earth rotating rigid body 1.3 Attitude representation Attitude representations are: Direct Cosine Matrix (DCM) Roll, Pitch, Yaw (RPY) Euler angles and rotation Quaternion Modified Rodrigues Parameters (MRP) Pivot parameters (latest proposal for satellite attitude representation) Attitude error Attitude error in quaternion pres q is given by: v q qdq d q4 d q4 vd v vTd q4 q1d q v is the desired attitude Of which q d 2d d q3d q4d q4d and q1 q v q 2 q3 q4 q4 is real attitude Thanks to its advantages, quaternion is still the most popular attitude representation for small satellite 1.4 Key criteria for attitude determination and control subsystem Key criteria for ADCS are: - Attitude accuracy parameters include attitude estimation and attitude control accuracies: o Pointing accuracy: difference in real and desired attitude in each axis: (θreal θcmd ) o Estimation accuracy: difference in estimated and real attitude: (θ flt θcmd ) o Rate error: difference between real and desired angular rates: (ωreal ωt arg et ) - Attitude stability - Responsiveness: transient and convergence time - Fault-tolerance capability Attitude control error places a significant impacts on the imaging accuracy on the ground and image quality as well So the acuracies shall be key critera for Earth obervation missions 1.5 Attitude estimation algorithms and on-board contraints The attitude estimation uses measurements from gyroscope and star tracker Therefore, in order to design an effective and practical estimator which is adaptive and fault-tolerant, each sensor characteristics and its impacts should be carefully studied The following cases shall be considered: - Angular rate sensor: impacts of drift and faulty sensor - Star tracker: impacts of noise and data unavailability (due to big bright objects) One the the key feature/contraint of the estimator is optimal design for hardware implementation which is of limited processing capacity It is pointed out by some researches that Kalman filters especially Extended kalman Filter (EKF) is showing significant advantages over traditional approaches such as TRIAD or QUEST in term of hardware implementation Adaptive methods are applicable in the conditions of the fluctuational satellite's parameters or faulty sensors However, due to the specific in-orbit requirements of reliability, accuracy, and and constraint of limited computing resources, adaptive methods have not yet been widely applied In control systems, fuzzy logic is popular for adtive mechanisim It is chosen thanks to the following features: - Fllexibility and comprehensibility - Easy interface - Ease of computation - Ease of verification Summary: Performances of the attiude estimator or ADCS is dependant on the following factors: - Atittude representatioin method - On-board contraints - Estimation algorithms CHAPTER II - SATELLITE MODEL AND SENSORS IN THE ATTITUDE ESTIMATION PROBLEMS 2.1 Satellite model attitude control with reaction wheel 2.1.1 Satellite model with reaction wheel as actuator Satellite model is described as below: Where hw is wheel mometums Ne is external torque Nc is commaned torque Is is satellite inertial matrix If the scalar part q4 is separated, the remained forms a Gibbs vector: The state vector is given: Commanded torque: u=Nc, then state equation of the satellite is: 2.1.2 Control law for attitude control For esase of design and simulation, the control law is selected as: u K pqe - K dωe Where: u is the commanded torque which is generated by reaction wheels K p , K d : control gains qe , ωe : errors in orientation and angular rate and defined as: Where: qs, qr is the current and required attitueds respectively ωe and ωr is the current and required angular rates In the mode of Earth pointing, the ADCS is to control and maintain the body angular rate in pitch axis as given below: 10 0 2* (rad/s) To Where To is the Earth rotation period In case of Sun synchronous orbit, To is around 90 minutes In imaging mode, the satellite attitude is following a programmed manner (the required attitude can be calculated on-board or uploaded from ground control station) The satellite model is linearized around earth pointing angular rate: [0, -ωo, 0]: x(t) = Ax(t) + Bu Nc (t) + Bd Ndist Where: x(t) is the state matrix and defined as [ω q h] h is the angular momentum of the reaction wheelsNc lực yêu cầu Ndist is external disturbance forces A, B are state matrices 2.2 Attitude sensors 2.2.1 Gyroscope A gyroscope is descibed as below : ω = ω + β + ηv β = ηu Where: ω is the measured angular rate, β is the timedependant drift and ηu , ηv are Gaussion white noise processes 11 2.2.2 Star tracker Star tracker is an optical device functioning to determine satellite attitude by precise imaging of stars The captured image is then compared to the star map in order to calculate the current attitude A star tracker is modelled as: qs q q Where : q s is the output quaternion of the sensor, q is the actual attitude, q is the sensor noise: E q s (t ) E q s (t )qTs (t ) σ 2s (t )I x Summary: Typical satellite model for ADCS analysis and simulation utilizes reaction wheels as actuators to control its attitude, and gyroscope and star tracker are used for attitude sensors This selection is enough to guarantee the practicality and trend in design of small Earth observation satellites CHAPTER III - ATTITUDE ESTIMATION BY MULTI SENSOR FUSION Atitude demermination is considered as optimal estimation solution based on multiple sources of sensors The estimation algorithm must evaluate the reliability of each sensor which is the sensor confidence factor 12 Some popular estimations methods are: Weighted function Extended Kalman Filter (EKF) Quaternion Estimation (QUEST) Pivot based method Adaptive method Adaptive methods are particularly effective in cases of imprecise system parameters However, the implementation of adaptive methods on-board satellites shows several disadvantages such as more memory utilization, computational burden and higher power consumption These are also constraints which must be balanced to ensure the realtime operation of the satellite Summary: In this chapter, the attitude estimation model for small Earth observation satellite has been described And the estimator by Kalam filter has been shown as well The model is the background for applying adaptive mechanism to improve the fault-tolerance of the estimator and the ADCS in general CHAPTER IV - PROPOSAL OF A ESTIMATION METHOD WITH GYROSCOPE DRIFT-COMPENSATION 4.1 Design of a drift-compensated estimator The state vector is chosen as: Where: q=[q1 q2 q3 q4] is real attitude β= [βx βy βz] is the drift vector of the gyroscope 13 EKF for attitude estimator is illustrated below: Table 0.1 EKF filter for drift-compensated estimation 4.2 Simulation results Simulation data: - Satelite inertial matrix: J 13.5 0 12.8 0 18.8 kg.m2 - Star tracker noises: [96” 16” 16”] (X,Y and Z axis) (3σ) - Drift constant: 6o/h - Angular random walk (ARW): 0.15o/ h - Earth pointing rate: 𝑟𝑎𝑑/𝑠 (Satellite obital period: T=90 90∗60 minutes) - Required angular rate: [-0.0036 -0.0074 0.0032] rad/s - Imaging period: To+200 to To+300 (second) 2∗𝜋 14 - External torque: τ=[0 0]; - Initial condition: x=[1 0 0 0]; - Control law: PID - Desired atttitude: roll manouver by an angle of 30o 4.2.1 Simulation result by weighted method Figure 0.1 Estimated attitude (Roll, Figure 0.2 Pointing errors Pitch, Yaw) Performance of the estimator: Axis/factor Roll (rad) Pitch (rad) Yaw (rad) Mean 0.0003805 0.0007924 0.0005978 Std deviation 0.0002736 0.0004816 0.0003729 Table 0.2 Performance of the weighted method for attitude estimator 15 4.2.2 Simulation results of EKF attitude estimator by gyro drift compensation Figure 0.3 Estimated attitude (Roll, Pitch, Figure 0.4 Pointing errors Yaw) Performances of the estimator are: Axis/Parameter Roll (rad) Pitch (rad) Yaw (rad) Mean -4.81 e-05 1.48 e-06 -1.66 e-05 Std deviation 0.0001515 0.0001493 0.0001348 Table 0.3 Pointing errors evaluation of the estimator Summary: The results show that kalman filter is fully capable of reliable attitude estimator CHAPTER V - PROPOSAL OF A FAULT-TOLERANCE ATTITUDE ESTIMATOR FOR SMALL EARTH OBSERVATION SATELLITE 5.1 Design of a Kalman filter for multi-sensor data fusion for attitude estimation A Gyro-stellar estimator (GSE) operation is described by the following steps: 16 Initialization q(0) q0 β(0) β0 Attitude prediction by kinematic ωk ω k ,Gyro equation βˆ k βˆ k qˆ k qˆ k ωk ,Gyro : gyro measurement f Innovation calculation zk βˆ k q(ω k ) 2qk , SST qˆ k qk , SST : SST measurement Corrections: - Xk ,Cor Attitude correction coefficient qk ,Cor - qˆ k βˆ k Gyro drift correction: dk ,Cor q k ,Cor K GSE z k d k ,Cor 1, Cor qˆ k 1,Cor βˆ k 1 q k ,Cor d k ,Cor 5.2 Application of fuzzy logic for tuning the estimator The fuzzy tuning mechanism is proposed to monitor and adjust the filter coefficients Where pure EKF, Q k and R k : Qk _ new Q0 2( k 1) R k _ new R0 2( k 1) is Q0 , R are (0.1) the tuning factor, if the estimator is a constant matrices Fuzzy based algorithm is developed with two inputs of meand and deviation values of the innovation Tunning factor outcome Init q(0) q0 β(0) β0 P ( k0 ) P0 R ( k0 ) R0 17 is the Attitude prediction by kinemtics equation ωk ,Gyro : gyro measurement Innovation calculation ωk βˆ k βˆ k qˆ k qˆ k zk q(ω k ) 2q k , SST qˆ k FLO(var( z k ), mean( z k )) qk , SST : SST measurement FLO: fuzzy logic observer βˆ k ω k ,Gyro Pk +1 = (I - K k,GSE )Pk Rk = Ro ( 2( k 1)) K k +1,GSE = Pk +1 / (Pk +1 + R k ) Corrections: - Attitude correction: qk ,Cor - Gyro drift correctios dk ,Cor Xk ,Cor q k ,Cor d k ,Cor qˆ k 1,Cor qˆ k βˆ k 1,Cor βˆ k Kk 1,GSE zk q k ,Cor d k ,Cor 5.3 Proposal of a fault-tolerance mechanism for attitude estimator on small Earth observation satellite A fault-tolerance mechanism for small earth observation satellite is proposed as follows: - If the gyrorcope is working normally: gyro measurements are used to estimate the attitude - If the gyroscope is degraded: reference angular rates are used instead of gyro measurements If the star tracker measurements are also interrupted for longer than the designed thresholds (due to charged particle, big bright objects…), the gyro measurement shall be used - If the gyroscope is faulty: reference angular rates are used instead of gyro measurements If the star tracker measurements are also 18 interrupted for longer than the designed thresholds, the dynamics euqation is integrated for attitude estimation 5.4 Simulation 5.4.1 Simulation in the normal mode Satellite parameters: - Inertial matrix: J 13.5 0 12.8 0 18.8 kg.m2 - Star tracker noise: [96’ 16‘ 16’] (3σ) - Gyro drift: 6o/h - Angular random walk (ARW): 0.15o/ h - Earth pointing angular rate: 2*pi/(90*60) rad/s (To=90 minutes) - Desired angular rate during imaging phase: [-0.0036 -0.0074 0.0032] rad/s - Imaging period: To+200 to To+300 (second) - External torque: τ=[0 0]; - Initial condition: x=[1 0 0 0]; Simulation result for Kalman filter: Figure 0.1 Estimated attitude by EKF Figure 0.2 Fuzzy-adapted EKF filter in case of noisy sensor 19 5.4.2 Simulation for imaging period Scenarios is assumed as: - Attitude for start imaging: [-10; 25; 20] o - Imaging angular rate [-0.0035 -0.0073 0.0034] rad/s; - Imaging periode: 100-200 (second) Simulation results: Normal operation: Figure 0.3 Attitude during imaging Figure 0.4 Angular rate during phase imaging Noisy sensors Figure 0.5 Estimated attitude Figure 0.6 Attitude error 20 Fault-tolerance estimation Figure 0.7 Estimated attitude Figure 0.8 Estimated angular rate Summary: EKF is effective in case of well-known system parameters and noise processes Nevertheless, various paramters are imprecise, so the filter may not be working as expected in this case This statement is convinced when multiple sensors are used In order to overcome this limiatation, fuzzy logic is applied to observe and evaluate the confidence of the output then reasonable adaptation mechanism is introduced to establish a fault-tolerance estimator 21 CONCLUSIONS On estimation methods: Kalman filter is showing effectiveness in case of normal operation in terms of accuracy, computation and compactness, which makes the filter easy for hardware implementation Adaptive mechanism by fuzzy logic is effective in the following cases: degraded sensor due to noisy measuments (star tracker) or accumulated noise (gyroscope drift) When the measuments are not reliable any longer (noisy or faulty sensors) then the adaptive mechanism is activated to ensure the fault-tolerance of the estimator Fault-tolerance mechanism: When the sensor data is no longer usable then the estimator will use alternative data such as: the other usable sensor; available data (desired orientation or angulatr rate) Due to in-orbit harsh operation conditions and strict requirements, the fault-tolerance mechanism is capable of maintaining the satellite operation for a limited period with fixed thresholds, otherwise safemode is activated These thresholds shall be thoroughly analyzed and calculated based on specific satellite and system design RECOMMENDATIONS - Further study should be done on attitude estimation algorithms which are optimal for limirted-resource hardware Focus should also be placed on hardware simulation such as FPGA and SoC (System on Chip) - Study on the Pivot parameter attitude presentation: This is the latest research idea and should be studied for futher application on satellite attitude determination and control 22 MAIN CONTRIBUTIONS OF THE THESIS The thesis focuses on design and simulation for the Attitude Determination and Control subsystem in general and Attitude estimation in particular for small Earth observation satellites associated with practical technical parameters and scenarios The thesis’s contributions are: Based on the function, operation and technical characteristics of the star tracker and gyroscope sensors, the author has proposed a data fusion approaches to reliably estimate the satellite attitude, with compact algorithms that are possible to be easily implemented on-board satellite hardware Proposal of a fault-tolerance approach for fuzzy adapted data fusion to ensure that attitude estimator performs well and reliably even in cases of unreliable measurements from attitude sensors 23 ... fusion of gyroscope sensor and star tracker OBJECTIVE OF THE THESIS The thesis focus on: study and proposal of an attitude methods by fusion of measurements from gyroscope sensor and star tracker. .. CONTRIBUTIONS OF THE THESIS The thesis focuses on design and simulation for the Attitude Determination and Control subsystem in general and Attitude estimation in particular for small Earth observation. .. dụng – Hà Nội, 19/12/2014 Small satellite attitude determination by gyroscope and star tracker fusion, International Conference on Information and Convergence Technology for Smart Society - Ho Chi