Flight Mechanics/Estimation Theory Symposium, 1989

Numerous topics in flight mechanics and estimation were discussed. Satellite attitude control, quaternion estimation, orbit and attitude determination, spacecraft maneuvers, spacecraft navigation, gyroscope calibration, spacecraft rendevous, and atmospheric drag model calculations for spacecraft lifetime prediction are among the topics covered

MIT Space Engineering Research Center

The Space Engineering Research Center (SERC) at MIT, started in Jul. 1988, has completed two years of research. The Center is approaching the operational phase of its first testbed, is midway through the construction of a second testbed, and is in the design phase of a third. We presently have seven participating faculty, four participating staff members, ten graduate students, and numerous undergraduates. This report reviews the testbed programs, individual graduate research, other SERC activities not funded by the Center, interaction with non-MIT organizations, and SERC milestones. Published papers made possible by SERC funding are included at the end of the report

헬름홀츠 케이지를 이용한 저궤도 큐브위성 자세결정 및 제어시스템의 HILS 검증

학위논문 (석사)-- 서울대학교 대학원 : 공과대학 기계항공공학부, 2019. 2. 기창돈.본 논문에서는 자기토커를 구동기로 탑재한 저궤도 큐브위성에 대해, 지구지향 자세유지를 위한 자세결정 및 제어시스템의 성능검증 기법을 제안한다. 반작용휠을 탑재한 일반적인 위성과 달리, 공간적 제약을 가지는 큐브위성의 효과적인 운용을 위해 단순하고 저중량, 저전력의 자기토커만을 구동기로 탑재하여 지구지향 자세유지를 수행한다. 이를 위해, 먼저 큐브위성 자세에 대한 운동방정식을 중력구배토크, 그리고 자기토커의 쌍극자모멘트와 지구 자기장의 외적으로 산출되는 입력 토크에 대해 표현하고, 시스템에 유입되는 불확실성을 잡음원으로 취급하여 선형 시스템 모델을 얻는다. 또한, 태양과 자기장 모델로부터 기준벡터를 정의하고 태양 센서와 자기장 센서, 그리고 자이로스코프 측정치를 융합하여 큐브위성의 자세를 추정하는 확장 칼만 필터를 구성한다. 여기에, 주어진 선형 시스템과 입력에 대해 비용함수를 구성하고 최적해를 산출함으로서 지구지향 자세를 유지하는 LQR 제어기를 설계한다. 제안된 시스템의 성능을 검증하기 위해, 지상환경의 다양한 제약조건을 고려한 HILS가 수행되어야 한다. 하지만, 자기토커만 탑재한 큐브위성은 작은 입력토크, 지구 자기장 크기에 비례한 출력결정, 비연성 제어구동 등의 구동성능 한계로 인해 지상환경에서 전술한 시스템의 효과적인 성능 검증이 어렵다. 지금까지 큐브위성 자세결정 및 제어시스템의 성능검증은 대부분 운용의 안정성 확보를 위한 각속도 안정화, 지구 자기장 정렬에 의존한 수동제어 방식, 그리고 반작용휠을 활용한 지구지향 자세유지의 HILS가 연구되어 왔다. 자기토커만을 탑재한 자세결정 및 제어시스템의 HILS가 제안된 바가 있으나, 지상환경의 제약조건으로 인하여 성능검증에 한계가 있었다. 이와 달리, 제안되는 HILS는 기존방법의 한계를 보완하여 다양한 오차가 내포하는 환경에서 자기토커만을 구동기로 탑재한 큐브위성 자세결정 및 제어시스템의 성능검증에 목표를 두고 있다. 따라서 본 논문에서는 자기토커의 외부자기장 크기에 비례한 출력특성에 착안하여, 헬름홀츠 케이지를 이용한 큐브위성 자세결정 및 제어시스템의 HILS 검증기법이 제안된다. 즉, 지상환경에서 통계적 오차특성을 내포하는 자기장으로 인한 추정 성능저하와 외란에 취약한 자기토커의 작은 입력토크로 인한 제어 성능저하 문제를 헬름홀츠 케이지로부터 생성된 자기장 벡터를 제어함으로써 해결하고자 한다. 이를 위해, 비오-샤바르 법칙을 활용하여 헬름홀츠 케이지의 전류-자기장 관계를 모델링하고 큐브위성을 포함한 공간의 자기장 균일성을 확보할 수 있는 헬름홀츠 케이지를 제작한다. 또한 제시된 헬름홀츠 케이지의 전류-자기장 모델로부터 전달함수를 근사하고 고전제어기법을 활용하면 헬름홀츠 케이지의 자기장 벡터 제어기를 손쉽게 설계할 수 있다. 여기에, 헬름홀츠 케이지 내부공간에 큐브위성을 실에 매달아 단일축 자세결정 및 제어시스템 HILS 환경을 구성하고, 자세결정 및 제어시스템의 HILS 검증을 수행한다. 이때, 실내에 구축된 실험환경에서 GPS 측정치를 산출할 수 없으므로 모사된 태양광과 헬름홀츠 케이지에서 생성되는 자기장의 평균 측정치를 기준벡터로 재정의하여 지구지향 자세를 모사한다. 제시된 HILS 환경에서 헬름홀츠 케이지를 기준으로 좌표계를 정의하면, 지상환경에서 큐브위성의 지구지향 자세유지에 대한 시뮬레이션을 구성할 수 있다. 이러한 시뮬레이션 결과에 근거하여 실제 실험결과와 비교하면, 제안된 자세결정 및 제어시스템의 성능을 해석할 수 있다. 제안된 방법의 유용성을 확인하기 위해, SNUGLITE(Seoul National University GNSS Laboratory satelliTE) 큐브위성의 단일축 자세결정 및 제어시스템 HILS 검증이 제시된다. 제안된 방법은 지상환경에서 큐브위성에 대표적으로 탑재되는 자기토커만을 활용하여, 큐브위성의 지구지향 자세유지를 위한 자세결정 및 제어시스템을 검증할 수 있음을 보인다. 실험결과로부터 기존 방법의 지상환경 제약조건으로 인한 HILS 검증 한계를 헬름홀츠 케이지를 활용하여 보완함을 보인다. 또한, 헬름홀츠 케이지를 활용하지 않는 기존 방법과 비교하여 자세결정 및 제어시스템의 추정 성능 및 제어 신뢰성을 효과적으로 검증할 수 있음을 확인한다. 제안된 HILS 검증기법은 간결성 및 실용성으로 인해 다양한 임무수행을 위한 큐브위성의 자세결정 및 제어시스템 검증에 활용될 것으로 기대된다.In this thesis, Hardware-In-the-Loop Simulation (HILS) verification of attitude determination and control system (ADCS) is addressed for low earth orbit cube-satellite equipped with a magnetorquer only. Unlike ordinary satellites equipped with reaction wheels, only a magnetorquer is mounted on cube-satellite due to spatial constraints. It is a simple, low-weight, and low-power consumption actuator that enables efficient operation of cube-satellite and aims to maintain nadir-pointing control. In order to achieve the objective of the proposed system, firstly, the equations of motion for the cube-satellite is expressed in terms of the gravity gradient torque, and the input torque calculated from the dipole moment of the magnetorquer and geomagnetic field. Then, a linear system model is obtained by interpreting the uncertainty flowing into the system as noise sources. In addition, extended Kalman filter equations are derived to estimate the attitude of the cube-satellite by defining the reference vector from the sun and magnetic field model, and fusing the sun sensor, magnetometer, and gyroscope measurements. Then, LQR controller can be designed to maintain nadir-pointing by calculating the optimal solution from the cost function composed of a given linear system and input. In order to verify the performance of the proposed system, HILS should be performed considering various constraints of the ground environment. However, it is difficult to verify the above-described system in a ground environment due to limitations in the performance of magnetorquer such as small input torque effected by the magnitude of the geomagnetic field, and decoupled input control. So far, it has been studied that the verification of cube-satellite ADCS for the stabilization of angular velocity, the passive control method which depends on geomagnetic field alignment, and HILS using reaction wheels. HILS of ADCS using only magnetorquer also has been proposed, but the performance analysis was limited due to the constraints of the ground environment. In contrast, the proposed HILS is aimed at verifying magnetorquer mounted cube-satellite ADCS that solves the limitations from unknown error factors of the ground environment. Therefore, in this thesis, HILS verification of cube-satellite ADCS using Helmholtz cage is proposed. It is focused on output characteristics proportional to the magnitude of the external magnetic field of the magnetorquer. In other words, it is solved by controlling the magnetic field vector generated from Helmholtz cage that is the degradation of the estimation performance due to the magnetic field including the statistical error characteristic in the indoor environment and the control performance deterioration due to the small input torque of the magnetorquer which is vulnerable to the disturbance. To construct a magnetic field vector from Helmholtz cage, it is designed using the Biot-Savat law to model the current-magnetic field relationship. Also, it is designed to have a size enough to ensure the magnetic field uniformity of the space including the cube-satellite. The magnetic field vector controller of Helmholtz cage can be easily designed by approximating the transfer function from the derived current-magnetic field equation and using the classical control technique. In this case, cube-satellite is suspended in the inner space of Helmholtz cage to perform single axis HILS verification of ADCS. Since the GPS measurement value cannot be calculated in the indoor experiment environment, the nadir-pointing reference vectors are redefined by the mean measurement values of the simulated sunlight and the magnetic field generated from Helmholtz cage. Then, by defining a coordinate system based on the Helmholtz cage in the proposed HILS environment, nadir-pointing control performance can be expected by the computer simulation. Based on these simulation results, the proposed system can be verified by comparison with actual experimental results. To demonstrate the validity of the proposed method, a single axis HILS verification of ADCS using SNUGLITE cube-satellite is presented. The proposed method can verify the performance of nadir-pointing control on the ground by using only the magnetorquer which is typically installed in cube-satellite. It is also confirmed that the estimation performance and the control reliability of ADCS can be verified effectively compared with the method which does not utilize Helmholtz cage. The proposed HILS verification technique is expected to be used for verification of cube-satellite ADCS for various tasks due to its simplicity and practicality.Abstract i Table of Contents v Nomenclature viii List of Figures x List of Tables xiii Chapter 1 Introduction 1 1.1. Brief Review of SNUGLITE Cube-Satellite Project 2 1.1.1. Introduction of SNUGLITE Cube-Satellite 2 1.1.2. SNUGLITE Configuration 4 1.1.3. Former Research of SNUGLITE ADCS 8 1.2. Motivation and Purpose 9 1.3. Literature Survey 11 1.4. Outline of Research 13 1.5. Contribution 15 Chapter 2 Algorithm of Attitude Determination and Control System 17 2.1. Overall System Configuration 18 2.2. Coordinate System 19 2.2.1. Earth-Centered Inertial (ECI) Frame 21 2.2.2. Earth-Centered Earth-Fixed (ECEF) Frame 21 2.2.3. Local Frame 22 2.2.4. Body Frame 23 2.3. Coordinate Transformations 24 2.3.1. Transformation Between ECEF and ECI Frame 25 2.3.2. Transformation Between ECI and Local Frame 25 2.3.3. Transformation Between Local and Body Frame 26 2.4. Dynamics Modeling 28 2.4.1. Nonlinear Equations of Motion 28 2.4.2. Linearized Equations of Motion 32 2.5. Angular Velocity Attenuation for Initial Phase 33 2.6. Attitude Determination Algorithm 34 2.6.1. TRIAD Method 35 2.6.2. Extended Kalman Filter 36 2.7. Attitude Control Algorithm 42 Chapter 3 A Solution for Magnetic Distortion of Cube-Satellite 45 3.1. Magnetometer Calibration for Time-varying Bias 46 3.1.1. Temperature Calibration 46 3.1.2. Current Compensation 50 3.1.3. Hard-Iron and Soft-Iron Compensation 57 3.2. Residual Magnetic Dipole Moment 60 3.3. Simulation 63 3.3.1. Simulation Envirionment 63 3.3.2. Results 69 Chapter 4 Hardware-In-the-Loop Simulation of Attitude Determination and Control System 81 4.1. Helmholtz Cage Design 82 4.1.1. Introduction 82 4.1.2. Mathematical Modeling and Simulation 85 4.1.3. CAD and Assembly 90 4.1.4. Driving Circuit Design 93 4.1.5. Magnetic Field Controller Design 96 4.2. Hardware-In-the-Loop-Simulation 102 4.2.1. HILS Configuration 102 4.2.2. Experiment Results 112 Chapter 5 Conclusion 117 References 120 Abstract in Korean 124Maste

Optimized Filter Design for Non-Differential GPS/IMU Integrated Navigation

The endeavours in improving the performance of a conventional non-differential GPS/MEMS IMU tightly-coupled navigation system through filter design, involving nonlinear filtering methods, inertial sensors' stochastic error modelling and the carrier phase implementation, are described and introduced in this thesis. The main work is summarised as follows. Firstly, the performance evaluation of a recently developed nonlinear filtering method, the Cubature Kalman filter (CKF), is analysed based on the Taylor expansion. The theoretical analysis indicates that the nonlinear filtering method CKF shows its benefits only when implemented in a nonlinear system. Accordingly, a nonlinear attitude expression with direction cosine matrix (DCM) is introduced to tightly-coupled navigation system in order to describe the misalignment between the true and the estimated navigation frames. The simulation and experiment results show that the CKF performs better than the extended Kalman filter (EKF) in the unobservable, large misalignment and GPS outage cases when attitude errors accumulate quickly, rendering the psi-angle expression invalid and subsequently showing certain nonlinearity. Secondly, the use of shaping filter theory to model the inertial sensors' stochastic errors in a navigation Kalman filter is also introduced. The coefficients of the inertial sensors' noises are determined from the Allan variance plot. The shaping filter transfer function is deduced from the power spectral density (PSD) of the noises for both stationary and non-stationary processes. All the coloured noises are modelled together in the navigation Kalman filter according to equivalence theory. The coasting performance shows that the shaping filter based modelling method has a similar and even smaller maximum position drift than the conventional 1st-order Markovian process modelling method during GPS outages, thus indicating its effectiveness. Thirdly, according to the methods of dealing with carrier phase ambiguities, tightly-coupled navigation systems with time differenced carrier phase (TDCP) and total carrier phase (TCP) as Kalman filter measurements are deduced. The simulation and experiment results show that the TDCP can improve the velocity estimation accuracy and smooth trajectories, but position accuracy can only achieve the single point positioning (SPP) level if the TDCP is augmented with the pseudo-range, while the TCP based method's position accuracy can reach the sub-meter level. In order to further improve the position accuracy of the TDCP based method, a particle filter (PF) with modified TDCP observation is implemented in the TDCP/IMU tightly-coupled navigation system. The modified TDCP is defined as the carrier phase difference between the reference and observation epochs. The absolute position accuracy is determined by the reference position accuracy. If the reference position is taken from DGPS, the absolute position accuracy can reach the sub-meter level. For TCP/IMU tightly-coupled navigation systems, because the implementation of TCP in the navigation Kalman filter introduces additional states to the state vector, a hybrid CKF+EKF filtering method with the CKF estimating nonlinear states and the EKF estimating linear states, is proposed to maintain the CKF's benefits while reducing the computational load. The navigation results indicate the effectiveness of the method. After applying the improvements, the performance of a non-differential GPS/MEMS IMU tightly-coupled navigation system can be greatly improved

1999 Flight Mechanics Symposium

This conference publication includes papers and abstracts presented at the Flight Mechanics Symposium held on May 18-20, 1999. Sponsored by the Guidance, Navigation and Control Center of Goddard Space Flight Center, this symposium featured technical papers on a wide range of issues related to orbit-attitude prediction, determination, and control; attitude sensor calibration; attitude determination error analysis; attitude dynamics; and orbit decay and maneuver strategy. Government, industry, and the academic community participated in the preparation and presentation of these papers

A COLLISION AVOIDANCE SYSTEM FOR AUTONOMOUS UNDERWATER VEHICLES

The work in this thesis is concerned with the development of a novel and practical collision avoidance system for autonomous underwater vehicles (AUVs). Synergistically, advanced stochastic motion planning methods, dynamics quantisation approaches, multivariable tracking controller designs, sonar data processing and workspace representation, are combined to enhance significantly the survivability of modern AUVs. The recent proliferation of autonomous AUV deployments for various missions such as seafloor surveying, scientific data gathering and mine hunting has demanded a substantial increase in vehicle autonomy. One matching requirement of such missions is to allow all the AUV to navigate safely in a dynamic and unstructured environment. Therefore, it is vital that a robust and effective collision avoidance system should be forthcoming in order to preserve the structural integrity of the vehicle whilst simultaneously increasing its autonomy. This thesis not only provides a holistic framework but also an arsenal of computational techniques in the design of a collision avoidance system for AUVs. The design of an obstacle avoidance system is first addressed. The core paradigm is the application of the Rapidly-exploring Random Tree (RRT) algorithm and the newly developed version for use as a motion planning tool. Later, this technique is merged with the Manoeuvre Automaton (MA) representation to address the inherent disadvantages of the RRT. A novel multi-node version which can also address time varying final state is suggested. Clearly, the reference trajectory generated by the aforementioned embedded planner must be tracked. Hence, the feasibility of employing the linear quadratic regulator (LQG) and the nonlinear kinematic based state-dependent Ricatti equation (SDRE) controller as trajectory trackers are explored. The obstacle detection module, which comprises of sonar processing and workspace representation submodules, is developed and tested on actual sonar data acquired in a sea-trial via a prototype forward looking sonar (AT500). The sonar processing techniques applied are fundamentally derived from the image processing perspective. Likewise, a novel occupancy grid using nonlinear function is proposed for the workspace representation of the AUV. Results are presented that demonstrate the ability of an AUV to navigate a complex environment. To the author's knowledge, it is the first time the above newly developed methodologies have been applied to an A UV collision avoidance system, and, therefore, it is considered that the work constitutes a contribution of knowledge in this area of work.J&S MARINE LT

Flight Mechanics/Estimation Theory Symposium 1995

This conference publication includes 41 papers and abstracts presented at the Flight Mechanics/ Estimation Theory Symposium on May 16-18, 1995. Sponsored by the Flight Dynamics Division of Goddard Space Flight Center, this symposium featured technical papers on a wide range of issues related to orbit-attitude prediction, determination, and control; attitude sensor calibration; attitude determination error analysis; attitude dynamics; and orbit decay and maneuver strategy. Government, industry, and the academic community participated in the preparation and presentation of these papers

Path planning, flow estimation, and dynamic control for underwater vehicles

Underwater vehicles such as robotic fish and long-endurance ocean-sampling platforms operate in challenging fluid environments. This dissertation incorporates models of the fluid environment in the vehicles' guidance, navigation, and control strategies while addressing uncertainties associated with estimates of the environment's state. Coherent flow structures may be on the same spatial scale as the vehicle or substantially larger than the vehicle. This dissertation argues that estimation and control tasks across widely varying spatial scales, from vehicle-scale to long-range, may be addressed using common tools of empirical observability analysis, nonlinear/non-Gaussian estimation, and output-feedback control. As an application in vehicle-scale flow estimation and control, this dissertation details the design, fabrication, and testing of a robotic fish with an artificial lateral-line inspired by the lateral-line flow-sensing organ present in fish. The robotic fish is capable of estimating the flow speed and relative angle of the oncoming flow. Using symmetric and asymmetric sensor configurations, the robot achieves the primitive fish behavior called rheotaxis, which describes a fish's tendency to orient upstream. For long-range flow estimation and control, path planning may be accomplished using observability-based path planning, which evaluates a finite set of candidate control inputs using a measure related to flow-field observability and selects an optimizer over the set. To incorporate prior information, this dissertation derives an augmented observability Gramian using an optimal estimation strategy known as Incremental 4D-Var. Examination of the minimum eigenvalue of an empirical version of this Gramian yields a novel measure for path planning, called the empirical augmented unobservability index. Numerical experiments show that this measure correctly selects the most informative paths given the prior information. As an application in long-range flow estimation and control, this dissertation considers estimation of an idealized pair of ocean eddies by an adaptive Lagrangian sensor (i.e., a platform that uses its position data as measurements of the fluid transport, after accounting for its own control action). The adaptive sampling is accomplished using the empirical augmented unobservability index, which is extended to non-Gaussian posterior densities using an approximate expected-cost calculation. Output feedback recursively improves estimates of the vehicle position and flow-field states