Modern Spacecraft Guidance, Navigation, And Control. From System Modeling To AI And Innovative Applications

Front Cover
Modern Spacecraft Guidance, Navigation, and Control
Modern Spacecraft Guidance, Navigation, and Control: FROM SYSTEM MODELING TO AI AND INNOVATIVE APPLICATIONS
Copyright
Contents
List of contributors
BIOGRAPHY
0 Introduction
	one - Introduction
		Modern spacecraft GNC: what, why, how, for whom?
			Book content
			How to use the book?
			What is not contained in this book?
		A brief historical review of classical spacecraft GNC
		GNC terminology
		GNC architecture: from requirements to preliminary design
			GNC subsystem design
				GNC modes
				System redundancy
				Mission phases
			Consider the anomalies
			Mode management
				Mode transition and finite state machine
				Automation, autonomy, and autonomicity
				On-board versus ground-based
			Verify the preliminary design
		Notation rules
			Notation table
			List of Acronyms
		References
ONE -  Fundamental GNC tools
	Two - Reference systems and planetary models
		Earth and planetary models
			Position representation
			Geoid and geopotential models
		Coordinate reference systems
			Heliocentric coordinate system, XYZ
			Geocentric equatorial coordinate system, IJK (ECI)
			Geocentric earth-fixed coordinate system, IFJFKF
			Topocentric coordinate systems
				Topocentric equatorial
				Topocentric horizon
			Lunar coordinate systems
				Mean earth/polar axis
				Principal axes
			Three-body synodic and inertial coordinate systems, XsYsZs and XIYIZI
				Lunar Centered ROTating
			Satellite-based coordinate systems
				Perifocal coordinate systems, PQW
				Satellite coordinate system, RSW (LVLH)
			Satellite body coordinate systems, b1b2b3
				Auxiliary satellite body coordinate systems
		Coordinate transformations
			ECI to ECEF
			ECI to PQW
			ECI to RSW (LVLH)
		Time
			Universal time
			Julian dates
		What is relevant for GNC?
		References
	Three . The space environment
		Perturbation sources
		External perturbations
			Gravity field of a central body
			Gravitational models
			Magnetic field
			Atmospheric drag
			Solar radiation pressure
				Eclipse
				Albedo and infrared emission
			Third-body perturbation
			Ephemerides
				Chebyshev polynomials
				Coefficients computation
				Chebyshev interpolation
		External perturbations modeling guidelines
			Gravity
			Magnetic field
			Atmospheric models
			Solar radiation
			Third-body perturbation
		Internal perturbations
			Flexibility
				Example of a discrete parameters modeling
				Example of a distributed parameters modeling
				Effects on dynamics and GNC
			Sloshing
			Parasitic forces and torques during thrusters firing
				Deviation angle
				Center of mass variation
				Thrust magnitude accuracy
				Effects on dynamics and GNC
			Electromagnetic disturbances
			Internal vibrations
				Reaction wheel jitter
			Parasitic forces and torques due to plume impingement
			Thermal snap
		Internal perturbations modeling guidelines
		What is relevant for GNC?
		References
	Four - Orbital dynamics
		Two-body problem
			Integrals of motion and orbital elements
				Integrals of motion
					Specific angular momentum
					Eccentricity vector
					Specific energy
				Orbital elements
				Two-line elements
			Geometrical classification of the conics
			Energetic analysis and cosmic velocities
			Operative classification of orbits
				Low Earth orbits
				Geosynchronous/geostationary orbits
				Medium Earth orbits
				Sun-synchronous orbits
			Time laws and orbital period
				Circular orbits
				Parabolic orbits
				Elliptic orbits
				Hyperbolic orbits
				Universal time law
				Summary
			Orbital perturbations
				A numerical approach: the Cowell\'s formulation
				An analytical approach: Gaussian Variation of Parameters
					Semimajor axis
					Eccentricity
					Inclination
					Right ascension of the ascending node
					True anomaly
					Argument of periapsis
			Validity range of the two-body problem
		Three-body problem
			Circular Restricted Three-Body Problem
			Elliptic Restricted Three-Body Problem
			Periodic Motion in the Restricted Three-Body Problem
				Circular Restricted Three-Body Problem
				Elliptic Restricted Three-Body Problem
		Irregular solar system bodies
			Spherical Harmonics Expansion Model
			Ellipsoidal model
			Mass concentration model
			Polyhedral model
		Relative orbital dynamics
			Linearization of the equations of motion
				True anomaly parametrization in linearized relative dynamics
			Linearized equations of motion for nearly circular orbits
				Analysis and characteristic of the unperturbed motion
					Concentric coplanar absolute orbit
					Circular relative orbit
					Stationary coplanar elliptical relative orbit
					Impulsive shots
			J2-perturbed relative dynamics
			Relative dynamics modeling using relative orbital elements
				Coordinates transformation
				Relative motion geometry
				Energy-matching condition and passive safety
				Perturbed relative dynamics with relative orbital elements
			Comparison of relative dynamics modeling
				Cartesian and relative orbital elements mapping
		References
	Five - Attitude dynamics
		Attitude kinematics
			Direction cosine matrix
			Euler angles
			Euler axis and angle
			Quaternions
				Successive rotations
				Relative quaternion
			Attitude variation in time
				Angular velocity
				Euler angles kinematics
				Quaternions kinematics
		Attitude dynamics
			Inertia matrix
			Rigid body dynamics
				Angular momentum
				Rotational kinetic energy
				Euler equation
			Attitude stability
			Dual spin dynamics
			Environmental torques
				Gravity gradient torque
				Magnetic torque
				Aerodynamic torque
				Solar radiation pressure torque
		Three-body problem attitude dynamics
		Relative attitude dynamics
		Multibody spacecraft dynamics
		References
	Six - Sensors
		Sensor modeling for GNC
			Elements of metrology
			Probability and stochastic processes
				Random variables
					Uniform random variables
					Gaussian random variables
				Stochastic processes
			Sensor calibration
			Errors modeling
				Bias
				Scale factor errors
				Noise and random errors
					Random errors with uniform distribution
				Quantization errors
				Misalignment and nonorthogonality errors
				Output saturation, temporal discretization, and latencies
		Sensor faults
		Orbit sensors
			GNSS sensors
				GNSS basics
				GNSS signals
				GNSS receivers
				GNSS accuracy
				Multiconstellation GNSS receivers
				GNSS sensor model
			Ground-based orbit determination
				Ground segment
				Space segment
				Ground-based orbit determination accuracy
		Attitude sensors
			Magnetometers
			Sun sensors
				Analog sun sensors
					Coarse sun sensors
					Fine sun sensors
				Digital Sun sensors
				Sun presence sensors
				Sun sensor model
			Horizon sensors
			Star sensors
			Performance comparison
		Inertial sensors
			Typical error sources
			Inertial sensors performances
			Allan variance and statistical error representation
			Gyroscope model
		Electro-optical sensors
			Cameras
				Applicability
				Design
			LIDAR
		Altimeters
			Altimetry principles
			Radar and laser altimeters
			Altimeter model
		References
	Seven - Actuators
		Actuator modeling for GNC
			Errors modeling
			Actuator faults
		Thrusters
			Thrusters assembly
			Thrust management and actuation function
			Thrusters model
		Reaction wheels
			Reaction wheels assembly
			Friction and microvibrations
			Multiple reaction wheels actuation function
			Reaction wheels performance
			Reaction wheels model
		Control moment gyros
		Magnetorquers
			Magnetorquers assembly
			Magnetorquers actuation function
			Magnetorquers performance
			Magnetorquers model
		References
Two- Spacecraft GNC
	Eight - Guidance
		What is guidance?
		On-board versus ground-based guidance
		Guidance applications
			Design process
				General design approach
				Understanding the dynamical system
				Guidance representations
				Optimization
					Classical formulation of the optimal control problem
					Indirect methods versus direct methods
					Trajectory optimization methods
					A simple example
				Interpolation
					Interpolation formulas
					Inverse interpolation
					Spline interpolation
				Application: rendezvous guidance
					Relative motion for rendezvous guidance applications
					Effect of velocity impulses
					Impulsive maneuvers and trajectories
						Two-point transfer
						Cotangential (Hohmann) transfer
						Trajectory-crossing maneuver
						Periodic (radial hop) transfer
						Drift modulation (tangential hop) transfer
						Multiple impulse transfer
						Out-of-plane maneuver
					Forced motion
				Application: attitude guidance
					One-axis pointing
					Two-axis pointing
						Extended vector normalization
					Reorientation
					Quaternion rotation: LVLH, PQW, and RSW
			Design of a guidance function
				Identification of guidance requirements
				Guidance modes
				Architecture
				Function library
		Guidance implementation best practices
		References
	Nine - Navigation
		What is navigation?
		On-board versus ground-based navigation
		Sequential filters
			Working principle
			Sequential filters for spacecraft navigation
				Kalman filter
				H∞ filter
				Extended Kalman filter
				Unscented Kalman filter
				Particle filter
			Parameters estimation
				State augmentation for parameter estimation
					Bias estimator
				Use of consider states—Schmidt–Kalman filter
		Batch estimation
			Least squares
			Dynamic effects
			Effect of observation errors
			Inclusion of a priori information data
			Problems in batch orbit determination
				Presence of nonlinearities
				Incorrect a priori statistics and unmodeled parameters
				Numerical problems
			Square root information filter
			U-D filter
		Absolute orbit navigation
			GNSS spacecraft navigation
				GNSS observables
					Pseudorange
					Carrier phase
					Doppler measurements
				Error effects
					Ionospheric effects
					Tropospheric effects
					Relativistic effects
					Earth tidal effects
					Multipath effects
				GNSS navigation approaches
					Precise point positioning
					Precise orbit determination
					Real-time navigation
						GNSS-INS integration
					Relative GNSS navigation
			Pulsar-based spacecraft navigation
				Clock errors
				Ephemerides error
			Ground-based orbit determination
		Absolute attitude navigation
			Triad
			Wahba problem
				SVD method
				Davenport q-method
				QUEST method
			Estimation of angular velocity
			Kalman filtering
			Complementary filter
		Relative navigation
		Image processing techniques
			Image representation
			Segmentation
				Local methods
				Global methods
			2D shape representation
				Contour-based shape representation
					Chain codes
					Geometric boundary-based features
					Fourier transforms
				Region-based shape representation
					Scalar region descriptors
					Moments
				Applicative case - circular object detection
					Centroid detection
					Limb detection and fitting
			3D vision
				Projective geometry
					Homography
					Point correspondence-based homography estimation
						Maximum likelihood estimation
						Robust estimation
				Pinhole camera model
					Camera calibration from a known scene
				Multiple views scene reconstruction
					Triangulation
					Projective reconstruction
					Pose estimation
				3D vision summary
			Two-views geometry
				Epipolar geometry
				Relative motion of a camera
					Fundamental matrix estimation
						Eight-point algorithm
						Seven-point algorithm
					Camera matrix and 3D point computation
				Stereo correspondence
			Application cases - from subpixel to resolved object
				Subpixel
				Few tenths of pixels
				Resolved object
					Known object
					Unknown object
			Image processing and spacecraft navigation
		Navigation budgets
			Estimation error and filter robustness
			Convergence
			Effect on the GNC chain
		Navigation implementation best practices
			How to choose the right sequential filter?
			Design, implementation, tuning, and useful checks for sequential filters
				General design considerations
				Implementation workflow
				Implementation efficiency
			How to choose the right batch filter?
				Implementation workflow
			Navigation filters tuning
		References
	Ten - Control
		What is control?
		Control design
			Basic terminology
			Properties of feedback control
			Control objective and performance
				Closed-loop stability
				Static and dynamic performance
				Disturbance and measurement noise rejection
				Robustness to uncertainty
			Controllability
			Control design in frequency domain
				Stability and stability margins
				Sensitivity functions
					Response to setpoint
					Disturbance rejection
					Noise measurement rejection
				Loop-shaping design
				Feedforward design
			Control design in the state space
				Stability analysis in state space
				State feedback control law
				Pole placement
				Pole placement for first-, second-, and high-order systems
				Feedforward term
				Integral action
			Limitations to control performance
				Bode\'s integral formula
				Nonminimum phase systems
			An introduction to control design for nonlinear systems
				Linearization
				Gain scheduling
				Feedback linearization
				Stability analysis for nonlinear systems
				Attitude regulation example
		Review of control methods
			PID control
			Linear quadratic regulator
				Finite-horizon linear quadratic regulator
				Infinite-horizon linear quadratic regulator
				Linear quadratic Gaussian control
			Adaptive control
				Model reference adaptive control
				Adaptive dynamical inversion
				Additional parameters estimation
				Convergence of parameters
				Adaptive control issues
			Robust control
				H-infinity
				Mu-control
				Robust adaptive controllers
			Model predictive control
				Robust model predictive control
			Sliding mode control
		Control budgets
		Control implementation best practices
		References
	Eleven - FDIR development approaches in space systems
		FDIR in space missions, terms, and definitions
			Terms and definitions
		Current FDIR system development process and industrial practices
		FDIR system hierarchical architecture and operational concepts
		FDIR system implementation in European Space missions
		FDIR system verification and validation approach
		FDIR concept and functional architecture in GNC applications: a short overview
		References
	Twelve - GNC verification and validation
		Why it is important?
		Statistical methods
		MIL test
			Modeling of AOCS/GNC algorithms
				Architecture
				Avionics delays
				Multirate
				Tunable parameters
				Requirements tracing
				GNC optimization
				Modeling rules
			Verification activities at MIL level
				Algorithms verification and validation
				Requirements verification
					Models requirement verification
					Code requirement verification
				Models profiling
				Modeling standards verification
				Model coverage verification
		SIL/PIL test
			Autocoding
			Software-in-the-loop
			Processor-in-the-loop
			Verification activities at SIL level
				Code functional verification
				Requirements verification
				Code standards verification
				Code coverage verification
			Verification activities at PIL level
		HIL test
			Examples of HIL testing for hardware verification
			Examples of HIL testing for software verification
		In-orbit test
		References
	Thirteen - On-board implementation
		Spacecraft avionics
			General-purpose processor or microcontroller
			Digital signal processor
			Graphical processing unit
			Field programmable gate array
			FPGAs in space: history, present, and future
			Application-specific integrated circuit
			System-on-chip
		On-board processing avionics
			Accommodation of GNC functions into the on-board SW
		On-board implementation alternatives
			Multiple processors
			Processor and multiple DSPs
			FPGA
				Single FPGA
				Multi-FPGA
				FPGA and hard-IP processor
				FPGA including softcore processor
				FPGA and FPGA including softcore processor
			System-on-chip
				FPGA SoC
				DSP or GPU SoCs
			ASIC
				ARM-based ASIC CPU
		On-board implementation and verification
		References
Three - AI and modern applications
	Fourteen - Applicative GNC cases and examples
		AOCS design
			AOCS design process and subsystem architecture
			Evaluation of criticalities
			System-level trade-offs
			Definition of AOCS modes
			Definition of control types
			Sensors selection and actuators sizing
		Orbital control system
			Impulsive and low-thrust maneuvers
			Orbital maneuvers
				Coplanar maneuvers
				Plane change maneuvers
				Lambert\'s problem
			Low-thrust trajectory design
			Station-keeping
		Attitude control system
			Detumbling
				Classic
				B-dot
			One-axis pointing
				Maximize secondary target
			Three-axis pointing
				Two loops
			Effects of disturbances
			Control with reaction wheels
				Desaturation
			Control with magnetorquers
			Solar panels pointing
			Robust attitude control of a spacecraft with two rotating flexible solar arrays
				Substructuring modeling
					Main body
					Flexible solar array with revolute joint
					Assembling of the whole spacecraft
				Robust attitude control synthesis
		Relative GNC
			Guidance for relative and proximity maneuvers
			Trajectory design and sensors selection
			Guidance and control strategies
				Impulsive
				Artificial potential field
					Active collision avoidance
					Tracking controller
				Model Predictive Control
				Optimal control
			Rendezvous in cislunar space
		On-board sensor processing
			Sensor failure detection, isolation, and recovery
			Autonomous on-board sensor calibration
			GNSS-INS integration for on-board orbit determination
		Irregular solar system bodies fly around
		GNC for planetary landing
			Planetary landing guidance
				Formulation
				Guidance algorithms
					Polynomial method
					Potential field method
					Zero-effort-miss/zero-effort-velocity method
					Pseudospectral method
					Convex optimization method
				Sensors and navigation
				Hazard avoidance
		References
	Fifteen - Modern Spacecraft GNC
		AI in space—Introduction
			Introduction
				AI, ML, DL, and ANN: What is the difference?
			Learning paradigms: supervised, unsupervised, and reinforcement learning
			Unsupervised learning: k-means clustering
			Supervised learning: regression and classification
				Linear regression
					Model representation
					Cost function for regression
					Parameter learning: gradient descent
					Feature engineering and polynomial regression
					Generalization: under- and overfitting, training, test, and validation set
				Logistic regression for binary classification
					Model representation
					Cost function for binary classification
				Artificial neural networks for multiclass classification
					Universal approximation theorem
					Model representation
					Cost function for multiclass classification
					ANN parameter learning: backpropagation and gradient descent
			Types of artificial neural networks
				Radial basis function neural network
				Convolutional neural networks
					Image classification networks
					Image segmentation networks
					Object detection network
				Recurrent neural networks
					Nonlinear autoregressive exogenous model
					Hopfield neural networks
					Long short-term memory
			Applications scenarios and AI challenges
		Artificial intelligence and navigation
			Introduction to pose estimation
			AI-based relative pose estimation
			Interface with navigation and uncertainty estimate
			Use case scenario: keypoints regression architecture
				Keypoints detection network – training, testing, and inference
				Covariance computation
				PnP solver for state filter initialization
				State estimator
		Validation of AI-based systems
			CNN validation – methods and metrics
				Camera intrinsic calibration
				Camera-to-mockup extrinsic calibration
				Closed-loop hand-eye calibration
				Error metrics
			Training augmentation techniques
			Use case scenario – validation of keypoints detection accuracy
		Reinforcement learning
			Deep reinforcement learning algorithms
				Q-Learning and deep Q-learning network
				Advantage actor-critic network
				Proximal policy optimization
				Model-based reinforcement Learning
			Inverse reinforcement learning
				Feature-matching approaches
				Maximum entropy
		AI use cases
			Neural dynamics reconstruction through neural networks
				Fully neural dynamics learning
				Dynamics acceleration reconstruction
				Parametric dynamics reconstruction
			Convolutional neural networks for planetary landing
			Deep reinforcement learning for uncooperative objects fly around and planetary exploration
				Meta-reinforcement learning
		AI on-board processors
		Innovative techniques for highly autonomous FDIR in GNC applications
			FDIR system evolution in the next years
			Model-based methods for implementing FDIR systems in GNC applications
			Data-driven techniques for implementing FDIR systems in GNC applications
			Development workflow for data-driven FDIR systems
			Challenges and next steps for the industrial implementation of advanced FDIR systems
		Small satellites/CubeSats
			Introduction
			Hardware limitations
				The burden of miniaturization
				Size and mass limitation
				Pointing performances
				Thrusters
			COTS components
				COTS or custom?
				Magnetometers
				Sun sensors and earth sensors
				Star trackers
				Inertial sensors
				GNSS receivers
				Reaction wheels
				Magnetic torquers
			GNC system example
				Inertial measurement unit
				Sun sensors
				Magnetometers
				Star trackers
				GNSS receiver
				Reaction wheels
				Magnetorquers
			Verification and testing limitations
				Software-in-the-loop
				Hardware performance tests
				Hardware functional tests
				Hardware-in-the-loop
		References
		Further reading
	Sixteen - Mathematical and geometrical rules
		Matrix algebra
			Square matrices
			Matrix multiplication
				Properties
			Matrix inversion
				Analytical computation
			Frobenius norm
			Matrix rank
			Eigenvectors
			Singular value decomposition
		Vector identities
			Vector norm
			Dot product
			Cross product
			Outer product
		Quaternion algebra
			Quaternion from two directions
		Basics of statistics
			Scalar statistics parameters
			Vector and matrix forms of statistic quantities
		ECI-ECEF transformation
			Polar motion
			Sidereal time
			Nutation
			Precession
		References
	Seventeen - Dynamical systems theory
		State-space models
		Discrete-time systems
		Transfer functions
		References
	Eighteen - Autocoding best practices
		List of main architectural and implementation rules
			Architectural rules
			Implementation rules
				Mandatory
				Strongly recommended
				Recommended
			Configuration parameters setup
		Reference
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	X
	Y
	Z
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