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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