Derivation of All Attitude Error Governing Equations for Attitude Filtering and Control

Younes, Ahmad Bani; Mortari, Daniele

doi:10.3390/s19214682

Cited by 16 publications

(7 citation statements)

References 23 publications

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“…where the term ∆ ∈ R 3 is a disturbance due to the attitude error control, R d is the desired rotation matrix, and R = R T R d describes the discrepancy between the vehicle attitude and the attitude command. The rotation matrix R verifies [33] R(e q ) = q 2 4e − q T ve q ve I + 2q ve q T ve − 2q 4e [q ve ×] ,…”

Section: Position Controlmentioning

confidence: 99%

“…The guidance law (33) only specifies the desired roll and pitch, but it can be extended to include the desired yaw. Let q ψ d represent the desired yaw quaternion, then the desired quaternion can be defined as follows:…”

Section: Position Controlmentioning

confidence: 99%

“…2 can be considered equivalent. Consequently, the last necessary bound for u comes from the quaternion extraction (33) and is given by −u t1 2 + t 2 1 + t 2 3 ≥ 0, which is equivalent to the following inequality…”

Section: Saturated Control Lawmentioning

confidence: 99%

See 2 more Smart Citations

Saturated Trajectory Tracking Controller in the Body-Frame for Quadrotors

Madeiras,

Cardeira,

Oliveira

et al. 2024

Drones

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This paper introduces a quadrotor trajectory tracking controller comprising a steady-state optimal position controller with a normed input saturation and modular integrative action coupled with a backstepping attitude controller. First, the translational and rotational dynamical models are designed in the body-fixed frame to avoid external rotations and are partitioned into an underactuated position system and a quaternion-based attitude system. Secondly, a controller is designed separately for each subsystem, namely, (i) the position controller synthesis is derived from the Maximum Principle, Lyapunov, and linear quadratic regulator (LQR) theory, ensuring the global exponential stability and steady-state optimality of the controller within the linear region, and global asymptotic stability is guaranteed for the saturation region when coupled with any local exponential stable attitude controller, and (ii) the attitude system, with the quaternion angles and the angular velocity as the controlled variables, is designed in the error space through the backstepping technique, which renders the overall system, position, and attitude, with desirable closed-loop properties that are almost global. The overall stability of the system is achieved through the propagation of the position interconnection term to the attitude system. To enhance the robustness of the tracking system, integrative action is devised for both position and attitude, with emphasis on the modular approach for the integrative action on the position controller. The proposed method is experimentally validated on board an off-the-shelf quadrotor to assess the resulting performance.

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Section: Position Controlmentioning

confidence: 99%

Section: Position Controlmentioning

confidence: 99%

See 1 more Smart Citation

Saturated Trajectory Tracking Controller in the Body-Frame for Quadrotors

Madeiras,

Cardeira,

Oliveira

et al. 2024

Drones

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show abstract

“…Just like the Rodrigues Parameters this method possess a singularity, but one where e is undefined when ϕ = 0. Similarly to the other attitude representations, the definition of the PA ϕ & PV e from the quaternion are below [30].…”

Section: Dual Principal Angle and Principal Vectormentioning

confidence: 99%

Dual Attitude Representations and Kinematics for Six-Degree-of-Freedom Spacecraft Dynamics

Stanfield

Younes

2023

IEEE Access

Self Cite

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This paper focuses on the development of three newly formed representations of dual attitude and their respective kinematics equations -Dual Classical Rodrigues Parameters, Dual Modified Rodrigues Parameters, Dual Principal Axis and Principal Angle (Dual Principal Rotation Vector). These three formulations are developed by building off of the theories and concepts used with Dual Quaternions and utilizing numerous attitude identities for quaternions to create new identities using dual quaternions and dual attitudes while detailing the process used throughout the derivation. The accompanying dual kinematic equations using these dual attitude parameters are also generated using their respective dual attitude coordinate systems. Furthermore, the new dual attitude representations with their respective, distinct kinematic equations and identities are validated against a simulated 6-DOF rigid body spacecraft control problem to verify equivalency across equations using the dual quaternion as a baseline.

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“…En referencia a las formas de descripción o representación de la orientación del segmento espacial como cuerpo rígido, se tienen opciones como la matriz de cosenos directores (dcm) o matriz de rotación, ángulos de Euler, parámetros de rotación principales, cuaterniones, parámetros clásicos de Rodrigues, parámetros modificados de Rodrigues o el concepto moderno de parámetros de orientación estereográfica (Schaub & Junkins, 2009). Entre estos conjuntos se pueden tener adiciones o restas para definir el movimiento relativo, integración numérica para predecir la orientación en el tiempo, o la derivación para determinar propiedades del cuerpo rígido en representación (Younes & Mortari, 2019).…”

Section: B Representaciones Movimiento De Orientación O Rotacionalunclassified

Diseño de misión, síntesis de factores operacionales y representaciones del segmento espacial, caso FACSAT y EMFF

Rodríguez-Pirateque

Esmeral

Garcia

et al. 2020

Ciencia y Poder Aéreo

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El presente artículo tiene como propósito el análisis del segmento espacial como parte del proceso de estructuración de un proyecto aeroespacial, partiendo del problema de desarticulación de procesos de diseño, omisión de factores operacionales y desconocimiento del comportamiento del segmento espacial en órbita. Para esto es necesario el recuento de los pasos requeridos en el diseño de misión de un sistema espacial, la arquitectura y subsistemas constitutivos del segmento genérico e identificación de factores operacionales útiles para el desarrollo del concepto de misión. Adicionalmente, se presentan diferentes formas de representación del movimiento de orientación y traslación del segmento espacial, como guía para el modelamiento de misiones de observación terrestre en órbita baja. Con base en esto se obtienen dos caracterizaciones como ejemplos prácticos para las necesidades de diseño y representación, tanto para el diseño de misión con la síntesis de objetivos de misión de un programa espacial, como para la representación del segmento espacial, frente a las necesidades de uso de un arreglo de misión de gran proximidad y con capacidades de maniobra en órbita, que incluso, pueda requerir no solo uno sino varios satélites en coordinación, todo esto mediante el modelo de vuelo de formación electromagnética (EMFF).

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Derivation of All Attitude Error Governing Equations for Attitude Filtering and Control

Cited by 16 publications

References 23 publications

Saturated Trajectory Tracking Controller in the Body-Frame for Quadrotors

Saturated Trajectory Tracking Controller in the Body-Frame for Quadrotors

Dual Attitude Representations and Kinematics for Six-Degree-of-Freedom Spacecraft Dynamics

Diseño de misión, síntesis de factores operacionales y representaciones del segmento espacial, caso FACSAT y EMFF

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