Dual Quaternions as a Tool for Modeling, Control, and Estimation for Spacecraft Robotic Servicing Missions

Tsiotras, Panagiotis; Valverde, Alfredo

doi:10.1007/s40295-019-00181-4

Cited by 19 publications

(10 citation statements)

References 32 publications

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“…The pose error kinematic equation of motion between frames B and D for the dual-quaternion is given by the following [ 28 ]:

which accounts for the angular rate of change, as well as the rate of change of displacement. In the same method of combining the translational and rotational equations of motion ( 8 ) and ( 10 ) into dual-quaternions, the relative pose equation in DQ form [ 28 ] is created and embeds both Equations ( 9 ) and ( 11 ). With one equation of computation, both dynamic equations are accounted for.…”

Section: System Dynamics: Proximity Operationmentioning

confidence: 99%

Dual-Quaternion Analytic LQR Control Design for Spacecraft Proximity Operations

Stanfield

Younes

2021

Sensors

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Proximity operations offer aggregate capability for a spacecraft operating in close proximity to another spacecraft, to perform on-orbit satellite servicing, or to a space object to perform debris removal. To utilize a spacecraft performing such advanced maneuvering operations and perceiving of the relative motion of a foreign spacecraft, these trajectories must be modeled accurately based on the coupled translational and rotational dynamics models. This paper presents work towards exploiting the dual-quaternion representations of spacecraft relative dynamics for proximity operations and developing a sub-optimal control law for efficient and robust maneuvers. A linearized model using dual-quaternions for the proximity operation was obtained, and its stability was verified using Monte Carlo simulations for the linear quadratic regulator solution. A sub-optimal control law using generalized higher order feedback gains in dual-quaternion form was developed based on small error approximations for the proximity operation and also verified through Monte Carlo simulations. Necessary information needed to understand the theory behind the use of the dual-quaternion is also overviewed within this paper, including the validity of using the dual-quaternions against their Cartesian or quaternion equivalents.

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“…The pose error kinematic equation of motion between frames B and D for the dual-quaternion is given by the following [ 28 ]:

Section: System Dynamics: Proximity Operationmentioning

confidence: 99%

Dual-Quaternion Analytic LQR Control Design for Spacecraft Proximity Operations

Stanfield

Younes

2021

Sensors

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“…In [17][18][19], several adaptive nonsingular terminal sliding mode control laws were designed for the fixed-time, 6-DOF tracking control of noncooperative spacecraft fly-around missions. In addition, there have been also some research studies concerned with 6-DOF integrated controls in spacecraft based on the dual quaternion representation [20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Indirect-Neural-Approximation-Based Fault-Tolerant Integrated Attitude and Position Control of Spacecraft Proximity Operations

Alsaade

Yao

Al-zahrani

et al. 2022

Sensors

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In this paper, a neural adaptive fault-tolerant control scheme is proposed for the integrated attitude and position control of spacecraft proximity operations in the presence of unknown parameters, disturbances, and actuator faults. The proposed controller is made up of a relative attitude control law and a relative position control law. Both the relative attitude control law and relative position control law are designed by adopting the neural networks (NNs) to approximate the upper bound of the lumped unknowns. Benefiting from the indirect neural approximation, the proposed controller does not need any model information for feedback. In addition, only two adaptive parameters are required for the indirect neural approximation, and the online calculation burden of the proposed controller is therefore significantly reduced. Lyapunov analysis shows that the overall closed-loop system is ultimately uniformly bounded. The proposed controller can ensure the relative attitude, angular velocity, position, and velocity stabilize into the small neighborhoods around the origin. Lastly, the effectiveness and superior performance of the proposed control scheme are confirmed by a simulated example.

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“…Recently, dual quaternion neural networks (Du-alQNNs) have been shown to be particularly suitable for modelling transformations in 3D space. Due to the 6 degrees of freedom (6DOF) of the the unit dual quaternion representation, DualQNNs can properly model rotations and translations of rigid bodies [19][20][21][22], or knowledge graph embeddings [23,24]. DualQNNs lay their foundations in dual quaternion numbers, which are a composition of two quaternions, thus particularly suitable for encapsulating eight-dimensional inputs.…”

Section: Introductionmentioning

confidence: 99%

Dual Quaternion Ambisonics Array for Six-Degree-of-Freedom Acoustic Representation

Grassucci¹,

Mancini²,

Brignone³

et al. 2022

Preprint

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Spatial audio methods are gaining a growing interest due to the spread of immersive audio experiences and applications, such as virtual and augmented reality. For these purposes, 3D audio signals are often acquired through arrays of Ambisonics microphones, each comprising four capsules that decompose the sound field in spherical harmonics. In this paper, we propose a dual quaternion representation of the spatial sound field acquired through an array of two First Order Ambisonics (FOA) microphones. The audio signals are encapsulated in a dual quaternion that leverages quaternion algebra properties to exploit correlations among them. This augmented representation with 6 degrees of freedom (6DOF) involves a more accurate coverage of the sound field, resulting in a more precise sound localization and a more immersive audio experience. We evaluate our approach on a sound event localization and detection (SELD) benchmark. We show that our dual quaternion SELD model with temporal convolution blocks (DualQSELD-TCN) achieves better results with respect to real and quaternion-valued baselines thanks to our augmented representation of the sound field. Full code is available at: https://github.com/ispamm/DualQSELD-TCN.

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Dual Quaternions as a Tool for Modeling, Control, and Estimation for Spacecraft Robotic Servicing Missions

Cited by 19 publications

References 32 publications

Dual-Quaternion Analytic LQR Control Design for Spacecraft Proximity Operations

Dual-Quaternion Analytic LQR Control Design for Spacecraft Proximity Operations

Indirect-Neural-Approximation-Based Fault-Tolerant Integrated Attitude and Position Control of Spacecraft Proximity Operations

Dual Quaternion Ambisonics Array for Six-Degree-of-Freedom Acoustic Representation

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