Optimized design and analysis of cable-based parallel manipulators for enhanced subsea operations

Ghaffar, Asim; Rahman, Muhammad Zia Ur; Leiva, Víctor; Castro, Cecilia

doi:10.1016/j.oceaneng.2024.117012

Ocean Engineering

2024

DOI: 10.1016/j.oceaneng.2024.117012

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Optimized design and analysis of cable-based parallel manipulators for enhanced subsea operations

Asim Ghaffar,

Muhammad Zia Ur Rahman,

Víctor Leiva

et al.

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References 42 publications

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Systems of quaternionic linear matrix equations: solution, computation, algorithm, and applications

Rehman,

Rahman,

Ghaffar

et al. 2024

MATH

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<p>In applied and computational mathematics, quaternions are fundamental in representing three-dimensional rotations. However, specific types of quaternionic linear matrix equations remain few explored. This study introduces new quaternionic linear matrix equations and their necessary and sufficient conditions for solvability. We employ a methodology involving lemmas and ranks of coefficient matrices to develop a novel algorithm. This algorithm is validated through numerical examples, showing its applications in advanced fields. In control theory, these equations are used for analyzing control systems, particularly for spacecraft attitude control in aerospace engineering and for control of arms in robotics. In quantum computing, quaternionic equations model quantum gates and transformations, which are important for algorithms and error correction, contributing to the development of fault-tolerant quantum computers. In signal processing, these equations enhance multidimensional signal filtering and noise reduction, with applications in color image processing and radar signal analysis. We extend our study to include cases of $ \eta $-Hermitian and i-Hermitian solutions. Our work represents an advancement in applied mathematics, providing computational methods for solving quaternionic matrix equations and expanding their practical applications.</p>

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Systems of quaternionic linear matrix equations: solution, computation, algorithm, and applications

Rehman,

Rahman,

Ghaffar

et al. 2024

MATH

View full text Add to dashboard Cite

show abstract

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Optimized design and analysis of cable-based parallel manipulators for enhanced subsea operations

Cited by 1 publication

References 42 publications

Systems of quaternionic linear matrix equations: solution, computation, algorithm, and applications

Systems of quaternionic linear matrix equations: solution, computation, algorithm, and applications

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