Generalization of the Moore–Penrose inverse

Stojanović, Katarina; Mosić, Dijana

doi:10.1007/s13398-020-00928-x

Cited by 10 publications

(12 citation statements)

References 29 publications

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“…Set different posture alignment paths for experiment and compare the experimental value with the model value. It can be found that the maximum error percentage is less than 1.61% which is lower than the maximum value of the error percentage 1.98% in comparative literature [30].…”

Section: Experiments Verificationmentioning

confidence: 94%

“…It can be seen from Table II that the dynamic modeling method proposed has a shorter calculation time and high efficiency, which is 56.28% lower than Moore–Penrose [30] and has more advantages in the design of dynamic controllers. The dynamic modeling method proposed can improve the anti-interference and anti-noise performance of the parallel posture alignment mechanism.…”

Section: Simulation Analysismentioning

confidence: 99%

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High-efficiency inverse dynamics modeling of parallel posture alignment mechanism with actuation redundancy

Wang

Sun

2023

Robotica

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The analytical expression of driving force is helpful to quickly plan the kinematic trajectory of parallel mechanism for automatic drilling and riveting. For parallel posture alignment mechanism, because of its closed-loop characteristics, the inverse dynamic solution is more complex, especially for parallel bracket with actuation redundancy. Considering that the telescopic rods are actually flexible parts, the dynamic analytical modeling is carried out with deformation supplementary equation. Taking the force at the spherical joint as the intermediate variable and the driving force of each active prismatic pair are analytically analyzed by vector cross-product. The modeling was verified by experiment. Compared with previous research methods, the analytical method proposed improves the solution accuracy of driving force slightly and reduces the driving force solution time by 56.28%, which is high efficiency. The maximum error percentage is 1.61%, and the experimental results show that the method of inverse dynamics modeling is practical. This paper can be used for driving force analysis of parallel posture alignment mechanism based on positioner in the field of aircraft assembly.

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Section: Experiments Verificationmentioning

confidence: 94%

Section: Simulation Analysismentioning

confidence: 99%

High-efficiency inverse dynamics modeling of parallel posture alignment mechanism with actuation redundancy

Wang

Sun

2023

Robotica

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“…To extend the concept of the Moore-Penrose inverse from an operator with closed range to a generalized Drazin invertible operator, the generalized Moore-Penrose inverse was introduced in [18] as a new generalized inverse. For A ∈ B(H) d , the generalized Moore-Penorse (or gMP) inverse of A is defined as unique solution to the system…”

Section: Ts (Ormentioning

confidence: 99%

“…the gMP inverse A ⋄ and the *gMP inverse A ⋄ reduce to the Moore-Penrose inverse A † [18]. Interesting properties of the gMP inverse can be found in [4,18].…”

Section: Ts (Ormentioning

confidence: 99%

Inner-gMP and gMP-inner inverses

Stojanovic,

Mosic

2024

Hacettepe Journal of Mathematics and Statistics

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Solving some systems of operator equations, new kinds of generalized inverses are introduced. Since these new inverses can be expressed by inner and gMP inverses, they are called inner-gMP and gMP-inner inverses. In this way, the concepts of gMP, 1MP and MP1 inverses are generalized. Various representations and characterizations of inner-gMP and gMP-inner inverses are presented. Using the inner and *gMP inverse, we define the inner-*gMP and *gMP-inner inverses which are new extensions of 1MP, MP1 and *gMP inverses. We apply inner-gMP and gMP-inner inverses as well as inner-*gMP and *gMP-inner inverses to solve several kinds of linear equations. Consequently, we obtain solvability of the normal equation which is connected to the least--squares solution. Numerical examples are given to illustrate our results.

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“…Let X be the MPCEP inverse of A; the authors of [8] proved that XAX = X, R(X * ) = R(A k ) and R(X) = R(A † A k ). A matrix (X) is called the generalized Moore-Penrose inverse (or gMP) of A [9] (Theorem 1 and Definition 1) if…”

Section: Introductionmentioning

confidence: 99%

Existence Criteria and Related Relation of the gMP Inverse of Matrices

Xu,

Zou,

Zuo

2024

Mathematics

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New characterizations of the gMP inverse are provided by the core part of the core-EP decomposition. We also answer the question as to whether X is the gMP inverse of A under the conditions of R(X)⊆R(A*Ak) or N((Ak)*)⊆N(X). We investigate the relationship between the core-EP inverse and the gMP inverse.Using the gMP inverse, the gMP relation is investigated in view of the core-EP decomposition.

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Generalization of the Moore–Penrose inverse

Cited by 10 publications

References 29 publications

High-efficiency inverse dynamics modeling of parallel posture alignment mechanism with actuation redundancy

High-efficiency inverse dynamics modeling of parallel posture alignment mechanism with actuation redundancy

Inner-gMP and gMP-inner inverses

Existence Criteria and Related Relation of the gMP Inverse of Matrices

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