Updating of Finite Element Models for Controlled Multibody Flexible Systems Through Modal Analysis

Richiedei, Dario; Trevisani, Alberto

doi:10.1007/978-3-030-23132-3_32

Cited by 2 publications

(4 citation statements)

References 7 publications

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“…In multibody system dynamics, springs are usually modeled as lumped parameters [53][54][55]; however, in the Rollo architecture, springs are not only elastic elements but mostly structural elements, and their mass can not be neglected. Each flexible modulus is composed of a spring and two steel attachments.…”

Section: Discussionmentioning

confidence: 99%

Dynamic Balance of the Head in a Flexible Legged Robot for Efficient Biped Locomotion

et al. 2021

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In the biped robotics domain, head oscillations may be extremely harmful, especially if the robot is teleoperated, since vibrations strongly reduce the operator’s spatial awareness. In particular, undesired head oscillations occur in under-actuated robots, where springs and passive mechanisms are used to achieve a human-like motion. This paper proposes an approach to reduce the vibrations of a biped robot’s head; the proposed solution does not affect the dynamic locomotion properties, on which specific control logic could have been already tuned. The approach is tested on Rollo, a flexible-biped-wheeled robot, whose head vibrates throughout the robot locomotion. The two requirements, i.e., head vibration reduction and unchanged Rollo locomotion properties, are traduced in constraints to the robot possible modifications. Based on a 1D finite element model of the robot, tuned on experimental modal analysis, the undesired vibration causes are detected, and a solution for their reduction is proposed. Rollo’s head vibration amplitude is attenuated using a tuned vibration absorber, which achieves impressive performance in the robot. An archetype of the proposed vibration absorber is tailored designed on Rollo, without invasive changes to the robot structure. The proposed approach solves a significant problem in the biped robotic research community. The approach used to reduce the Rollo head oscillations may be utilized in other biped robot machines with or without flexible legs.

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Section: Discussionmentioning

confidence: 99%

Dynamic Balance of the Head in a Flexible Legged Robot for Efficient Biped Locomotion

et al. 2021

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“…In Equation 13, symbol * denotes the conjugate transpose, as λ, φ, and ψ may be complex valued. The quadratic eigenvalue problem in Equations (12) and (13) has 2n do f eigenvalues, which are symmetric with respect to the real axis of the complex plane, being the system matrices real [35]. This means that the system eigenvalues can be either real or complex, but in the last case, they occur in complex conjugate pairs as well as the corresponding eigenvectors: if λ 1 = λ r + iλ i is a system eigenvalue, then λ 2 = λ r − iλ i is a system eigenvalue too, and the corresponding eigenvectors are φ 1 = φ r + iφ i and φ 2 = φ r − iφ i , respectively.…”

Section: Modal Analysis For Systems With Nonsymmetric Matricesmentioning

confidence: 99%

“…where N ∈ R n do f ×n do f can be any nonsingular matrix; here it is considered N = M. The quadratic (Equations (12) and (13)) and the generalized (Equations (14) and (15)) eigenvalue problems have the same 2n do f eigenvalues, whereas the corresponding eigenvectors are correlated by the following relations,…”

Section: Modal Analysis For Systems With Nonsymmetric Matricesmentioning

confidence: 99%

“…The dynamic behavior of a mechanical system can be easily studied by means of modal analysis, which provides the system modal parameters or characteristics (i.e., natural frequencies, mode shapes, and damping ratios). The knowledge of the modal characteristics is a fundamental requirement for the implementation of several advanced model-based engineering techniques, such as motion planning [1], control design [2,3], stability analysis [4,5], model reduction [6][7][8][9][10], model updating [11][12][13], and structural modification [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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Flexible-Link Multibody System Eigenvalue Analysis Parameterized with Respect to Rigid-Body Motion

Palomba¹,

Vidoni²

2019

Applied Sciences

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The dynamics of flexible multibody systems (FMBSs) is governed by ordinary differential equations or differential-algebraic equations, depending on the modeling approach chosen. In both the cases, the resulting models are highly nonlinear. Thus, they are not directly suitable for the application of the modal analysis and the development of modal models, which are very useful for several advanced engineering techniques (e.g., motion planning, control, and stability analysis of flexible multibody systems). To define and solve an eigenvalue problem for FMBSs, the system dynamics has to be linearized about a selected configuration. However, as modal parameters vary nonlinearly with the system configuration, they should be recomputed for each change of the operating point. This procedure is computationally demanding. Additionally, it does not provide any numerical or analytical correlation between the eigenpairs computed in the different operating points. This paper discusses a parametric modal analysis approach for FMBSs, which allows to derive an analytical polynomial expression for the eigenpairs as function of the system configuration, by solving a single eigenvalue problem and using only matrix operations. The availability of a similar modal model, which explicitly depends on the system configuration, can be very helpful for, e.g., model-based motion planning and control strategies towards to zero residual vibration employing the system modal characteristics. Moreover, it allows for an easy sensitivity analysis of modal characteristics to parameter uncertainties. After the theoretical development, the method is applied and validated on a flexible multibody system, specifically using the Equivalent Rigid Link System dynamic formulation. Finally, numerical results are presented and discussed.

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Updating of Finite Element Models for Controlled Multibody Flexible Systems Through Modal Analysis

Cited by 2 publications

References 7 publications

Dynamic Balance of the Head in a Flexible Legged Robot for Efficient Biped Locomotion

Dynamic Balance of the Head in a Flexible Legged Robot for Efficient Biped Locomotion

Flexible-Link Multibody System Eigenvalue Analysis Parameterized with Respect to Rigid-Body Motion

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