Investigation of the Influence of Pseudoinverse Matrix Calculations on Multibody Dynamics Simulations by Means of the Udwadia-Kalaba Formulation

Falco, Diego de; Pennestrı̀, Ettore; Vita, L.

doi:10.1061/(asce)0893-1321(2009)22:4(365)

Cited by 52 publications

(20 citation statements)

References 10 publications

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“…A generalized Udwadia-Kalaba type formulation [38,40,41] may also be obtained by a transformation of Eq. (80) as the mass matrix singularity is avoided.…”

Section: Discussion Of Modified Physical Orthogonal Project Methodsmentioning

confidence: 99%

“…When the weight matrix A is taken as the singular mass matrix M, the Moore-Penrose pseudoinverse of the coefficients matrix in Eq. (43) can be expressed in the following form [38,41]:…”

Section: Generalized Physical Orthogonal Projection Methods (Gpopm)mentioning

confidence: 99%

“…(14) can be eliminated by several approaches [1,16], such as Maggi's formulation, the null space formulation [26], the Udwadia-Kalaba formulations [40], the Udwadia-Phohomsiri formulation [33], the leastsquares block solution where the Moore-Penrose pseudo-inverse method is used for the singular mass matrix problem [38,41], and so on. Based on a comparative study in [38], optimal performances have been recorded for the methods based on the least-squares block solution for a moderate size problem which is also considered here.…”

Section: Spatial Multibody Dynamics Equationsmentioning

confidence: 99%

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A constraint violation suppressing formulation for spatial multibody dynamics with singular mass matrix

Zhang

Liu

2015

Multibody Syst Dyn

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The constraint violation problem of spatial multibody systems is analyzed in this paper. The mass matrix is singular in the equations of motion when the Euler parameters with the normalization constraints are used to describe the orientation of the spatial rigid body. The constrained and weighted least-squares-based geometrical projection method is implemented to suppress the constraint violation during numerical integration, and the explicit correction formulation can be obtained by the block matrix inversion scheme. The mass matrix weighted correction formulation gives the physically consistent energy norm, but it needs the mass matrix to be positive definite. To extend the physically consistent correction formulation for solving spatial multibody systems' constraint violation problems with a singular mass matrix, a Modified Mass-Orthogonal Projection Method (MMOPM) and a Generalized Physical Orthogonal Projection Method (GPOPM) are proposed. MMOPM modifies the mass matrix directly by adding a penalty factor matrix which appears in the mass-orthogonal projection method and leads to a positive definite weight matrix that satisfies the block matrix inversion scheme condition. GPOPM is a generalization of the physical orthogonal projection method where the constrained least-squares method is weighted by the positive semi-definite mass matrix and the correction formulation is given by using the generalized block matrix inversion scheme. Numerical results show the feasibility and accuracy of the presented MMOPM and GPOPM. The constraints in position and velocity can reach machine precision during numerical integration. The elimination of violation of position constrains may require few iterations, while the violation of velocity constraints is removed in one step, and GPOPM is more accurate in velocity correction than MMOPM.

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“…A generalized Udwadia-Kalaba type formulation [38,40,41] may also be obtained by a transformation of Eq. (80) as the mass matrix singularity is avoided.…”

Section: Discussion Of Modified Physical Orthogonal Project Methodsmentioning

confidence: 99%

“…When the weight matrix A is taken as the singular mass matrix M, the Moore-Penrose pseudoinverse of the coefficients matrix in Eq. (43) can be expressed in the following form [38,41]:…”

Section: Generalized Physical Orthogonal Projection Methods (Gpopm)mentioning

confidence: 99%

Section: Spatial Multibody Dynamics Equationsmentioning

confidence: 99%

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A constraint violation suppressing formulation for spatial multibody dynamics with singular mass matrix

Zhang

Liu

2015

Multibody Syst Dyn

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“…According to Udwadia and Kalaba theory, [27][28][29][30][31][32] we first establish the dynamic model of the link mechanism by four angle coordinates, which not only makes the modeling process simple and effective but also reduces the dimension of the dynamic equation. In addition, there is no need to solve the complicated Lagrange multipliers during the modeling process.…”

Section: Introductionmentioning

confidence: 99%

Udwadia–Kalaba theory for the control of bulldozer link lever

Zhao

Zhen

et al. 2018

Advances in Mechanical Engineering

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We propose to apply Udwadia-Kalaba theory to the bulldozer dynamics analysis. The bulldozer system is divided into several subsystems by this approach, which simplifies the modeling process for multi-link mechanism. Based on this approach, the constraints are classified into structure constraints and performance constraints. Structure constraints are used to set up dynamic model without regard for trajectory. Performance constraints are the desired trajectory. Then, according to the equation of motion of the unconstrained system established by Lagrange approach and system constraints which include structure and performance constraints, an explicit, closed-form analytical expression for the control force can be obtained by solving Udwadia-Kalaba equation. We demonstrate that this approach does not need to solve Lagrange multiplier, which is always difficult to obtain. However, for bulldozer link lever system, the initial conditions are difficult to satisfy the constraints in the actual situation. Thus, the problem of initial condition deviation is taken into consideration. In the end, the numerical simulations are done to prove that the trajectory of the bulldozer satisfies the designed one and the real-time forces are conveniently acquired.

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“…In the case of the parametric identification problem, one needs to construct analytical expressions in terms of the desired parameters and correlate them with experimental data in order to identify the parameters of interest [62,63]. For this purpose, simple least-square methods, as well as more advanced gradient-based optimization techniques relying on the adjoint method can be used for minimizing the error between the time responses observed in experimental measurements and the time evolutions predicted by the mathematical model based on the unknown parameters [64][65][66][67][68][69]. On the other hand, in the case of the model identification problem in the time domain, one needs to find a linear dynamical model directly that embodies the best fit for an input and output dataset measured for a given mechanical system.…”

Section: Introductionmentioning

confidence: 99%

System Identification Algorithm for Computing the Modal Parameters of Linear Mechanical Systems

Pappalardo

Guida

2018

Machines

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Abstract:The goal of this investigation is to construct a computational procedure for identifying the modal parameters of linear mechanical systems. The methodology employed in the paper is based on the Eigensystem Realization Algorithm implemented in conjunction with the Observer/Kalman Filter Identification method (ERA/OKID). This method represents an effective and efficient system identification numerical procedure based on the time domain. The algorithm developed in this work is tested by means of numerical experiments on a full-car vehicle model. To this end, the modal parameters necessary for the design of active and semi-active suspension systems are obtained for the vehicle system considered as an illustrative example. In order to analyze the performance of the methodology developed in this investigation, the system identification numerical procedure was tested considering two case studies, namely a full state measurement and an incomplete state measurement. As expected, the numerical results found for the identified dynamical model showed a good agreement with the modal parameters of the mechanical system model. Furthermore, numerical results demonstrated that the proposed method has good performance considering a scenario in which the signal-to-noise ratio of the input and output measurements is relatively high. The method developed in this paper can be effectively used for solving important engineering problems such as the design of control systems for road vehicles.

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Investigation of the Influence of Pseudoinverse Matrix Calculations on Multibody Dynamics Simulations by Means of the Udwadia-Kalaba Formulation

Cited by 52 publications

References 10 publications

A constraint violation suppressing formulation for spatial multibody dynamics with singular mass matrix

A constraint violation suppressing formulation for spatial multibody dynamics with singular mass matrix

Udwadia–Kalaba theory for the control of bulldozer link lever

System Identification Algorithm for Computing the Modal Parameters of Linear Mechanical Systems

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