A new switching strategy for addressing Euler parameters in dynamic modeling and simulation of rigid multibody systems

Haghshenas-Jaryani, Mahdi; Bowling, Alan

doi:10.1007/s11044-012-9333-8

Cited by 10 publications

(6 citation statements)

References 15 publications

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“…As pointed out in the introduction, a three-parametric description of rotations may lead to singularities [3][4][5][33][34][35][36][37] in the equations of motion. Therefore, a description in terms of four parameters, so-called quaternions for Euler parameters, is used.…”

Section: Spatial Multibody Dynamics Equations With Quaternions 21 Atmentioning

confidence: 99%

“…For example, in the spatial multibody dynamics, the mass matrix could be singular when more than six coordinates are used to define the position and the attitude of the rigid body [33][34][35]. This is always the case when Euler parameters or natural coordinates are used, which can avoid the drawback that the minimal set of orientation coordinates including three independent parameters (e.g., Euler angles, Bryan angles, Rodriguez parameters, etc.)…”

Section: Introductionmentioning

confidence: 99%

“…This is always the case when Euler parameters or natural coordinates are used, which can avoid the drawback that the minimal set of orientation coordinates including three independent parameters (e.g., Euler angles, Bryan angles, Rodriguez parameters, etc.) have a singular position in those locations where these parameters are not defined unequivocally [3][4][5][33][34][35][36][37]. In other occasions, it is possible to assign a null mass and inertia tensor to a body simply because its inertia is very small, e.g., when some massless link members are present [30,33,34].…”

Section: Introductionmentioning

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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Section: Spatial Multibody Dynamics Equations With Quaternions 21 Atmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

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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“…As already stated, in general, it is assumed that the mass matrix is always invertible. However, it has been demonstrated in many research studies that the mass matrix can be singular, namely when more than six coordinates are considered to define the pose of a rigid body [39,41,90,111,112]. Another problem can appear when a body in the system under analysis has extremely small inertia [39,90,111].…”

Section: Equations Of Motion For Constrained Multibody Systemsmentioning

confidence: 99%

On the constraints violation in forward dynamics of multibody systems

2016

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It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton-Euler's approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian and the coordinate partitioning method.

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“…In short, even though the theory of rigid-body systems has been well-established for centuries, the efficient computational implementation of complex multibody systems is still a challenging topic [95,96]. Recent publications on this matter outline the necessity of going further into this topic [37,41,42,49,53,56]. These publications have served as basic references during the development of this Thesis.…”

Section: Challenges and Motivationmentioning

confidence: 99%

Contributions to Topological Formulations for the Dynamic Simulation of Vehicles

Pan¹

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First and foremost, I am deeply grateful for the continuous support, insight and patience of my supervisors, Javier García de Jalón and Alfonso Callejo. Without their help and gentle prodding, this Thesis would not have been completed. I would like to express my special appreciation to Javier García de Jalón. He taught me so much in the past four years, and introduced me to the field of multibody dynamics. A very big thank you goes to my co-supervisor Alfonso Callejo for his detailed guidance and constant feedback, as well as József Kövecses; they both hosted my research stay at the Centre for Intelligent Machines (McGill University).

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A new switching strategy for addressing Euler parameters in dynamic modeling and simulation of rigid multibody systems

Cited by 10 publications

References 15 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

On the constraints violation in forward dynamics of multibody systems

Contributions to Topological Formulations for the Dynamic Simulation of Vehicles

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