Penalty, Semi-Recursive and Hybrid Methods for MBS Real-Time Dynamics in the Context of Structural Integrators

Cuadrado, Javier; Dopico, Domingo Calvo; Naya, Miguel Ángel; González, Manuel

doi:10.1023/b:mubo.0000044421.04658.de

Cited by 49 publications

(31 citation statements)

References 19 publications

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“…[13] proposes an orthogonal projection on the null-space of the invariant, while in [22,1,7,9] a massorthogonal projection is employed, and tested in several examples with very good results. References [10,11] propose a projection based on the mass matrix plus other terms related to the linearized damping and elastic forces of the system, which is numerically more efficient. In fact, from a purely mathematical point of view, any positive definite matrix qualifies for a coordinate projection, which justifies the interest in searching for a practical criterion for selecting the projection matrix.…”

mentioning

confidence: 99%

Energy considerations for the stabilization of constrained mechanical systems with velocity projection

Orden

2009

Nonlinear Dyn

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International audienceThere are many difficulties involved in the numerical integration of index-3 Differential Algebraic Equations (DAEs), mainly related to stability, in the context of mechanical systems. An integrator that exactly enforces the constraint at position level may produce a discrete solution that departs from the velocity and/or acceleration constraint manifolds (invariants). This behavior affects the stability of the numerical scheme, resulting in the use of stabilization techniques based on enforcing the invariants. A coordinate projection is a post-stabilization technique where the solution obtained by a suitable DAE integrator is forced back to the invariant manifolds. This paper analyzes the energy balance of a velocity projection, providing an alternative interpretation of its effect on the stability and a practical criterion for the projection matrix selection

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mentioning

confidence: 99%

Energy considerations for the stabilization of constrained mechanical systems with velocity projection

Orden

2009

Nonlinear Dyn

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“…2 that the observer based on the penalty method behaves worse than the one based on the matrix-R method. The reason is that, while the measured coordinate s is perfectly followed by the observer, the remaining coordinates 1 x , 1 y , 2 x , 2 y , are not consistent with the distance s, since the penalty terms are not capable of ensuring the constraint satisfaction under the large forces introduced by the EKF. And this happens for any value of the penalty factor.…”

Section: Examplementioning

confidence: 99%

“…However, current state-of-the-art knowledge in multibody dynamics opens the possibility of considering complex multibody models in real-time state observer applications, as long as specialized schemes are employed [1]. The advantage is that more information can be extracted from the model.…”

Section: Introductionmentioning

confidence: 99%

Real-time state observers based on multibody models and the extended Kalman filter

et al. 2009

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This work is a preliminary study on the use of the extended Kalman filter (EKF) for the state estimation of multibody systems. The observers based on the EKF are described by first-order differential equations, with independent, non-constrained coordinates. Therefore, it should be investigated how to formulate the equations of motion of the multibody systems so that efficient, robust and accurate observers can be derived, which can serve to develop advanced real-time applications. In the paper, two options are considered: a state-space reduction method and the penalty method. Both methods are tested on a four-bar mechanism with a linear spring-damper. The results enable us to analyze the pros and cons of each method and provide clues for future research.

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“…Analogously, Equation (37) shows the difference equations of the integrator which express the velocities and accelerations at the second stage as functions of the positions at the same stage, plus some positions, velocities and accelerations at the current time-step and the first stage. Therefore, Equations (36) and (37) possess the same form as the difference equations of Newmark-type integrators, which means that the strategy followed in the authors' previous works to combine the three dynamic formulations with those integrators at time-step level [1,4], may now be applied with SDIRK integrators at stage level. As said in Section 2, the motion equations for the two formulations in dependent co-ordinates were stated through an index-3 augmented Lagrangian scheme [3] …”

Section: Alternative Bmentioning

confidence: 99%

“…In a second work [4], a new comparison among the three formulations was carried out. Given that Newmark-type integrators, widely used in structural dynamics, had shown to adapt well to the equations of motion of multibody systems, even for real-time purposes [5,6], the trapezoidal rule was substituted by different structural integrators: Newmark dissipative schemes, HHT rule, and the Generalized-family.…”

Section: Introductionmentioning

confidence: 99%

Two implementations of IRK integrators for real‐time multibody dynamics

Dopico

Lugrís

González

et al. 2005

Numerical Meth Engineering

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SUMMARYRecently, several authors have proposed the use of implicit Runge-Kutta (IRK) integrators for the dynamics of multibody systems. On the other hand, Newmark-type or structural integrators have shown to be appropriate when real-time performance is demanded in that field. Therefore, the following question arises: might the IRK integrators be suitable for real-time purposes? And, provided the answer is positive: might they be preferable to the Newmark-type family? This paper reports an investigation which has been conducted by the authors in order to get insight into the two questions formulated above. Since, based on previous experiences, it can be suspected that the performance of the integrators may be dependent on the type of dynamic formulation applied, the following three formulations have been considered for the study: a global penalty formulation in dependent natural co-ordinates (many constraints), a topological semi-recursive penalty formulation in dependent relative co-ordinates (few constraints), and a topological semi-recursive formulation in independent relative co-ordinates (no constraints).As representative of the IRK family, a two-stage SDIRK integrator has been selected due to its low associated computational burden, while, on the side of the structural integrators, the trapezoidal rule has been chosen. Two alternative implementations have been proposed to combine the dynamic formulations and the SDIRK integrator.A very demanding maneuver of the whole model of a vehicle has been simulated through all the possible combinations dynamic-formulation/integrator, for different time-steps. Conclusions have been drawn based on the obtained results, which provide some practical criteria for those interested in achieving real-time performance for large and complex multibody systems.

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Penalty, Semi-Recursive and Hybrid Methods for MBS Real-Time Dynamics in the Context of Structural Integrators

Abstract: Abstract. The continuously improved performance of personal computers enables the realtime motion simulation of complex multibody systems

Cited by 49 publications

References 19 publications

Energy considerations for the stabilization of constrained mechanical systems with velocity projection

Energy considerations for the stabilization of constrained mechanical systems with velocity projection

Real-time state observers based on multibody models and the extended Kalman filter

Two implementations of IRK integrators for real‐time multibody dynamics

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