Performance investigation and constraint stabilization approach for the orthogonal complement-based divide-and-conquer algorithm

Khan, Imad M.; Anderson, Kurt S.

doi:10.1016/j.mechmachtheory.2013.04.009

Cited by 17 publications

(11 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To reduce this numerical drift, constraint stabilization methods have been proposed that either amend the motion equations [3,20] or correct the numerical solution by projecting it to the constraint manifold h −1 (0) [2,4,11,32]. All these methods aim at minimizing or correcting, rather than avoiding, constraint violations.…”

Section: Constraint Satisfaction For a General C-space Lie Groupmentioning

confidence: 99%

“…If the constraints restrict the motion to a subgroup H = h −1 (0) ⊂ G, and thus the velocities to the corresponding subalgebra of g, the brackets in terms of feasible velocities in (20) form a basis for this subalgebra. Consequently, (i) belongs to the smallest Lie subalgebra of g containing the constrained body velocity V, and the configuration increment C (t i ) belongs to the corresponding subgroup of the c-space Lie group G, (occasionally called the completion group).…”

Section: Assumption 1 the Configuration Update Increment Is Determinementioning

confidence: 99%

“…This inevitably leads to constraint violation that are of the order of the accuracy of the integration scheme. Various constraint stabilization methods were introduced to remedy this problem [4,20].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A note on the motion representation and configuration update in time stepping schemes for the constrained rigid body

Müller

2015

Bit Numer Math

View full text Add to dashboard Cite

The dynamics of a holonomically constrained rigid body can be modeled by Newton-Euler equations subjected to geometric constraints. This is frequently formulated as a differential-algebraic equation (DAE) system of index 1. In multibody system (MBS) dynamics it is common (1) to numerically solve this system by means of integration schemes for ordinary differential equations, and (2) to treat the rigid body motion on the direct product Lie group SO (3)×R 3 , although rigid body motions form the semidirect product Lie group SE (3). It is has been observed that the constraint satisfaction depends on which Lie group is used as configuration space (c-space). In this paper the problem is considered from a geometric perspective. It is shown that the constraints are exactly satisfied by a numerical integration scheme if they define a subgroup of the c-space. The subgroups of SE (3) have a significance for modeling mechanical systems, including lower kinematic (Reuleaux) pairs and are implicitly used in MBS modeling. It is concluded that SE (3) is the appropriate cspace for numerical DAE modeling of a constrained rigid body. This result does not immediately apply to MBS, however.

show abstract

Section: Constraint Satisfaction For a General C-space Lie Groupmentioning

confidence: 99%

Section: Assumption 1 the Configuration Update Increment Is Determinementioning

confidence: 99%

See 1 more Smart Citation

A note on the motion representation and configuration update in time stepping schemes for the constrained rigid body

Müller

2015

Bit Numer Math

View full text Add to dashboard Cite

show abstract

“…where H ∈ R 6×n f represents the joint's motion subspace (n f -number of degrees of freedom for the joint) and D ∈ R 6×(6−n f ) is associated with the joint's constrained directions [24,26]. We assume that both matrices H and D consist of ones and zeros.…”

Section: Joint Velocities and Constraint Force Impulsesmentioning

confidence: 99%

“…Recently, the divide-and-conquer based schemes [17] have attracted significant attention to the development of efficient parallel algorithms for large MBS, partially due to the fact that computationally powerful multicore processors or graphics processor units are cheaply available on the market. Various algorithms that are effectively based on the Featherstone's DCA are elaborated with myriad of extensions to, e.g., humanoid robot simulations [22], molecular dynamics simulations, real-time applications, discontinuous changes in the system topology [23], sensitivity analysis, constraint enforcement [24][25][26][27], nonholonomic constraints, flexible multibody systems, or generalized constraint treatment. Advances in the application of the DCA approach to large multibody system simulations can be found in [28].…”

Section: Introductionmentioning

confidence: 99%

A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems

2016

View full text Add to dashboard Cite

This paper presents a novel recursive divide-and-conquer formulation for the simulation of complex constrained multibody system dynamics based on Hamilton's canonical equations (HDCA). The systems under consideration are subjected to holonomic, independent constraints and may include serial chains, tree chains, or closed-loop topologies. Although Hamilton's canonical equations exhibit many advantageous features compared to their acceleration based counterparts, it appears that there is a lack of dedicated parallel algorithms for multi-rigid-body system dynamics based on the Hamiltonian formulation. The developed HDCA formulation leads to a two-stage procedure. In the first phase, the approach utilizes the divide and conquer scheme, i.e., a hierarchic assembly-disassembly process to traverse the multibody system topology in a binary tree manner. The purpose of this step is to evaluate the joint velocities and constraint force impulses. The process exhibits linear O(n) (n -number of bodies) and logarithmic O(log 2 n) numerical cost, in serial and parallel implementations, respectively. The time derivatives of the total momenta are directly evaluated in the second parallelizable step of the algorithm. Sample closed-loop test cases indicate very small constraint violation errors at the position and velocity level as well as marginal energy drift without any additional form of constraint stabilization techniques involved in the solution process. The results are comparatively set against more standard acceleration based Featherstone's DCA approach to indicate the performance of the HDCA algorithm.

show abstract

An o(n) complexity recursive algorithm for multi‐flexible‐body dynamics based on absolute nodal coordinate formulation

2016

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary A new algorithm called recursive absolute nodal coordinate formulation algorithm (REC‐ANCF) is presented for dynamic analysis of multi‐flexible‐body system including nonlinear large deformation. This method utilizes the absolute nodal coordinate formulation (ANCF) to describe flexible bodies, and establishes a kinematic and dynamic recursive relationship for the whole system based on the articulated‐body algorithm (ABA). In the ordinary differential equations (ODEs) obtained by the REC‐ANCF, a simple form of the system generalized Jacobian matrix and generalized mass matrix is obtained. Thus, a recursive forward dynamic solution is proposed to solve the ODEs one element by one element through an appropriate matrix manipulation. Utilizing the parent array to describe the topological structure, the REC‐ANCF is suitable for generalized tree multibody systems. Besides, the cutting joint method is used in simple closed‐loop systems to make sure the O(n) algorithm complexity of the REC‐ANCF. Compared with common ANCF algorithms, the REC‐ANCF has several advantages: the optimal algorithm complexity (O(n)) under limited processors, simple derivational process, no location or speed constraint violation problem, higher algorithm accuracy. The validity and efficiency of this method are verified by several numerical tests. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

Performance investigation and constraint stabilization approach for the orthogonal complement-based divide-and-conquer algorithm

Cited by 17 publications

References 24 publications

A note on the motion representation and configuration update in time stepping schemes for the constrained rigid body

A note on the motion representation and configuration update in time stepping schemes for the constrained rigid body

A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems

An o(n) complexity recursive algorithm for multi‐flexible‐body dynamics based on absolute nodal coordinate formulation

Contact Info

Product

Resources

About