NDLI: A new factorization of the mass matrix for optimal serial and parallel calculation of multibody dynamics

Content Provider	Springer Nature Link
Author	Fijany, Amir Featherstone, Roy
Copyright Year	2012
Abstract	This paper describes a new factorization of the inverse of the joint-space inertia matrix M. In this factorization, M $^{−1}$ is directly obtained as the product of a set of sparse matrices wherein, for a serial chain, only the inversion of a block-tridiagonal matrix is needed. In other words, this factorization reduces the inversion of a dense matrix to that of a block-tridiagonal one. As a result, this factorization leads to both an optimal serial and an optimal parallel algorithm, that is, a serial algorithm with a complexity of O(N) and a parallel algorithm with a time complexity of O(logN) on a computer with O(N) processors. The novel feature of this algorithm is that it first calculates the interbody forces. Once these forces are known, the accelerations are easily calculated. We discuss the extension of the algorithm to the task of calculating the forward dynamics of a kinematic tree consisting of a single main chain plus any number of short side branches. We also show that this new factorization of M $^{−1}$ leads to a new factorization of the operational-space inverse inertia, Λ $^{−1}$, in the form of a product involving sparse matrices. We show that this factorization can be exploited for optimal serial and parallel computation of Λ $^{−1}$, that is, a serial algorithm with a complexity of O(N) and a parallel algorithm with a time complexity of O(logN) on a computer with O(N) processors.
Starting Page	169
Ending Page	187
Page Count	19
File Format	PDF
ISSN	13845640
Journal	Multibody System Dynamics
Volume Number	29
Issue Number	2
e-ISSN	1573272X
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-06-13
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multibody dynamics, Robot dynamics, Mass matrix factorization, Parallel computation Vibration, Dynamical Systems, Control Optimization Electrical Engineering Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Mechanical Engineering Aerospace Engineering Modeling and Simulation Computer Science Applications

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