A Topology-Based Approach for Exploiting Sparsity in Multibody Dynamics in Cartesian Formulation*

摘要

In this paper, a new method for efficiently computing accelerations and La-grange multipliers in the equations of multibody dynamics is presented. These quantities are the solution of a system of linear equations that has a coefficient matrix with the special structure of an optimization matrix. This matrix is likely to have a large number of zero entries, according to the connectivity among bodies of the mechanical system. This method takes advantage of both the special structure and the sparsity of the coefficient matrix. Simple manipulations bring the original problem of solving a system of n +mequations in n +munknowns to an equivalent problem in which a positive definite system of dimensionm#xD7;mhas to be solved for the Lagrange multipliers. Accelerations are then efficiently determined. For certain mechanical system models, the bandwidth of them#xD7;mpositive definite matrix can be reduced significantly by appropriately numbering the joints connecting bodies of the model. Numerical experiments show the effectiveness of the proposed algorithm.