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

Abstract

The introductory paper on the orthogonal complement-based divide-and-conquer algorithm (ODCA) lacked in properly characterizing the growth rate of the constraint violation error and the singularity handling capabilities of the algorithm [1]. In this paper, we investigate the performance of the ODCA with regards to constraint error growth and singularity handling capabilities. Moreover we introduce a new inverse dynamics-based constraint stabilization approach. The proposed method is applicable to general multibody systems with arbitrary number of closed kinematic loops. We compare the ODCA with augmented [2] and reduction [3] methods. Our results indicate that the error growth rate for the ODCA falls between these two traditional techniques. Moreover, using benchmark numerical problems, we illustrate the effectiveness of the stabilization scheme.