Numerical analysis of robot dynamics algorithms

Abstract

This thesis presents two issues related to robot dynamics algorithms. We first discuss the planar robot dynamics algorithms because it is useful to study robot motion in the plane before generalizing to 3D. The planar versions of the three most commonly used dynamics algorithms, the recursive Newton-Euler algorithm (RNEA), the articulated-body algorithm (ABA)) and the composite rigid-body algorithm (CRBA) are obtained by using planar vectors, tensors and coordinate transforms. It is shown that the planar algorithms are asymptotically between 4 and 4.8 times faster than their comparable spatial counterparts. Moreover, the numerical accuracy of robot dynamics algorithms need to be equally considered. Investigations into the numerical accuracy of the RNEA, the ABA, the CRBA, the constraint force algorithm (CFA), the divide-and-conquer algorithm (DCA) and pivoted divide-and-conquer algorithm (DCAp) are explored. It is shown by the empirical study that the three parallel algorithms, the CFA, the DCA, and the DCAp, are significantly less accurate than the two serial algorithms, the ABA and CRBA. However, the performances of the planar versions of dynamics algorithms are different, and the accuracy of the parallel algorithms is comparable with the serial ones. In addition, we use the CESTAC (Controle et Estimation Stochastique des Arrondic de Calculs) and the affine arithmetic (AA) to estimate the propagation of round-off errors in robot dynamics algorithms. The accomplishments provided in this thesis represent better understanding of the performances of the existing robot dynamics algorithms.