Year: 2024
Type: article
Abstract: We present PV-OSIMr, an efficient algorithm for computing the Delassus matrix (also known as the inverse operational space inertia matrix) for a kinematic tree, with the lowest order computational complexity known in literature. PV-OSIMr is derived by optimizing the recently proposed PV-OSIM algorithm using the compositionality of the force and motion propagators. It has a computational complexity of$O(n+m^{2})$compared to$ O(n + m^{2}d)$of the PV-OSIM algorithm and$O(n+md +m^{2})$of the extended force propagator algorithm (EFPA), where$n$is the number of joints,$m$is the number of constraints and$d$is the depth of the kinematic tree. Since the Delassus matrix is an$m \times m$sized matrix and its computation must consider all the$n$joints, PV-OSIMr's asymptotic computational complexity is optimal. We further benchmark our algorithm and find it to be often more efficient than the PV-OSIM and EFPA in practice.
Authors: Ajay Suresha Sathya, Wilm Decré, Jan Swevers
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402915815