Details of Second-Order Partial Derivatives of Rigid-Body Inverse Dynamics
Robotics
2023-08-01 v5
Abstract
The details of second-order partial derivatives of rigid-body Inverse/Forward dynamics are provided. Several properties and identities using Spatial Vector Algebra are listed, along with their detailed derivations. The expressions build upon previous work by the author on first-order partial derivatives of inverse dynamics. The first/second-order derivatives are also extended for systems with external forces. Finally, the KKT Forward dynamics and Impact dynamics derivatives are derived.
Keywords
Cite
@article{arxiv.2203.00679,
title = {Details of Second-Order Partial Derivatives of Rigid-Body Inverse Dynamics},
author = {Shubham Singh and Ryan P. Russell and Patrick M. Wensing},
journal= {arXiv preprint arXiv:2203.00679},
year = {2023}
}