The Complex-Step Derivative Approximation on Matrix Lie Groups
Abstract
The complex-step derivative approximation is a numerical differentiation technique that can achieve analytical accuracy, to machine precision, with a single function evaluation. In this letter, the complex-step derivative approximation is extended to be compatible with elements of matrix Lie groups. As with the standard complex-step derivative, the method is still able to achieve analytical accuracy, up to machine precision, with a single function evaluation. Compared to a central-difference scheme, the proposed complex-step approach is shown to have superior accuracy. The approach is applied to two different pose estimation problems, and is able to recover the same results as an analytical method when available.
Cite
@article{arxiv.2105.02744,
title = {The Complex-Step Derivative Approximation on Matrix Lie Groups},
author = {Charles Champagne Cossette and Alex Walsh and James Richard Forbes},
journal= {arXiv preprint arXiv:2105.02744},
year = {2021}
}
Comments
8 pages, 8 figures, accepted to Robotics and Automation Letters, presented at ICRA 2020