# Inverse, forward and other dynamic computations computationally optimized with sparse matrix factorizations

## TL;DR

This paper introduces an optimized algorithm for computing the dynamics of articulated rigid bodies using sparse matrix factorizations, reducing computational complexity compared to traditional methods.

## Contribution

The authors develop a novel off-line optimized sparse matrix factorization approach to efficiently compute inverse and forward dynamics of articulated bodies.

## Key findings

- Reduces floating point operations compared to recursive Newton-Euler and articulated body algorithms.
- Performs well on classical dynamic problems with lower computational complexity.
- Validated through tests showing numerical efficiency even without existing gold standards.

## Abstract

We propose an algorithm to compute the dynamics of articulated rigid-bodies with different sensor distributions. Prior to the on-line computations, the proposed algorithm performs an off-line optimisation step to simplify the computational complexity of the underlying solution. This optimisation step consists in formulating the dynamic computations as a system of linear equations. The computational complexity of computing the associated solution is reduced by performing a permuted LU-factorisation with off-line optimised permutations. We apply our algorithm to solve classical dynamic problems: inverse and forward dynamics. The computational complexity of the proposed solution is compared to `gold standard' algorithms: recursive Newton-Euler and articulated body algorithm. It is shown that our algorithm reduces the number of floating point operations with respect to previous approaches. We also evaluate the numerical complexity of our algorithm by performing tests on dynamic computations for which no gold standard is available.