Numerical Methods to Compute the Coriolis Matrix and Christoffel Symbols for Rigid-Body Systems
| Autor: | Echeandia, Sebastian, Wensing, Patrick M. |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1115/1.4051169 |
| Popis: | This article presents methods to efficiently compute the Coriolis matrix and underlying Christoffel symbols (of the first kind) for tree-structure rigid-body systems. The algorithms can be executed purely numerically, without requiring partial derivatives as in unscalable symbolic techniques. The computations share a recursive structure in common with classical methods such as the Composite-Rigid-Body Algorithm and are of the lowest possible order: $O(Nd)$ for the Coriolis matrix and $O(Nd^2)$ for the Christoffel symbols, where $N$ is the number of bodies and $d$ is the depth of the kinematic tree. Implementation in C/C++ shows computation times on the order of 10-20 $\mu$s for the Coriolis matrix and 40-120 $\mu$s for the Christoffel symbols on systems with 20 degrees of freedom. The results demonstrate feasibility for the adoption of these algorithms within high-rate ($>$1kHz) loops for model-based control applications. Comment: Author version of paper in the ASME Journal of Computational and Nonlinear Dynamics. Includes two footnotes added post-publication |
| Databáze: | arXiv |
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