论文标题
计算Coriolis矩阵和刚体系统的Christoffel符号的数值方法
Numerical Methods to Compute the Coriolis Matrix and Christoffel Symbols for Rigid-Body Systems
论文作者
论文摘要
本文介绍了有效计算Coriolis矩阵的方法，并为树结构刚体系统（第一类）（第一类）的基础符号（的基础）符号。该算法可以纯粹是数值执行的，而无需像不可估量的符号技术一样需要部分衍生物。这些计算与经典方法（例如复合 - 韧性算法）共同具有共同的结构，并且可能是最低的顺序：Coriolis Matrix的$ O（ND）$和ChristOffel符号的$ O（ND^2）$，其中$ n $是$ n $是尸体的数量，$ d $是$ d $的深度。 C/C ++的实现显示了Coriolis矩阵的10-20美元$ $ s的计算时间，以及具有20个自由度的系统上的基督佛尔符号的40-120 $ $ s。结果表明，在基于模型的控制应用程序中采用这些算法的可行性。
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 $μ$s for the Coriolis matrix and 40-120 $μ$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.
