Solving Cosserat Rod Models via Collocation and the Magnus Expansion
Solving Cosserat Rod Models via Collocation and the Magnus Expansion
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DOI：
10.1109/iros45743.2020.9340827
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发表时间：
2020-08
期刊：
影响因子：
--
通讯作者：
A. Orekhov;N. Simaan
中科院分区：
文献类型：
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作者：
A. Orekhov;N. Simaan
为连续体机器人选择运动学模型通常涉及在精度和计算复杂性之间进行权衡。一种常见的建模方法是使用Cosserat杆方程，这已被证明是准确的许多类型的连续体机器人。然而，这种方法，仍然提出了显着的计算成本，特别是当许多Cosserat杆耦合通过运动约束。在这项工作中，我们提出了一种数值方法，结合正交配置的局部杆曲率和前向积分的Cosserat杆运动方程通过马格努斯展开，使平衡形状被写为矩阵指数的产品。我们提供了一个约束的最大步长，以保证收敛的Cosserat棒的情况下的马格努斯展开，在模拟中与其他方法进行比较，并展示了速度和精度之间的权衡第四和第六阶马格努斯展开以及不同数量的配置点。我们的研究结果表明，该方法可以找到精确的解决方案的Cosserat棒方程，并可能在计算速度的竞争力。
Choosing a kinematic model for a continuum robot typically involves making a tradeoff between accuracy and computational complexity. One common modeling approach is to use the Cosserat rod equations, which have been shown to be accurate for many types of continuum robots. This approach, however, still presents significant computational cost, particularly when many Cosserat rods are coupled via kinematic constraints. In this work, we propose a numerical method that combines orthogonal collocation on the local rod curvature and forward integration of the Cosserat rod kinematic equations via the Magnus expansion, allowing the equilibrium shape to be written as a product of matrix exponentials. We provide a bound on the maximum step size to guarantee convergence of the Magnus expansion for the case of Cosserat rods, compare in simulation against other approaches, and demonstrate the tradeoffs between speed and accuracy for the fourth and sixth order Magnus expansions as well as for different numbers of collocation points. Our results show that the proposed method can find accurate solutions to the Cosserat rod equations and can potentially be competitive in computation speed.