Motion Planning for an Articulated Body in a Perfect Planar Fluid
Motion Planning for an Articulated Body in a Perfect Planar Fluid
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完美平面流体中铰接体的运动规划
DOI：
10.1137/060649884
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Dzhelil Rufat
中科院分区：
文献类型：
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作者：
J. Melli;C. Rowley;Dzhelil Rufat
了解内部形状变化导致的类似鱼的运动可能会导致水下推进机制的改进。我们使用几何框架来考虑势流中铰接二维体的简化问题。本文以当前的几何理论为基础，表明尽管欧几里得变换群是非阿贝尔群，但仍然可以利用可用于阿贝尔群的某些工具，利用该群的半直积结构。特别地，旋转分量中的完整可以被明确地计算为由形状空间中的路径包围的面积的函数。我们使用该工具为具有两个形状变量的铰接体开发开环步态，使用机械连接的曲率图，将形状空间中的运动与整个身体的运动联系起来。将机械连接的数值计算结果与假设接头进行流体动力学解耦的理论结果进行比较。最后，我们考虑一种使用单参数步态族进行平面轨迹跟踪的简单方法。
Understanding fish-like locomotion as a result of internal shape changes may result in improved un- derwater propulsion mechanisms. We use a geometric framework to consider the simplified problem of an articulated two-dimensional body in a potential flow. This paper builds upon the current geometric theory by showing that although the group of Euclidean transformations is non-Abelian, certain tools available for Abelian groups may still be exploited, making use of the semidirect-product structure of this group. In particular, the holonomy in the rotation component may be explicitly computed as a function of the area enclosed by a path in shape space. We use this tool to develop open-loop gaits for an articulated body with two shape variables, using plots of the curvature of the mechanical connection, which relates motion in the shape space to motion of the overall body. Results from numerical computations of the mechanical connection are compared to theoretical re- sults assuming the joints are hydrodynamically decoupled. Finally, we consider a simple method for trajectory tracking in the plane, using a one-parameter family of gaits.