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arXiv 1107.0803cs.CGcs.RO
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基于流形样本的运动规划

Motion Planning via Manifold Samples

Tel-Aviv University(特拉维夫大学);Hebrew University(希伯来大学)

Oren Salzman, Michael Hemmer, Barak Raveh, Dan Halperin

摘要:

我们提出了一个通用的和模块化的机器人路径规划的算法框架。我们的框架结合了几何方法的准确和完整的低维配置空间的分析,以及实用的,相当简单的采样为基础的方法,适用于更高的维度。为了促进先进的几何算法转化为实际应用,我们建议采取的样本是整个低维流形的配置空间,捕捉配置空间的连通性比孤立的点样本好得多。低维流形分析的几何算法提供了强大的原始操作。框架的模块化设计使得能够独立地优化每个模块化组件。事实上,我们已经开发,实施和优化了一个原始的操作完整和精确的组合分析的一组流形,使用安排曲线的合理功能和概念的通用编程。这反过来又使我们能够实现我们的框架的多边形机器人的具体情况下,多边形障碍物之间的平移和旋转。我们证明了几个精心设计的组件的集成导致显着的加速比流行的PRM基于采样的算法,这代表了更简单的方法,在实践中是普遍的。我们预见我们的框架可能的扩展,以解决高维问题超出运动规划。

英文摘要:

We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably simpler sampling-based approaches that are appropriate for higher dimensions. In order to facilitate the transfer of advanced geometric algorithms into practical use, we suggest taking samples that are entire low-dimensional manifolds of the configuration space that capture the connectivity of the configuration space much better than isolated point samples. Geometric algorithms for analysis of low-dimensional manifolds then provide powerful primitive operations. The modular design of the framework enables independent optimization of each modular component. Indeed, we have developed, implemented and optimized a primitive operation for complete and exact combinatorial analysis of a certain set of manifolds, using arrangements of curves of rational functions and concepts of generic programming. This in turn enabled us to implement our framework for the concrete case of a polygonal robot translating and rotating amidst polygonal obstacles. We demonstrate that the integration of several carefully engineered components leads to significant speedup over the popular PRM sampling-based algorithm, which represents the more simplistic approach that is prevalent in practice. We foresee possible extensions of our framework to solving high-dimensional problems beyond motion planning.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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