Application of Cellular Automata Theory in the Search Method of Workspace of Parallel Manipulator
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摘要: 针对传统并联机构工作空间搜索法所得边界精度低、效率低等问题，提出一种通用的基于元胞自动机理论的快速搜索方法。该方法以元胞自动机中邻域思想和黄金分割法原理为基础，研究了并联机构工作空间求解的数值法，并总结出这些方法的不足。通过引入元胞自动机的邻域提取粗糙化边界和搜索方向，并将黄金分割二分法引入维度搜索中，以实现任意精度的边界点搜索，其后仿真算例检验了此方法的有效性与快速性，并与极坐标搜索法、蒙特卡洛法、精确化处理进行对比。分析表明：该算法在求解精度、效率具有明显优势，并且适用于二维、三维的并联机构工作空间的求解。Abstract: In terms of the traditional search method of workspace having the boundary problem of low accuracy and low efficiency, a general fast search method was put forward via the theory of cellular automata. This algorithm based on the thought of neighborhood of cellular automata and the golden section method. First, the traditional numerical methods of the workspace of parallel mechanism were studied and summarized their deficiency; the method introduced the neighborhood of cellular automata so as to extract roughness boundary and the search direction. Then, the golden section method was introduced into dimension search so as to realize search of arbitrary precision of boundary point. The quickness and the effectiveness of algorithm are tested by simulation examples, and compared with polar coordinate searching method, Monte Carlo method and the process of precision processing show that the algorithm has obvious advantages in the accuracy and efficiency, and is suitable for 2D or 3D the workspace problems of parallel manipulator.
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Key words:
- parallel manipulator /
- workspace /
- cellular automaton /
- neighborhood /
- golden section method
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表 3 极坐标边界搜索法与元胞黄金分割法对比
a 算法 可达工作空间耗时 姿态工作空间耗时 极坐标搜索法 677.222 105 39.776 22 元胞黄金分割法 2.328 487 0.823 79 
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表 4 蒙特卡洛法算法与元胞黄金分割法对比
s 算法 可达工作空间耗时 姿态工作空间耗时 蒙特卡洛法 90.168 225 48.752 804 元胞黄金分割法 46.480 772 9.767 137
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