采用进化算法的Gough-Stewart 平台优化设计

Optimal design of the Gough-Stewart platform using evolutionary algorithms

摘要:

针对基于传统雅克比矩阵建立Gough-Stewart平台(GSP) 的可操作度没有明确的物理意义,且随表示单位不同而发生变化的问题,基于量纲一的雅克比矩阵建立了不随表示单位变化的新可操作度指标．将多态进化算法AEGA应用于GSP单目标函数的优化设计中,得到多组备选方案,最终为设计者提供多组优化参数．为了解决多目标同时优化的问题,把多目标进化算法NSGA-II应用于GSP的优化设计中,得到多组优化解,即Pareto优化解集．以用作运动模拟器的GSP为例进行优化设计分析,验证了方法的可行性,该方法比传统单目标函数优化设计更符合工程实际．

Abstract:

Because the manipulability index based on conventional Jacobian matrix of Gough-Stewart platform (GSP) is with no physical meaning and variant with the change of units, a new invariant manipulability index of GSP is established based on a dimensionless Jacobian matrix. A multimodal evolutionary algorithm, AEGA, is proposed to search the optimal solutions for the optimal design of GSP with only one objective function, and then many solutions are found as the candidates for the designer. To solve the problem with two or more objective functions needed to optimize simultaneously, one of the multi-objective evolutionary algorithms, Elitist Non-Dominated Sorting Genetic Algorithm version II (NSGA-II), is applied to the optimal design process of GSP, then many sets of trade-off solutions, namely, the Pareto optimal set parameters, are found. To illustrate the proposed methodology, a practical GSP as a motion simulator is optimized. The results validate the usefulness to solve the mentioned problems by using the applied optimal algorithms which could meet more engineering demands in practice than using the conventional optimal design method in single objective function.