基于凸集理论的绳牵引串并联机器人工作空间算法

为求解m≥n（m为绳索数目,n为机构自由度）绳牵引串并联机器人的力旋量可行工作空间,提出一种基于凸集理论的非迭代求解算法。该算法利用闵可夫斯基之和的性质构造绳索的旋量集,借助非迭代的数学思想验证该旋量集是否完全包含外部旋量集。首先,通过确定初始超平面找出凸集所有的边界超平面,根据初始超平面偏移的距离确定边界超平面投影位置; 然后推导出旋量平衡的判定表达式,并采用数值分析的方法得到绳牵引机器人的力旋量可行工作空间;最后,采用该算法对两种典型的绳牵引串并联机器人进行工作空间求解,结果验证了所提出的基于凸集理论工作空间求解方法的有效性。

Workspace Algorithm of Cable-driven Serial and Parallel Manipulators Based on Convex Set Theory

In order to solve the wrench feasible workspace of n-degrees-of-freedom serial and parallel manipulators driven by m cables, a non-iterative algorithm was proposed based on covex set theory. The properties of Minkowski Sum was introduced to construct the cable wrench set, and a non-iterative mathematical method was presented to verify if the wrench set fully included the external wrench set. Firstly, all boundary hyperplanes of convex set would be found by determining initial hyperplane. The projected boundary positions were determined according to the offset distance of the initial hyperplane. Then the explicit expression of the wrench equilibrium was deduced, and the wrench feasible workspace of cable-driven manipulator was obtained by using numerical analysis. The results demonstrate the effectiveness of the wrench feasible workspace analysis method based on convex set theory.