基于CoDeSys环境下的并联机器人非线性方程求解  

Parallel robot nonlinear equation solution based on CoDeSys environment

作　　者：陈池梅[1,2] 陈利学[2] 

机构地区：[1]重庆医科大学附属第一医院信息中心,重庆400016 [2]西南石油大学计算机科学学院,四川成都610500

出　　处：《计算机工程与科学》2016年第4期720-725,共6页Computer Engineering & Science

基　　金：国家863计划(2011AA404701);国家自然科学基金(51177099)

摘　　要：机器人技术发展到现在,虽然已经得到了突飞猛进的进步,但是对于并联机器人运动学正解的封闭解问题依然是机器人技术的瓶颈,在实际应用中采用的广义几何法和方程组的数值解法等,不但推导过程非常复杂,而且在求解的过程中还存在解不唯一的问题。为了避免上述问题,根据多元函数的Taylor公式推导出了一种基于三元非线性方程组牛顿迭代法的并联机器人运动学正解算法;同时,基于其数学原理,也可以得到并联机器人的反解。Taylor法以其自身的优势,巧妙地解决繁琐的并联机器人运动学正解多解取舍问题,直接获得了工作空间内满足运动连续性的合理解。该算法的迭代次数少,收敛速度快,是一种非常有潜力的方法。最后将该算法应用到CoDeSys开发环境,通过配置方式,证明Codesys环境下并联机器人运动学可实时灵活应用。So far,the problem of Kinematics of the closed-form solution remains a technical problem,and currently the most popular method in practice is the use of numerical solution method and the generalized geometric equations method.However,the derivations of these methods are very complicated,and there is no unique solution in the process of solving equations.To avoid these problems,we propose a triple nonlinear equation of parallel robot Newton iteration algorithm based on the Taylor formula multivariate function.Based on the mathematical principles,the anti-parallel robot solutions can be obtained.The Taylor algorithm avoids multiple solutions trade-offs skillfully,and the solution meets the demand of continuous exercise directly.In terms of rate of convergence,this algorithm is very promising.We apply the proposed algorithm in the CoDeSys environment,which proves that parallel kinematics can be applied flexibly in real time in CoDeSys environment via configuration.

关 键 词：非线性方程 牛顿迭代 泰勒公式 并联机器人 多元函数 

分 类 号：TP242.3[自动化与计算机技术—检测技术与自动化装置]