基于多元Taylor法的并联机器人运动学研究∗

摘要

So far, the problem of Kinematics of the closed-form solution is still a technical problem, now the most popular method in reality is the use of numerical solution method and the generalized geometric e-quations method. However, the derivations of these methods are very complicated, and there is a problem of no unique solution in the process of solving equations. To avoid these problems , a triple nonlinear equation of parallel robot Newton iteration algorithm is deduced based on Taylor formula multivariate function, at the same time , Based on the mathematical principles , the anti-parallel robot solutions can be obtained. Taylor algorithm avoid multiple solutions trade-offs skillfully , get the solution that meet the exercise of continuity directly. As the rate of convergence, this algorithm is a very promising algorithm.%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，在实际应用中采用广义几何法和方程组的数值解法等，不过首先推导过程非常的复杂，且在求解的过程中还存在解不唯一等问题。因此，为了避免上述问题，文中根据多元函数的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。