基于六维线性插值的六自由度机械臂逆运动学方程求解方法

针对一般结构的六自由度（DOF）机械臂逆运动学方程求解困难的问题，提出六维线性插值理论。首先，从大量的经验数据中搜索7个相邻的非线性相关的节点组成超体；然后，利用这7个节点得到六元一次线性预测函数；最后，使用预测函数进行插值和反插值运算预测位姿和关节角。使用Matlab仿真按照正运动学方程产生100万组经验数据，并对目标位姿进行反向插值，迭代预测6个关节角。实验结果表明，相比径向基网络（RBFN）、六维线性反插值法，所提方法能够更快、更准地逼近目标位姿。所提方法是基于数据的算法，避免了复杂的理论，可以满足机器人日常应用的要求。

Inverse kinematics equation solving method for six degrees of freedom manipulator based on six dimensional linear interpolation

A six-dimensional linear interpolation theory was proposed to solve the difficult problem of the inverse kinematics equation of six Degree Of Freedom (DOF) manipulator with general structure. Firstly, seven adjacent non-linear correlation nodes were searched from a large number of empirical data to compose hyper-body. Secondly, these seven nodes were used to obtain a six-dimensional linear predictive function. Finally, the predictive function was used to interpolate and inversely interpolate to predict poses and joint angles. The Matlab simulation was used to generate one million group of empirical data according to the positive kinematics equation, and the target pose was inversely interpolated iteratively to predict six joint angles. The experimental results show that compared with the Radial Basis Function Network (RBFN) and the six-dimensional linear inverse interpolation method, the proposed method can approach the target pose faster and more accuratly. The proposed method is based on data, which avoids complicated theory and can meet the requirements of robot daily applications.