空间6R串联机械手逆运动学分析的新方法研究

Research on the Novel Method for Inverse Kinematics Analysis of Spatial 6R Serial Manipulators

为了解决空间6R串联机械手的逆运动学问题使用矩阵方法建模时,需要进行矢量运算或投影运算的问题,基于四维旋转矩阵和倍矩阵,提出了一种建模新方法。根据三维空间刚体变换的四维旋转矩阵和倍矩阵表示,建立空间6R串联机械手的正运动学方程。通过变量分离,直接得到14个逆运动学基本约束方程;通过线性消元和Sylvester结式消元,将其转化为求解一个16阶矩阵的特征值问题,得到该问题的16组解。采用数值实例和SolidWorks仿真验证了新方法的正确性。新方法的优势在于可以直接得到14个逆运动学约束方程,不需要进行矢量运算或者投影等,并且由于新方法将三维空间中的平移变换近似为四维空间中的旋转变换,故而可以统一求解含有R、P和C副的空间串联机械手逆运动学问题。

In order to cope with the requirements of vector operation and projection operation,in the process of kinematic modeling using the matrix method for the inverse kinematic analysis of spatial 6R serial manipulators,a novel modeling method for the problem is proposed based on the 4D rotational matrix and the double matrix.On the basis of the representations of the 4D rotational matrix and the double matrix of the spatial rigid body transformation,the forward kinematic equations of a spatial 6R serial manipulator are formulated.By variables separation,the 14 inverse kinematic equations are readily obtained from the novel formulation.The 16 sets of solution are the corresponding eigenvalue of the 16-order coefficient matrix by the linear elimination and Sylvester resultant elimination from the fourteen equations.The numerical example and the corresponding 3D configuration based on SolidWorks are provided to verified the correctness.The advantage of the new method lies in that 14 kinematic constraint equations are readily obtained without vector operation and projection operation,and the new method regards the spatial rigid-body translation as the special case of the four-dimensional rotation,and therefore it can deal with revolute,prismatic and cylindrical joint in a uniform matter.