机器人相对雅可比矩阵解析求解方法研究

为了简化冗余度机器人雅可比矩阵的求解，本文给出了一种雅可比矩阵解析求解方法，该方法是将基坐标系建立在中间关节上，从而得到机器人的相对雅可比矩阵，使得雅可比矩阵表达简单，利用现有的公式对雅可比矩阵中的元素进行改写，将矢量叉乘变为矢量点乘，通过改写可以将雅可比矩阵中的元素计算用公式解析表达，使得计算过程简单，方便，与微分变换法和矢量叉乘法相比较，该方法概念清晰，计算规范，通过示例验证，该方法是正确的。

Study of new analytic solution of robotic relative Jacobian matrix

A Jacobian matrix analytic solution is presented to simplify the calculation of the Jacobian matrix for redundant robot. The merit of this method is to place the base coordinate system in the middle joint to acquire relative Jacobian matrix and make expression of Jacobian matrix simplified. After the formula of documents are used to rewrite elements of Jacobian matrix, the vector cross product is changed into the vector dot product in Jacobian matrix. By rewriting elements of Jacobian matrix, the all formula are explicitly expressed and calculation process is simple and convenient. Compared with the differential transformation and the vector cross product methods, this method is conceptually clear and mathematically canonical. A calculation example shows this method is practical.