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本文以冗余度机器人的逆运动学为基础，引入了扩展雅可比矩阵的概念；给出了便于讨论可操作度的几个重要定理；推导出了一般限制条件下的逆运动学最优解与最小范数解的关系．这对冗余度机器人的最优轨迹规划有重要意义．
In this paper, based on the inverse kinematics of redundant robots, the concept of extending Jacobi matrix is introduced. Some important theorems are given to facilitate the discussion of operability. An optimal inverse kinematics solution is derived under general constraints Relationship with Minimal Norm Solution. This is of great significance to the optimal trajectory planning of redundant robots.