Abstract: The link bar coordinate systems is established based on axis direction of joint axis. The coordinate system transformation matrix is derived according to Denavit-Hartenberg （D-H） notation, the forward kinematics model in the light of coordinate system transformation matrix is set up, the inverse kinematics model is set up based on forward kinematics model, the inverse kinematics model is multiple object optimization problem, the optimal solution of inverse kinematics model has the characteristic of high accuracy and minimizes the rotation extent. For the purpose of solving inverse kinematics model, the adaptive mutation multiple population differential evolution algorithm is proposed, multi-population strategy improves the ability of information sharing by individuals, and adaptive mutation method can promote the diversity of individuals, and the numerical results indicate that the new algorithm can solve inverse kinematics model efficiently.

Key words: manipulator, joint, degree of freedom, rotation extent

摘要： 根据机械臂关节轴线方向建立了连杆坐标系，利用Denavit-Hartenberg（D-H）法得到连杆坐标系变换矩阵；通过连杆坐标系变换矩阵得到机械臂正运动控制模型；通过正运动模型得到逆运动控制模型，逆运动控制模型是多目标约束优化问题，该模型的最优解既可以保证控制精度，又可以保证各个关节角变动幅度的总代价（定义为旋转副）达到最小。为了求解机械臂逆运动模型，提出了自适应多种群差分演化算法（AMPDE），多种群策略可以提升个体共享群体信息的能力，自适应变异策略可以提升种群多样性，数值实验表明该算法可以有效求解机械臂逆运动学模型。

关键词: 机械臂, 关节, 自由度, 旋转副