引用本文: 谢习华, 范诗萌, 周烜亦, 李智勇. 基于改进差分进化算法的机械臂运动学逆解[J]. 机器人, 2019, 41(1): 50-57.
XIE Xihua, FAN Shimeng, ZHOU Xuanyi, LI Zhiyong. Inverse Kinematics of Manipulator Based on the Improved Differential Evolution Algorithm[J]. ROBOT, 2019, 41(1): 50-57.
 Citation: XIE Xihua, FAN Shimeng, ZHOU Xuanyi, LI Zhiyong. Inverse Kinematics of Manipulator Based on the Improved Differential Evolution Algorithm[J]. ROBOT, 2019, 41(1): 50-57.

## Inverse Kinematics of Manipulator Based on the Improved Differential Evolution Algorithm

• 摘要: 以9自由度液压机械臂为研究对象，建立求解位姿逆解的非线性方程组.以末端执行器位姿误差最小为优化指标建立目标函数，将非线性方程求解问题转化为最优化问题，并应用差分进化（DE）算法求解该问题.首先，为了避免位置和姿态收敛精度的不同，引入自适应权值系数进行平衡.然后，为克服基本DE算法难以平衡全局探索能力和局部开发能力的缺陷，结合DE/rand/1/bin和DE/best/1/bin两种进化模式，改进自适应变异差分进化（SAMDE）算法，提高了算法的收敛精度和收敛速度.最后，采用对称映射法对不满足关节角边界范围的个体进行处理，提高了收敛精度.开展了与基本DE算法的对比试验，仿真结果表明，该算法的收敛精度和收敛速度优于基本差分进化算法，且能够大幅度提高算法的稳定性.

Abstract: For a 9-DOF (degree of freedom) hydraulic manipulator, a set of nonlinear equations are established to solve its inverse kinematics of position and orientation. An objective function is proposed to minimize the position and orientation error of the end-effector, and the solution problem of the nonlinear equations is transformed into an optimization problem, which is solved by the differential evolution (DE) algorithm. Firstly, self-adaptive weight coefficients are introduced to avoid the difference of the convergence accuracy of position error and orientation error. In order to overcome the difficulty of the basic DE algorithm in balancing the global and local exploitation abilities, DE/rand/1/bin and DE/best/1/bin, the two evolution models are combined to improve the self-adaptive mutation differential evolution (SAMDE) algorithm, resulting in better convergence accuracy and convergence rate. Finally, the reflection approach is applied to dealing with the individuals exceeding the boundary of the joint angles, and thus the convergence accuracy is improved. Some contrastive experiments with the basic DE algorithm are conducted. The simulation results indicate that the proposed method outperforms the basic DE algorithm in terms of convergence accuracy and convergence rate, and improves the stability significantly.

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