中文摘要：

以6自由度TX60型Staubli工业机械臂为研究对象，通过运动学分析，建立求解该机械臂位置逆解的非线性方程组。以末端执行器位姿误差最小为目标函数，将非线性方程组转化为无约束优化模型，并应用差分进化算法（Differential evolution algorithm，DE）求解该问题。为克服基本DE难以平衡收敛精度和计算可靠性的缺陷，提出一种自适应分工复合形差分进化算法（Adaptivedivision complex DE algorithm，ADCDE），以增强优化性能。该算法将种群自适应划分为开采子群和勘探子群，前者采用DE／best／2／bin策略生成变异个体，而后者采用复合形算子生成变异个体。给出工程应用实例，应用ADCDE求串联机械臂的位置逆解。仿真结果表明，该算法的计算精度和可靠性优于对比算法，应用较少计算开销即可求出高精度位置逆解，且能求得所有可能逆解，验证了该方法的有效性和可行性。

英文摘要：

A 6-DOF Stautli industrial robot manipulator of TX60 type is regarded as the research object, and then nonlinear equations are constructed to solve its inverse positional problems by means of kinematics analysis. Taking the minimizing pose error of the end-effector as the objective function, this study transforms the nonlinear equations into an unconstrained optimization model and employs a differential evolution （DE） algorithm to solve this problem. To overcome the defects of the simple DE algorithm that is difficult to keep balance between the convergence accuracy and the calculation reliability, an adaptive division complex DE （ADCDE） algorithm is presented to enhance its optimizing performance. This proposed algorithm divides adaptively the population into exploitation and exploration subgroups, furthermore, the former and latter apply the DE/best/2/bin strategy and the complex operator to generate mutation individuals, respectively. With a study case for engineering application, the ADCDE algorithm is implemented to find the inverse positional solutions of a serial robot manipulator. Simulation results indicate that the presented algorithm outperforms the compared algorithms in term of computational precision and reliability, and the inverse solutions with high precision and all possible ones can be obtained by this algorithm with light calculation cost. Moreover, these results also verify the effectiveness and feasibility of this approach.