Inverse kinematics is an important and challenging problem in the operation of industrial manipulators. This study proposes a simple inverse kinematics calculation scheme for an industrial serial manipulator. The proposed technique can calculate appropriate values of the joint variables to realize the desired end-effector position and orientation while considering the motion costs of each joint. Two scalar functions are defined for the joint variables: one is to evaluate the end-effector position and orientation, whereas the other is to evaluate the motion efficiency of the joints. By combining the two scalar functions, the inverse kinematics calculation of the manipulator is formulated as a numerical optimization problem. Furthermore, a simple algorithm for solving the inverse kinematics via the aforementioned optimization is constructed on the basis of the simultaneous perturbation stochastic approximation with a norm-limited update vector (NLSPSA). The proposed scheme considers not only the accuracy of the position and orientation of the end-effector but also the efficiency of the robot movement. Therefore, it yields a practical result of the inverse problem. Moreover, the proposed algorithm is simple and easy to implement owing to the high calculation efficiency of NLSPSA. Finally, the effectiveness of the proposed method is verified through numerical examples using a redundant manipulator.

翻译：逆运动学是工业机械臂操作中一个关键且具有挑战性的问题。本研究提出了一种适用于工业串联机械臂的简单逆运动学计算方案。所提技术能够在考虑各关节运动成本的同时，计算恰当的关节变量值以实现期望的末端执行器位姿。针对关节变量定义了两个标量函数：一个用于评估末端执行器的位置与姿态，另一个用于评估关节的运动效率。通过结合这两个标量函数，将机械臂的逆运动学计算转化为数值优化问题。此外，基于带范数限制更新向量的同步扰动随机逼近（NLSPSA）方法，构建了通过上述优化求解逆运动学的简单算法。该方案不仅考虑了末端执行器位姿的精度，还兼顾了机器人运动的效率，因此能得到逆问题的实用结果。同时，由于NLSPSA的计算效率高，所提算法简单且易于实现。最后，通过使用冗余机械臂的数值算例验证了该方法的有效性。