Yonezawa Ansei, Yonezawa Heisei, Kajiwara Itsuro
IEEE Trans Cybern. 2024 Sep;54(9):4903-4914. doi: 10.1109/TCYB.2024.3372989. Epub 2024 Aug 26.
Inverse kinematics (IK) is an important and challenging problem in the operation of industrial manipulators. This study proposes a simple IK 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 IK calculation of the manipulator is formulated as a numerical optimization problem. Furthermore, a simple algorithm for solving the IK 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.
逆运动学（IK）是工业机器人操作中的一个重要且具有挑战性的问题。本研究针对工业串联机器人提出了一种简单的IK计算方案。所提出的技术能够在考虑每个关节运动成本的同时，计算出合适的关节变量值，以实现期望的末端执行器位置和姿态。为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和姿态，另一个用于评估关节的运动效率。通过将这两个标量函数相结合，将机器人的IK计算表述为一个数值优化问题。此外，基于具有范数限制更新向量的同时扰动随机逼近（NLSPSA），构建了一种通过上述优化求解IK的简单算法。所提出的方案不仅考虑了末端执行器位置和姿态的精度，还考虑了机器人运动的效率。因此，它得出了逆问题的实际结果。此外，由于NLSPSA的高计算效率，所提出的算法简单且易于实现。最后，通过使用冗余机器人的数值示例验证了所提方法的有效性。
