With many degrees of freedom (DOFs), a hyper-redundant manipulator has superior dexterity and flexible manipulation ability. However, its inverse kinematics and configuration planning are very challenging. With the increase in the number of DOFs, the corresponding computation load or training set will be much larger for traditional methods (such as the generalized inverse method and the artificial neural network method). In this paper, a segmented geometry method is proposed for a spatial hyper-redundant manipulator to solve the above problems. Similar to the human arm, the hyper-redundant manipulator is segmented into three sections from geometry, i.e., shoulder, elbow, and wrist. Then, its kinematics can be solved separately according to the segmentation, which reduces the complexity of the solution and simplifies the computation of the inverse kinematics. Furthermore, the configuration is parameterized by several parameters, i.e., the arm-angle, space arc parameters, and desired direction vector. The shoulder has proximal four DOFs, which is redundant for positioning the elbow and avoiding the joint limit. The arm-angle parameter is defined to solve the redundancy. The wrist consists of the distal two DOFs, and its joints are determined to match the desired direction vector of the end-effector. All the other joints (except for the joints belonging to shoulder and wrist) compose the elbow. These joint angles are solved by using space arc-based method. The configuration planning for avoiding joint limit, obstacles, and inspecting narrow pipeline are detailed for practical applications. Finally, circular trajectory tracking and pipeline inspection are, respectively, simulated and experimented on a 20-DOFs hyper-redundant manipulator. The results show that the proposed method can give solutions of the three-dimensional-pose-determining problem and the configuration-planning problem. The computation of the inverse kinematics is simplified for real-time control. It can also be applied to other spatial hyper-redundant manipulators with similar serial configurations.

中文翻译：

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空间超冗余机械臂运动学和配置规划的分割几何方法

具有多自由度（DOF）的超冗余机械手具有优越的灵巧性和灵活的操纵能力。然而，它的逆运动学和配置规划非常具有挑战性。随着DOF数量的增加，传统方法（如广义逆方法和人工神经网络方法）相应的计算量或训练集会大很多。针对上述问题，本文针对空间超冗余机械臂提出了一种分割几何方法。与人的手臂类似，超冗余机械手从几何上分为三个部分，即肩部、肘部和手腕。然后，它的运动学可以根据分割单独求解，这降低了解决方案的复杂性并简化了逆运动学的计算。此外，该配置由几个参数参数化，即臂角、空间弧参数和所需方向矢量。肩部有近端四个自由度，这对于定位肘部和避免关节限制是多余的。定义 arm-angle 参数以解决冗余问题。手腕由远端的两个自由度组成，其关节被确定为匹配末端执行器的所需方向向量。所有其他关节（肩关节和腕关节除外）都构成肘部。这些关节角度是通过使用基于空间弧的方法来求解的。详细规划了避免关节限位、障碍物、检查狭窄管道的配置规划，以供实际应用。最后，圆形轨迹跟踪和管道检查分别在 20 自由度超冗余机械手上进行了模拟和实验。结果表明，所提出的方法可以解决三维姿态确定问题和配置规划问题。为实时控制简化了逆运动学的计算。它也可以应用于具有类似串行配置的其他空间超冗余机械手。