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Models for three new screw-based IK sub-problems using geometric descriptions and their applications

机译：使用几何描述的三个新的基于螺钉的IK子问题的模型及其应用

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摘要

This study presents three new screw-based inverse kinematics (IK) sub-problems and their corresponding models, which could be applied to find the IK solutions for manipulators with rotational joints. The three sub-problems are described as: rotation about three axes with two intersecting axes that do not intersect with a third axis or three non-intersecting and non-coplanar axes; rotation about four axes and either the second or third joint angle is known; and rotation about five axes and the second and fourth joint angles are known. In the IK models, the rotational motion of a single point located outside of the axes can be described by using a system of multivariate quadratic equations based on the geometrical relationship. According to these descriptions, each sub-problem is converted into three PK-1 sub-problems. To demonstrate the generality of the sub-problems to different manipulators, the IK models were used to solve the IK problems for the robots with four, six, and eight degrees of freedom (DOF) respectively. Moreover, considering the 4-DOF robot (a redundant manipulator) as the research object, the computational efficiency and applicability of the presented IK models were proven by applying the IK solutions to a robotic trajectory planning problem with obstacle avoidance in a real setting. (C) 2018 Published by Elsevier Inc.
机译：这项研究提出了三个新的基于螺钉的逆运动学（IK）子问题及其对应的模型，这些子问题可用于找到带有旋转关节的机械手的IK解决方案。三个子问题描述为：绕三个轴旋转，其中两个相交轴不与第三轴或三个不相交且不共面的轴相交；绕四个轴旋转，第二或第三关节角是已知的；围绕五个轴的旋转以及第二和第四关节角度是已知的。在IK模型中，可以使用基于几何关系的多元二次方程组来描述位于轴外的单个点的旋转运动。根据这些描述，每个子问题都转换为三个PK-1子问题。为了演示子问题对不同机械手的通用性，分别使用IK模型来解决具有四个，六个和八个自由度（DOF）的机器人的IK问题。此外，以4自由度机器人（冗余操纵器）为研究对象，通过将IK解决方案应用于实际环境中避障的机器人轨迹规划问题，证明了所提出IK模型的计算效率和适用性。 （C）2018由Elsevier Inc.发布

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