Pseudoinverse-based jerk-level solutions of D3Z0, D2Z1, D1Z2 and D0Z3 types to redundant manipulator's inverse kinematics

Hongzhou Tan, Jiawei Luo, Xiaotian Yu, Dongsheng Guo, Yunong Zhang
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引用次数: 6

Abstract

The pseudoinverse-based method, as a conventional method, is generally used in the motion planning and control of velocity and/or acceleration level(s) to solve the complicated inverse-kinematics (IK) problem. In this paper, we firstly propose a simple pseudoinverse-based solution at the jerk level to solve the IK problem by using direct derivative dynamics (DDD or D3 for short) thrice and without using Zhang dynamics (ZD), which is thus termed D3Z0 type. Note that, though the D3Z0 solution is simple, it has some inherent weaknesses, such as low control precision and lack of necessary feedbacks. Therefore, as an important branch of dynamics methods, ZD is adopted to solve the above weaknesses. According to the number of times of using ZD, three enhanced solutions termed D2Z1, D1Z2 and D0Z3 types are then proposed and investigated. Specifically, D2Z1 means that we use 3D twice and ZD once to construct the solution, and D1Z2 and D0Z3 can be obtained and defined similarly. Moreover, feedbacks of position, velocity and acceleration levels can be partially or fully incorporated into the D2Z1, D1Z2 and D0Z3 solutions. Meanwhile, based on D3Z0, D2Z1, D1Z2 and D0Z3 solutions, a relatively complete framework of DZ-type solutions is thus proposed for solving the IK problem at the jerk level. Finally, simulation results performed on a five-link redundant manipulator substantiate the effectiveness and superiority of the DZ-type solutions for manipulator motion planning and control, which further show both smooth and efficient tracking performance, especially for solving the jerk-level IK redundancy of manipulators.
基于伪逆的D3Z0、D2Z1、D1Z2和D0Z3型冗余机械手逆运动学解
基于伪逆的方法是一种传统的方法,通常用于速度和/或加速度水平的运动规划和控制,以解决复杂的逆运动学问题。在本文中,我们首先提出了一种简单的基于伪逆的解,通过三次使用直接导数动力学(DDD或简称D3)而不使用张动力学(ZD)来解决IK问题,因此称为D3Z0型。请注意,虽然D3Z0解决方案很简单,但它有一些固有的弱点,例如控制精度低和缺乏必要的反馈。因此,采用ZD作为动力学方法的一个重要分支来解决上述弱点。根据ZD的使用次数,提出并研究了D2Z1、D1Z2和D0Z3三种增强溶液。具体来说,D2Z1意味着我们使用3D两次,使用ZD一次来构建解,D1Z2和D0Z3可以类似地得到和定义。此外,位置、速度和加速度水平的反馈可以部分或全部纳入D2Z1、D1Z2和D0Z3解决方案。同时,在D3Z0、D2Z1、D1Z2和D0Z3解的基础上,提出了一个相对完整的dz型解框架,用于在jerk层面解决IK问题。最后,以五连杆冗余度机械手为例进行仿真,验证了dz型方案在机械手运动规划与控制方面的有效性和优越性,进一步显示了其平滑高效的跟踪性能,特别是在解决机械手的瞬变级IK冗余度方面。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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