Chinese Journal of Mechanical Engineering >

2020 , Vol. 33 >Issue 4: 62 - 62

DOI: https://doi.org/10.1186/s10033-020-00481-z

Review

A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism

  • Xinming Huo ,
  • Shuofei Yang ,
  • Binbin Lian ,
  • Tao Sun ,
  • Yimin Song
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  • 1. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300350, China;
    2. Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Kowloon 999077, Hong Kong, China

收稿日期: 2020-04-29

  修回日期: 2020-08-11

  网络出版日期: 2020-11-06

基金资助

Supported in part by National Key R & D Program of China (Grant No. 2018YFB1307800), National Natural Science Foundation of China (Grant Nos.51875391, 51675366), and Tianjin Science and Technology Planning Project (Grant Nos. 18YFS DZC00010, 18YFZCSF00590)

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A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism

  • Xinming Huo ,
  • Shuofei Yang ,
  • Binbin Lian ,
  • Tao Sun ,
  • Yimin Song
Expand
  • 1. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300350, China;
    2. Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Kowloon 999077, Hong Kong, China

Received date: 2020-04-29

  Revised date: 2020-08-11

  Online published: 2020-11-06

Supported by

Supported in part by National Key R & D Program of China (Grant No. 2018YFB1307800), National Natural Science Foundation of China (Grant Nos.51875391, 51675366), and Tianjin Science and Technology Planning Project (Grant Nos. 18YFS DZC00010, 18YFZCSF00590)

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摘要

Topology and performance are the two main topics dealt in the development of robotic mechanisms. However, it is still a challenge to connect them by integrating the modeling and design process of both parts in a unified frame. As the properties associated with topology and performance, finite motion and instantaneous motion of the robot play key roles in the procedure. On the purpose of providing a fundamental preparation for integrated modeling and design, this paper carries out a review on the existing unified mathematic frameworks for motion description and computation, involving matrix Lie group and Lie algebra, dual quaternion and pure dual quaternion, finite screw and instantaneous screw. Besides the application in robotics, the review of the work from these mathematicians concentrates on the description, composition and intersection operations of the finite and instantaneous motions, especially on the exponential-differential maps which connect the two sides. Furthermore, an in-depth discussion is worked out by investigating the algebraical relationship among these methods and their further progress in integrated robotic development. The presented review offers insightful investigation to the motion description and computation, and therefore would help designers to choose appropriate mathematical tool in the integrated design and modeling and design of mechanisms and robots.

关键词： Robotic mechanism; Integrated method; Matrix Lie group; Dual quaternion; Finite screw

本文引用格式

Xinming Huo , Shuofei Yang , Binbin Lian , Tao Sun , Yimin Song . A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism[J]. Chinese Journal of Mechanical Engineering, 2020 , 33(4) : 62 -62 . DOI: 10.1186/s10033-020-00481-z

Abstract

Topology and performance are the two main topics dealt in the development of robotic mechanisms. However, it is still a challenge to connect them by integrating the modeling and design process of both parts in a unified frame. As the properties associated with topology and performance, finite motion and instantaneous motion of the robot play key roles in the procedure. On the purpose of providing a fundamental preparation for integrated modeling and design, this paper carries out a review on the existing unified mathematic frameworks for motion description and computation, involving matrix Lie group and Lie algebra, dual quaternion and pure dual quaternion, finite screw and instantaneous screw. Besides the application in robotics, the review of the work from these mathematicians concentrates on the description, composition and intersection operations of the finite and instantaneous motions, especially on the exponential-differential maps which connect the two sides. Furthermore, an in-depth discussion is worked out by investigating the algebraical relationship among these methods and their further progress in integrated robotic development. The presented review offers insightful investigation to the motion description and computation, and therefore would help designers to choose appropriate mathematical tool in the integrated design and modeling and design of mechanisms and robots.

Key words： Robotic mechanism; Integrated method; Matrix Lie group; Dual quaternion; Finite screw

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