Nonlinear Dynamics

, Volume 93, Issue 2, pp 487–504 | Cite as

Inverse dynamic analysis and position error evaluation of the heavy-duty industrial robot with elastic joints: an efficient approach based on Lie group

  • Kun Yang
  • Wenyu Yang
  • Chunming Wang
Original Paper


Heavy-duty industrial robots have great advantages in the manufacturing industry. Considering the heavy process load and low stiffness of the robot, an accurate and efficient dynamic model plays an important role in the behavior analysis and performance improvement in the robot. This paper presents a novel methodology for the inverse dynamic analysis of the heavy-duty industrial robot with elastic joints. In particular, high-order kinematics and dynamics are concisely deduced using Lie group to deal with elastic joints for the robot inverse dynamic analysis. Meanwhile, position errors of the end-effector due to elastic joints are evaluated through the inverse dynamic analysis when the robot is in heavy-duty applications. Compared with previous approaches, the advantage of proposed method is that new formulas for inverse dynamic analysis are shown to be more concise and computationally efficient using Lie group. Moreover, the position error evaluation method considering dynamic forces is proved to be more accurate than the traditional method when the robot is in the high-speed application. Because of the high computational efficiency and accurate evaluation results, the proposed approach is applicable to trajectory optimization and position error compensation, especially for the robot in heavy-load and high-speed applications.


Inverse dynamic analysis Lie group Position errors Heavy-duty industrial robot Elastic joints 



This work is supported by the Major State Basic Research Development Program of China (973 Program, Grant No. 2014CB046704) and National Science and Technology Support Plan (Grant No. 2014BAB13B01).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Materials Science and EngineeringHuazhong University of Science and TechnologyWuhanChina
  2. 2.State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhanChina

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