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Analytical inverse kinematics solution and global arm angle optimization method for 7-DOF redundant robotic arms without offset.

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Title: Analytical inverse kinematics solution and global arm angle optimization method for 7-DOF redundant robotic arms without offset.
Authors: Zhang, Miao1 (AUTHOR) miaozhang@tust.edu.cn, Mei, Songyang1 (AUTHOR) songyangmei@mail.tust.edu.cn, He, Hao1 (AUTHOR) haohe@mail.tust.edu.cn, Han, Xiaoguang1 (AUTHOR) xiaoguanghan@tust.edu.cn, Li, Zhiwu2,3 (AUTHOR) zwli@must.edu.mo
Source: ISA Transactions. Jun2026, Vol. 173, p425-436. 12p.
Subjects: Kinematics, Spherical geometry, Constraints (Physics), Robotic trajectory control, Industrial robots, Risk assessment
Abstract: In this paper, a novel analytical inverse kinematics solution method is proposed for seven-degree-of-freedom (7-DOF) redundant robotic arms without offset. Building upon the inverse kinematics solution, an arm angle optimization strategy is introduced to determine the optimal configuration among multiple feasible solutions. Based on spherical geometry, an arm angle is constructed, and the mapping relationships between joint angles and the arm angle are derived. The feasible interval of the arm angle is identified by analyzing joint limits and singularity conditions. A mechanism is introduced to prevent joint angles from approaching their limit positions, incorporating constraints on joint velocity and acceleration. Furthermore, a dynamic risk assessment and smooth update strategy is proposed, which integrates the boundary repulsion effect and the central attractive guidance mechanism for the global optimization of the arm angle parameters. Simulation results indicate that, relative to state-of-the-art optimization methods, the proposed algorithm exhibits notable advantages in terms of trajectory tracking error, average arm angle change rate, joint angle variation, maximum joint velocity, maximum joint acceleration, and computational time. [Display omitted] • An analytical method for solving inverse kinematics is introduced by constructing the arm angle using spherical geometry. • An arm angle adjustment method integrates dynamic risk assessment, boundary exclusion, and central attractive guidance. • An arm angle update mechanism enforces kinematic constraints and applies an exponentially weighted moving average. [ABSTRACT FROM AUTHOR]
Copyright of ISA Transactions is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
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Header DbId: egs
DbLabel: Engineering Source
An: 193721963
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Analytical inverse kinematics solution and global arm angle optimization method for 7-DOF redundant robotic arms without offset.
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  Label: Authors
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Miao%22">Zhang, Miao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> miaozhang@tust.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Mei%2C+Songyang%22">Mei, Songyang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> songyangmei@mail.tust.edu.cn</i><br /><searchLink fieldCode="AR" term="%22He%2C+Hao%22">He, Hao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> haohe@mail.tust.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Han%2C+Xiaoguang%22">Han, Xiaoguang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xiaoguanghan@tust.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Zhiwu%22">Li, Zhiwu</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> zwli@must.edu.mo</i>
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  Group: Src
  Data: <searchLink fieldCode="JN" term="%22ISA+Transactions%22">ISA Transactions</searchLink>. Jun2026, Vol. 173, p425-436. 12p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Kinematics%22">Kinematics</searchLink><br /><searchLink fieldCode="DE" term="%22Spherical+geometry%22">Spherical geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Constraints+%28Physics%29%22">Constraints (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Robotic+trajectory+control%22">Robotic trajectory control</searchLink><br /><searchLink fieldCode="DE" term="%22Industrial+robots%22">Industrial robots</searchLink><br /><searchLink fieldCode="DE" term="%22Risk+assessment%22">Risk assessment</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, a novel analytical inverse kinematics solution method is proposed for seven-degree-of-freedom (7-DOF) redundant robotic arms without offset. Building upon the inverse kinematics solution, an arm angle optimization strategy is introduced to determine the optimal configuration among multiple feasible solutions. Based on spherical geometry, an arm angle is constructed, and the mapping relationships between joint angles and the arm angle are derived. The feasible interval of the arm angle is identified by analyzing joint limits and singularity conditions. A mechanism is introduced to prevent joint angles from approaching their limit positions, incorporating constraints on joint velocity and acceleration. Furthermore, a dynamic risk assessment and smooth update strategy is proposed, which integrates the boundary repulsion effect and the central attractive guidance mechanism for the global optimization of the arm angle parameters. Simulation results indicate that, relative to state-of-the-art optimization methods, the proposed algorithm exhibits notable advantages in terms of trajectory tracking error, average arm angle change rate, joint angle variation, maximum joint velocity, maximum joint acceleration, and computational time. [Display omitted] • An analytical method for solving inverse kinematics is introduced by constructing the arm angle using spherical geometry. • An arm angle adjustment method integrates dynamic risk assessment, boundary exclusion, and central attractive guidance. • An arm angle update mechanism enforces kinematic constraints and applies an exponentially weighted moving average. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of ISA Transactions is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.isatra.2026.03.028
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 12
        StartPage: 425
    Subjects:
      – SubjectFull: Kinematics
        Type: general
      – SubjectFull: Spherical geometry
        Type: general
      – SubjectFull: Constraints (Physics)
        Type: general
      – SubjectFull: Robotic trajectory control
        Type: general
      – SubjectFull: Industrial robots
        Type: general
      – SubjectFull: Risk assessment
        Type: general
    Titles:
      – TitleFull: Analytical inverse kinematics solution and global arm angle optimization method for 7-DOF redundant robotic arms without offset.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Zhang, Miao
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            NameFull: Mei, Songyang
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            NameFull: He, Hao
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            NameFull: Han, Xiaoguang
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            NameFull: Li, Zhiwu
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          Dates:
            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 173
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