Redundancy parameterization and inverse kinematics of 7-DOF revolute manipulators
Seven-degree-of-freedom (DOF) robot arms have one redundant DOF for obstacle and singularity avoidance which must be parameterized to fully specify the joint angles for a given end effector pose. Commonly used 7-DOF revolute (7R) industrial manipulators from ABB, Motoman, and KUKA and space manipula...
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| Vydané v: | Mechanism and machine theory Ročník 204; s. 105824 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Goddard Space Flight Center
Elsevier Ltd
01.12.2024
Elsevier |
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| ISSN: | 0094-114X |
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| Abstract | Seven-degree-of-freedom (DOF) robot arms have one redundant DOF for obstacle and singularity avoidance which must be parameterized to fully specify the joint angles for a given end effector pose. Commonly used 7-DOF revolute (7R) industrial manipulators from ABB, Motoman, and KUKA and space manipulators like SSRMS or FREND are conventionally parameterized by the shoulder–elbow–wrist (SEW) angle for path planning and teleoperation. We introduce the general SEW angle which generalizes the conventional SEW angle with an arbitrary reference direction function. Redundancy parameterizations such as the conventional SEW angle encounter an algorithmic singularity along a line in the workspace. We introduce a reference direction function choice called the stereographic SEW angle which has a singularity only along a half-line which can be out of reach, enlarging the usable workspace. We prove all parameterizations have an algorithmic singularity. Finally, using the general SEW angle and subproblem decomposition, we provide efficient singularity-robust inverse kinematics solutions which are often closed-form but may involve a 1D or 2D search. Search-based solutions may be converted to finding polynomial roots. Examples are available in a publicly accessible repository.
•A new robot redundancy parameterization has a singularity only along a half-line.•New stereographic shoulder–elbow–wrist angle Jacobian and singularities found.•Algorithmic singularities are unavoidable for any redundancy parameterization.•Inverse kinematics efficiently solved for 7-degree-of-freedom revolute manipulators.•Search-based inverse kinematics solutions may be converted to polynomial root finding. |
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| AbstractList | Seven degree-of-freedom (DOF) robot arms have one redundant DOF for obstacle and singularity avoidance. This DOF does not change the end effector motion and must be parameterized to fully specify the joint angles for a given end effector pose. For 7-DOF revolute (7R) manipulators, we introduce the generalized shoulder-elbow-wrist (SEW) angle, a generalization of the widely-used conventional SEW angle but with an arbitrary reference direction function, along with Jacobian expressions and singularity analysis. Other redundancy parameterizations including the conventional SEW angle encounter an algorithmic singularity along a line in the workspace. We introduce a reference direction function choice called the stereographic SEW angle which has a singularity only along a half-line and can be placed out of reach. We prove such a singularity is unavoidable for any parameterization. Finally, using the general SEW angle and the subproblem decomposition method, we provide efficient singularity-robust inverse kinematics solutions for 7R manipulators which are often closed-form but may involve a 1D or (in general) 2D search. Search-based solutions may be converted to finding polynomial roots. Examples are available in a publicly accessible repository. Seven-degree-of-freedom (DOF) robot arms have one redundant DOF for obstacle and singularity avoidance which must be parameterized to fully specify the joint angles for a given end effector pose. Commonly used 7-DOF revolute (7R) industrial manipulators from ABB, Motoman, and KUKA and space manipulators like SSRMS or FREND are conventionally parameterized by the shoulder–elbow–wrist (SEW) angle for path planning and teleoperation. We introduce the general SEW angle which generalizes the conventional SEW angle with an arbitrary reference direction function. Redundancy parameterizations such as the conventional SEW angle encounter an algorithmic singularity along a line in the workspace. We introduce a reference direction function choice called the stereographic SEW angle which has a singularity only along a half-line which can be out of reach, enlarging the usable workspace. We prove all parameterizations have an algorithmic singularity. Finally, using the general SEW angle and subproblem decomposition, we provide efficient singularity-robust inverse kinematics solutions which are often closed-form but may involve a 1D or 2D search. Search-based solutions may be converted to finding polynomial roots. Examples are available in a publicly accessible repository. •A new robot redundancy parameterization has a singularity only along a half-line.•New stereographic shoulder–elbow–wrist angle Jacobian and singularities found.•Algorithmic singularities are unavoidable for any redundancy parameterization.•Inverse kinematics efficiently solved for 7-degree-of-freedom revolute manipulators.•Search-based inverse kinematics solutions may be converted to polynomial root finding. |
| ArticleNumber | 105824 |
| Audience | PUBLIC |
| Author | Elias, Alexander J. Wen, John T. |
| Author_xml | – sequence: 1 givenname: Alexander J. orcidid: 0000-0003-0896-3314 surname: Elias fullname: Elias, Alexander J. email: eliasa3@rpi.edu – sequence: 2 givenname: John T. orcidid: 0000-0002-5123-5411 surname: Wen fullname: Wen, John T. email: wenj@rpi.edu |
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| Cites_doi | 10.1177/1729881420925297 10.3390/s21217257 10.1007/s12555-017-0486-3 10.1016/j.actaastro.2014.09.003 10.1002/rob.4620120702 10.5875/ausmt.v2i4.172 10.1109/ACCESS.2020.2966768 10.1016/j.robot.2023.104377 10.1109/TBME.2012.2194489 10.1109/ACCESS.2019.2895741 10.1016/j.cagd.2016.05.008 10.1109/70.88062 10.2514/6.2007-6323 10.1115/1.4055677 10.1016/j.jfranklin.2020.11.020 10.1016/j.mechmachtheory.2017.10.025 10.1002/rob.4620080505 10.1007/s10846-016-0449-6 10.2514/6.2009-1870 10.4169/amer.math.monthly.123.5.502 10.1016/j.aei.2022.101812 10.1109/70.585902 10.1163/156855306778792461 10.1177/027836499201100504 10.1016/j.mechmachtheory.2017.12.005 10.1109/JRA.1987.1087111 10.1016/j.asr.2023.06.058 10.1007/s10846-021-01338-w 10.1007/s11465-021-0630-x 10.1109/LRA.2019.2897145 10.1163/1568553041257422 10.1016/S0921-8890(97)00054-7 10.1002/1097-4563(200009)17:9<453::AID-ROB1>3.0.CO;2-A 10.1177/1729881418814695 10.1007/BF01209164 |
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| Keywords | Industrial robots Humanoid robot systems Space robotics and automation Redundant robots Kinematics Telerobotics and teleoperation Redundant Robots Telerobotics And Teleoperation Space Robots And Automation Industrial Robots |
| Language | English |
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| Notes | GSFC Goddard Space Flight Center |
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| Snippet | Seven-degree-of-freedom (DOF) robot arms have one redundant DOF for obstacle and singularity avoidance which must be parameterized to fully specify the joint... Seven degree-of-freedom (DOF) robot arms have one redundant DOF for obstacle and singularity avoidance. This DOF does not change the end effector motion and... |
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| SubjectTerms | Electronics and Electrical Engineering Humanoid robot systems Industrial robots Kinematics Redundant robots Space robotics and automation Telerobotics and teleoperation |
| Title | Redundancy parameterization and inverse kinematics of 7-DOF revolute manipulators |
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