An Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators

Different from traditional redundant manipulators, the redundant manipulators used in the surgical environment require the end effector (EE) to have high pose (position and orientation) accuracy to ensure the smooth progress of the operation. When analyzing the inverse kinematics (IK) of traditional...

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Autores principales:	Xinglei Zhang, Binghui Fan, Chuanjiang Wang, Xiaolin Cheng
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	inverse kinematics redundant surgical manipulator joint position limits kinematic singularity improved weighted gradient projection method Chemical technology TP1-1185
Acceso en línea:	https://doaj.org/article/561b6b2a417246359c4cfeef68a325cf
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spelling	oai:doaj.org-article:561b6b2a417246359c4cfeef68a325cf2021-11-11T19:18:05ZAn Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators10.3390/s212173621424-8220https://doaj.org/article/561b6b2a417246359c4cfeef68a325cf2021-11-01T00:00:00Zhttps://www.mdpi.com/1424-8220/21/21/7362https://doaj.org/toc/1424-8220Different from traditional redundant manipulators, the redundant manipulators used in the surgical environment require the end effector (EE) to have high pose (position and orientation) accuracy to ensure the smooth progress of the operation. When analyzing the inverse kinematics (IK) of traditional redundant manipulators, gradient-projection method (GPM) and weighted least-norm (WLN) method are commonly used methods to avoid joint position limits. However, for the traditional GPM and WLN method, when joints are close to their limits, they stop moving, which greatly reduces the accuracy of the IK solution. When robotic manipulators enter a singular region, although traditional damped least-squares (DLS) algorithms are used to handle singularities effectively, motion errors of the EE will be introduced. Furthermore, selecting singular region through trial and error may cause some joint velocities exceed their corresponding limits. More importantly, traditional DLS algorithms cannot guide robotic manipulators away from singular regions. Inspired by the merits of GPM, WLN, and DLS methods, an improved weighted gradient projection method (IWGPM) is proposed to solve the IK problem of redundant manipulators used in the surgical environment with avoiding joint position limits and singularities. The weighted matrix of the WLN method and the damping factor of the DLS algorithm have been improved, and a joint limit repulsive potential field function and singular repulsive potential field function belong to the null space are introduced to completely keep joints away from the damping interval and redundant manipulators away from the unsafe region. To verify the validity of the proposed IWGPM, simulations on a 7 degree of freedom (DOF) redundant manipulator used in laparoscopic surgery indicate that the proposed method can not only achieve higher accuracy IK solution but also avoid joint position limits and singularities effectively by comparing them with the results of the traditional GPM and WLN method, respectively. Furthermore, based on the proposed IWGPM, simulation tests in two cases show that joint position limits have a great impact on the orientation accuracy, and singular potential energy function has a great impact on the position accuracy.Xinglei ZhangBinghui FanChuanjiang WangXiaolin ChengMDPI AGarticleinverse kinematicsredundant surgical manipulatorjoint position limitskinematic singularityimproved weighted gradient projection methodChemical technologyTP1-1185ENSensors, Vol 21, Iss 7362, p 7362 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	inverse kinematics redundant surgical manipulator joint position limits kinematic singularity improved weighted gradient projection method Chemical technology TP1-1185
spellingShingle	inverse kinematics redundant surgical manipulator joint position limits kinematic singularity improved weighted gradient projection method Chemical technology TP1-1185 Xinglei Zhang Binghui Fan Chuanjiang Wang Xiaolin Cheng An Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators
description	Different from traditional redundant manipulators, the redundant manipulators used in the surgical environment require the end effector (EE) to have high pose (position and orientation) accuracy to ensure the smooth progress of the operation. When analyzing the inverse kinematics (IK) of traditional redundant manipulators, gradient-projection method (GPM) and weighted least-norm (WLN) method are commonly used methods to avoid joint position limits. However, for the traditional GPM and WLN method, when joints are close to their limits, they stop moving, which greatly reduces the accuracy of the IK solution. When robotic manipulators enter a singular region, although traditional damped least-squares (DLS) algorithms are used to handle singularities effectively, motion errors of the EE will be introduced. Furthermore, selecting singular region through trial and error may cause some joint velocities exceed their corresponding limits. More importantly, traditional DLS algorithms cannot guide robotic manipulators away from singular regions. Inspired by the merits of GPM, WLN, and DLS methods, an improved weighted gradient projection method (IWGPM) is proposed to solve the IK problem of redundant manipulators used in the surgical environment with avoiding joint position limits and singularities. The weighted matrix of the WLN method and the damping factor of the DLS algorithm have been improved, and a joint limit repulsive potential field function and singular repulsive potential field function belong to the null space are introduced to completely keep joints away from the damping interval and redundant manipulators away from the unsafe region. To verify the validity of the proposed IWGPM, simulations on a 7 degree of freedom (DOF) redundant manipulator used in laparoscopic surgery indicate that the proposed method can not only achieve higher accuracy IK solution but also avoid joint position limits and singularities effectively by comparing them with the results of the traditional GPM and WLN method, respectively. Furthermore, based on the proposed IWGPM, simulation tests in two cases show that joint position limits have a great impact on the orientation accuracy, and singular potential energy function has a great impact on the position accuracy.
format	article
author	Xinglei Zhang Binghui Fan Chuanjiang Wang Xiaolin Cheng
author_facet	Xinglei Zhang Binghui Fan Chuanjiang Wang Xiaolin Cheng
author_sort	Xinglei Zhang
title	An Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators
title_short	An Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators
title_full	An Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators
title_fullStr	An Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators
title_full_unstemmed	An Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators
title_sort	improved weighted gradient projection method for inverse kinematics of redundant surgical manipulators
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/561b6b2a417246359c4cfeef68a325cf
work_keys_str_mv	AT xingleizhang animprovedweightedgradientprojectionmethodforinversekinematicsofredundantsurgicalmanipulators AT binghuifan animprovedweightedgradientprojectionmethodforinversekinematicsofredundantsurgicalmanipulators AT chuanjiangwang animprovedweightedgradientprojectionmethodforinversekinematicsofredundantsurgicalmanipulators AT xiaolincheng animprovedweightedgradientprojectionmethodforinversekinematicsofredundantsurgicalmanipulators AT xingleizhang improvedweightedgradientprojectionmethodforinversekinematicsofredundantsurgicalmanipulators AT binghuifan improvedweightedgradientprojectionmethodforinversekinematicsofredundantsurgicalmanipulators AT chuanjiangwang improvedweightedgradientprojectionmethodforinversekinematicsofredundantsurgicalmanipulators AT xiaolincheng improvedweightedgradientprojectionmethodforinversekinematicsofredundantsurgicalmanipulators
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An Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators

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