Shape Representation and Modeling of Tendon-Driven Continuum Robots Using Euler Arc Splines
Due to the compliance of tendon-driven continuum robots, carrying a load or experiencing a tip force result in variations in backbone curvature. While the spatial robot configuration theoretically needs an infinite number of parameters for exact description, it can be well approximated using Euler A...
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| Veröffentlicht in: | IEEE robotics and automation letters Jg. 7; H. 3; S. 1 - 8 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.07.2022
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| ISSN: | 2377-3766, 2377-3766 |
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| Abstract | Due to the compliance of tendon-driven continuum robots, carrying a load or experiencing a tip force result in variations in backbone curvature. While the spatial robot configuration theoretically needs an infinite number of parameters for exact description, it can be well approximated using Euler Arc Splines which use only six of them. In this letter, we first show the accuracy of this representation by fitting the Euler Arc splines directly to experimentally measured robot shapes. Additionally, we propose a 3D static model that can account for gravity, friction and tip forces. We demonstrate the utility of using efficient parameterization by analyzing the computation time of the proposed model and then, using it to propose a hybrid model that combines physics-based model with observed data. The average tip error for the Euler arc spline representation is <inline-formula><tex-math notation="LaTeX">0.43</tex-math></inline-formula>% and the proposed static model is <inline-formula><tex-math notation="LaTeX">3.25</tex-math></inline-formula>% w.r.t. robot length. The average computation time is <inline-formula><tex-math notation="LaTeX">0.56 \,\mathrm{ms}</tex-math></inline-formula> for nonplanar deformations for a robot with ten disks. The hybrid model reduces the maximum error predicted by the static model from <inline-formula><tex-math notation="LaTeX">8.6</tex-math></inline-formula>% to <inline-formula><tex-math notation="LaTeX">5.1</tex-math></inline-formula>% w.r.t. robot length, while using 30 observations for training. |
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| AbstractList | Due to the compliance of tendon-driven continuum robots, carrying a load or experiencing a tip force result in variations in backbone curvature. While the spatial robot configuration theoretically needs an infinite number of parameters for exact description, it can be well approximated using Euler Arc Splines which use only six of them. In this letter, we first show the accuracy of this representation by fitting the Euler Arc splines directly to experimentally measured robot shapes. Additionally, we propose a 3D static model that can account for gravity, friction and tip forces. We demonstrate the utility of using efficient parameterization by analyzing the computation time of the proposed model and then, using it to propose a hybrid model that combines physics-based model with observed data. The average tip error for the Euler arc spline representation is <inline-formula><tex-math notation="LaTeX">0.43</tex-math></inline-formula>% and the proposed static model is <inline-formula><tex-math notation="LaTeX">3.25</tex-math></inline-formula>% w.r.t. robot length. The average computation time is <inline-formula><tex-math notation="LaTeX">0.56 \,\mathrm{ms}</tex-math></inline-formula> for nonplanar deformations for a robot with ten disks. The hybrid model reduces the maximum error predicted by the static model from <inline-formula><tex-math notation="LaTeX">8.6</tex-math></inline-formula>% to <inline-formula><tex-math notation="LaTeX">5.1</tex-math></inline-formula>% w.r.t. robot length, while using 30 observations for training. Due to the compliance of tendon-driven continuum robots, carrying a load or experiencing a tip force result in variations in backbone curvature. While the spatial robot configuration theoretically needs an infinite number of parameters for exact description, it can be well approximated using Euler Arc Splines which use only six of them. In this letter, we first show the accuracy of this representation by fitting the Euler Arc splines directly to experimentally measured robot shapes. Additionally, we propose a 3D static model that can account for gravity, friction and tip forces. We demonstrate the utility of using efficient parameterization by analyzing the computation time of the proposed model and then, using it to propose a hybrid model that combines physics-based model with observed data. The average tip error for the Euler arc spline representation is [Formula Omitted]% and the proposed static model is [Formula Omitted]% w.r.t. robot length. The average computation time is [Formula Omitted] for nonplanar deformations for a robot with ten disks. The hybrid model reduces the maximum error predicted by the static model from [Formula Omitted]% to [Formula Omitted]% w.r.t. robot length, while using 30 observations for training. Due to the compliance of tendon-driven continuum robots, carrying a load or experiencing a tip force result in variations in backbone curvature. While the spatial robot configuration theoretically needs an infinite number of parameters for exact description, it can be well approximated using Euler Arc Splines which use only six of them. In this letter, we first show the accuracy of this representation by fitting the Euler Arc splines directly to experimentally measured robot shapes. Additionally, we propose a 3D static model that can account for gravity, friction and tip forces. We demonstrate the utility of using efficient parameterization by analyzing the computation time of the proposed model and then, using it to propose a hybrid model that combines physics-based model with observed data. The average tip error for the Euler arc spline representation is 0.43% and the proposed static model is 3.25% w.r.t. robot length. The average computation time is 0.56 ms for nonplanar deformations for a robot with ten disks. The hybrid model reduces the maximum error predicted by the static model from 8.6% to 5.1% w.r.t. robot length, while using 30 observations for training. |
| Author | Peyron, Quentin Burgner-Kahrs, Jessica Rao, Priyanka |
| Author_xml | – sequence: 1 givenname: Priyanka orcidid: 0000-0001-8188-9603 surname: Rao fullname: Rao, Priyanka organization: Continuum Robotics Laboratory, Department of Mathematical & Computational Sciences, University of Toronto, Toronto, ON, Canada – sequence: 2 givenname: Quentin orcidid: 0000-0003-2628-1464 surname: Peyron fullname: Peyron, Quentin organization: Continuum Robotics Laboratory, Department of Mathematical & Computational Sciences, University of Toronto, Toronto, ON, Canada – sequence: 3 givenname: Jessica orcidid: 0000-0001-9185-3970 surname: Burgner-Kahrs fullname: Burgner-Kahrs, Jessica organization: Continuum Robotics Laboratory, Department of Mathematical & Computational Sciences, University of Toronto, Toronto, ON, Canada |
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| SubjectTerms | Analytical models and Learning for Soft Robots Automatic Computational modeling Computing time Control Data models Disks Engineering Sciences Flexible Robotics Kinematics Modeling Parameterization Representations Robots Shape Splines (mathematics) Static models Three dimensional models Three-dimensional displays |
| Title | Shape Representation and Modeling of Tendon-Driven Continuum Robots Using Euler Arc Splines |
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