Robot dynamics: A recursive algorithm for efficient calculation of Christoffel symbols
•Christoffel symbols of the first kind are calculated recursively.•Calculations based on inertial parameters and transformations matrices.•Execution time and numerical error as performance indicators.•Compares favourably with existing methods.•MATLAB running code is available. Christoffel symbols of...
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| Published in: | Mechanism and machine theory Vol. 142; p. 103589 |
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| Format: | Journal Article |
| Language: | English |
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01.12.2019
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| ISSN: | 0094-114X, 1873-3999 |
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| Abstract | •Christoffel symbols of the first kind are calculated recursively.•Calculations based on inertial parameters and transformations matrices.•Execution time and numerical error as performance indicators.•Compares favourably with existing methods.•MATLAB running code is available.
Christoffel symbols of the first kind are very important in robot dynamics. They are used for tuning various proposed robot controllers, for determining the bounds on Coriolis/Centrifugal matrix, for mathematical formulation of optimal trajectory calculation, among others. In the literature of robot dynamics, Christoffel symbols of the first kind are calculated from Lagrangian dynamics using an off-line generated symbolic formula. In this study we present a novel and efficient recursive, non-symbolic, method where Christoffel symbols of the first kind are calculated on-the-fly based on the inertial parameters of robot’s links and their transformation matrices. The proposed method was analyzed in terms of execution time, computational complexity and numerical error. Results show that the proposed algorithm compares favorably with existing methods. |
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| AbstractList | Christoffel symbols of the first kind are very important in robot dynamics. They are used for tuning various proposed robot controllers, for determining the bounds on Coriolis/Centrifugal matrix, for mathematical formulation of optimal trajectory calculation, among others. In the literature of robot dynamics, Christoffel symbols of the first kind are calculated from Lagrangian dynamics using an off-line generated symbolic formula. In this study we present a novel and efficient recursive, non-symbolic, method where Christoffel symbols of the first kind are calculated on-the-fly based on the inertial parameters of robot’s links and their transformation matrices. The proposed method was analyzed in terms of execution time, computational complexity and numerical error. Results show that the proposed algorithm compares favorably with existing methods. •Christoffel symbols of the first kind are calculated recursively.•Calculations based on inertial parameters and transformations matrices.•Execution time and numerical error as performance indicators.•Compares favourably with existing methods.•MATLAB running code is available. Christoffel symbols of the first kind are very important in robot dynamics. They are used for tuning various proposed robot controllers, for determining the bounds on Coriolis/Centrifugal matrix, for mathematical formulation of optimal trajectory calculation, among others. In the literature of robot dynamics, Christoffel symbols of the first kind are calculated from Lagrangian dynamics using an off-line generated symbolic formula. In this study we present a novel and efficient recursive, non-symbolic, method where Christoffel symbols of the first kind are calculated on-the-fly based on the inertial parameters of robot’s links and their transformation matrices. The proposed method was analyzed in terms of execution time, computational complexity and numerical error. Results show that the proposed algorithm compares favorably with existing methods. |
| ArticleNumber | 103589 |
| Author | Bearee, Richard Safeea, Mohammad Neto, Pedro |
| Author_xml | – sequence: 1 givenname: Mohammad surname: Safeea fullname: Safeea, Mohammad email: ms@uc.pt organization: University of Coimbra, Department of Mechanical Engineering, Coimbra 3030-788, Portugal – sequence: 2 givenname: Pedro surname: Neto fullname: Neto, Pedro email: pedro.neto@dem.uc.pt organization: University of Coimbra, Department of Mechanical Engineering, Coimbra 3030-788, Portugal – sequence: 3 givenname: Richard surname: Bearee fullname: Bearee, Richard email: Richard.BEAREE@ensam.eu organization: Arts et Métiers, LISPEN, Lille 59800, France |
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| Cites_doi | 10.1177/0278364905054928 10.1109/TAC.2009.2028959 10.1109/9.83543 10.1002/rob.4620040604 10.1109/70.86088 10.1177/02783649922066628 10.1109/70.210803 10.1016/S0167-6911(00)00038-4 10.1109/TNN.2007.894070 10.1109/JRA.1987.1087090 10.1007/978-3-319-32552-1 10.1080/00207179.2013.875224 10.1002/oca.2234 10.1049/iet-cta.2012.0505 10.1109/9.402235 10.1163/156855395X00427 10.1115/1.3149599 10.1177/02783649922066619 10.1016/S0167-6911(00)00077-3 10.1115/1.4044216 |
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| Keywords | Recursive algorithms Christoffel symbols Dynamicss Bioengineering Mechanics of Materials |
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Control Lett. doi: 10.1016/S0167-6911(00)00077-3 – year: 2019 ident: 10.1016/j.mechmachtheory.2019.103589_bib0024 article-title: Non-convex time-optimal trajectory planning for robot manipulators publication-title: J. Dyn. Syst. Meas.Control doi: 10.1115/1.4044216 |
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| Snippet | •Christoffel symbols of the first kind are calculated recursively.•Calculations based on inertial parameters and transformations matrices.•Execution time and... Christoffel symbols of the first kind are very important in robot dynamics. They are used for tuning various proposed robot controllers, for determining the... |
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| SubjectTerms | Christoffel symbols Dynamicss Engineering Sciences Recursive algorithms |
| Title | Robot dynamics: A recursive algorithm for efficient calculation of Christoffel symbols |
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