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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| References | Featherstone (bib0011) 2005; 24 Featherstone (bib0010) 1999; 18 Safeea, Bearee, Neto (bib0012) 2018 Luh, Walker, Paul (bib0008) 1980; 102 Qu, Dorsey (bib0018) 1991; 36 Siciliano, Khatib (bib0028) 2016 Cervantes, Alvarez-Ramirez (bib0017) 2001; 42 Khalil (bib0005) 2010 Tomei (bib0015) 1991; 7 Nagy, Vajk (bib0024) 2019 Neuman, Murray (bib0004) 1987; 4 Ortega, Loria, Kelly (bib0019) 1995; 40 Featherstone, Orin (bib0007) 2000 H. Hoifodt, Dynamic modeling and simulation of robot manipulators: the newton-euler formulation (2011). Gunawardana, Ghorbel (bib0013) 1999; 14 Mulero-Martinez (bib0020) 2007; 18 Pfeiffer, Johanni (bib0022) 1987; 3 Liu, Yu (bib0003) 2013; 7 Siciliano, Sciavicco, Villani, Oriolo (bib0021) 2010 Lynch, Park (bib0026) 2017 Misner, Thorne, Wheeler (bib0002) 1973 Kelly (bib0014) 1993; 9 Lipp, Boyd (bib0023) 2014; 87 Reynoso-Mora, Chen, Tomizuka (bib0030) 2016; 37 Alvarez-Ramirez, Cervantes, Kelly (bib0016) 2000; 41 Craig (bib0029) 2005; vol. 3 Featherstone (bib0009) 1999; 18 LaValle (bib0027) 2006 Sciavicco, Siciliano, Villani (bib0001) 1995; 10 Verscheure, Demeulenäre, Swevers, De Schutter, Diehl (bib0031) 2009; 54 Yin, Yuh (bib0025) 1989 Featherstone (10.1016/j.mechmachtheory.2019.103589_bib0007) 2000 Gunawardana (10.1016/j.mechmachtheory.2019.103589_bib0013) 1999; 14 Featherstone (10.1016/j.mechmachtheory.2019.103589_bib0011) 2005; 24 Tomei (10.1016/j.mechmachtheory.2019.103589_bib0015) 1991; 7 Mulero-Martinez (10.1016/j.mechmachtheory.2019.103589_bib0020) 2007; 18 Lipp (10.1016/j.mechmachtheory.2019.103589_bib0023) 2014; 87 Kelly (10.1016/j.mechmachtheory.2019.103589_bib0014) 1993; 9 Sciavicco (10.1016/j.mechmachtheory.2019.103589_bib0001) 1995; 10 Reynoso-Mora (10.1016/j.mechmachtheory.2019.103589_bib0030) 2016; 37 Cervantes (10.1016/j.mechmachtheory.2019.103589_bib0017) 2001; 42 LaValle (10.1016/j.mechmachtheory.2019.103589_bib0027) 2006 10.1016/j.mechmachtheory.2019.103589_bib0006 Ortega (10.1016/j.mechmachtheory.2019.103589_bib0019) 1995; 40 Siciliano (10.1016/j.mechmachtheory.2019.103589_bib0021) 2010 Nagy (10.1016/j.mechmachtheory.2019.103589_bib0024) 2019 Verscheure (10.1016/j.mechmachtheory.2019.103589_bib0031) 2009; 54 Featherstone (10.1016/j.mechmachtheory.2019.103589_bib0009) 1999; 18 Liu (10.1016/j.mechmachtheory.2019.103589_bib0003) 2013; 7 Pfeiffer (10.1016/j.mechmachtheory.2019.103589_bib0022) 1987; 3 Craig (10.1016/j.mechmachtheory.2019.103589_bib0029) 2005; vol. 3 Alvarez-Ramirez (10.1016/j.mechmachtheory.2019.103589_bib0016) 2000; 41 Luh (10.1016/j.mechmachtheory.2019.103589_bib0008) 1980; 102 Lynch (10.1016/j.mechmachtheory.2019.103589_bib0026) 2017 Misner (10.1016/j.mechmachtheory.2019.103589_bib0002) 1973 Qu (10.1016/j.mechmachtheory.2019.103589_bib0018) 1991; 36 Neuman (10.1016/j.mechmachtheory.2019.103589_bib0004) 1987; 4 Featherstone (10.1016/j.mechmachtheory.2019.103589_bib0010) 1999; 18 Safeea (10.1016/j.mechmachtheory.2019.103589_bib0012) 2018 Yin (10.1016/j.mechmachtheory.2019.103589_bib0025) 1989 Siciliano (10.1016/j.mechmachtheory.2019.103589_bib0028) 2016 Khalil (10.1016/j.mechmachtheory.2019.103589_bib0005) 2010 |
| References_xml | – volume: 7 start-page: 565 year: 1991 end-page: 570 ident: bib0015 article-title: Adaptive PD controller for robot manipulators publication-title: IEEE Trans. Rob. Autom. – start-page: 826 year: 2000 end-page: 834 ident: bib0007 article-title: Robot dynamics: equations and algorithms publication-title: ICRA – volume: 18 start-page: 876 year: 1999 end-page: 892 ident: bib0010 article-title: A divide-and-conquer articulated-body algorithm for parallel o (log (n)) calculation of rigid-body dynamics. Part 2: trees, loops, and accuracy publication-title: Int. J. Rob. Res. – volume: 7 start-page: 921 year: 2013 end-page: 935 ident: bib0003 article-title: A survey of underactuated mechanical systems publication-title: IET Control Theory Appl. – year: 2010 ident: bib0021 article-title: Robotics: Modelling, Planning and Control – reference: H. Hoifodt, Dynamic modeling and simulation of robot manipulators: the newton-euler formulation (2011). – volume: 40 start-page: 1432 year: 1995 end-page: 1436 ident: bib0019 article-title: A semiglobally stable output feedback PI/sup 2/D regulator for robot manipulators publication-title: IEEE Trans. Autom. Control – volume: 9 start-page: 117 year: 1993 end-page: 119 ident: bib0014 article-title: Comments on adaptive pd controller for robot manipulators publication-title: IEEE Trans. Rob. Autom. – start-page: 1812 year: 1989 end-page: 1817 ident: bib0025 article-title: An efficient algorithm for automatic generation of manipulator dynamic equations publication-title: Robotics and Automation, 1989. Proceedings., 1989 IEEE International Conference on – volume: 36 start-page: 1081 year: 1991 end-page: 1084 ident: bib0018 article-title: Robust tracking control of robots by a linear feedback law publication-title: IEEE Trans. Autom. Control – year: 2006 ident: bib0027 article-title: Planning Algorithms – volume: 54 start-page: 2318 year: 2009 end-page: 2327 ident: bib0031 article-title: Time-Optimal Path Tracking for Robots: A Convex Optimization Approach publication-title: IEEE Trans. Autom. Control – year: 2010 ident: bib0005 article-title: Dynamic modeling of robots using recursive newton-euler techniques publication-title: ICINCO2010 – year: 1973 ident: bib0002 article-title: Gravitation – volume: 102 start-page: 69 year: 1980 end-page: 76 ident: bib0008 article-title: On-line computational scheme for mechanical manipulators publication-title: J. Dyn. Syst. Meas.Control – volume: 18 start-page: 867 year: 1999 end-page: 875 ident: bib0009 article-title: A divide-and-conquer articulated-body algorithm for parallel o (log (n)) calculation of rigid-body dynamics. Part 1: basic algorithm publication-title: Int. J. Rob. Res. – year: 2019 ident: bib0024 article-title: Non-convex time-optimal trajectory planning for robot manipulators publication-title: J. Dyn. Syst. Meas.Control – volume: 42 start-page: 37 year: 2001 end-page: 46 ident: bib0017 article-title: On the PID tracking control of robot manipulators publication-title: Syst. Control Lett. – volume: vol. 3 year: 2005 ident: bib0029 article-title: Introduction to Robotics: Mechanics and Control – volume: 4 start-page: 743 year: 1987 end-page: 769 ident: bib0004 article-title: Symbolically efficient formulations for computational robot dynamics publication-title: J. Rob. Syst. – volume: 87 start-page: 1297 year: 2014 end-page: 1311 ident: bib0023 article-title: Minimum-time speed optimisation over a fixed path publication-title: International Journal of Control – start-page: 5614 year: 2018 end-page: 5619 ident: bib0012 article-title: Reducing the computational complexity of mass-matrix calculation for high DOF robots publication-title: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) – volume: 10 start-page: 317 year: 1995 end-page: 334 ident: bib0001 article-title: Lagrange and newton-euler dynamic modeling of a gear-driven robot manipulator with inclusion of motor inertia effects publication-title: Adv. Rob. – volume: 14 start-page: 45 year: 1999 end-page: 53 ident: bib0013 article-title: On the uniform boundedness of the coriolis/centrifugal terms in the robot equations of motion publication-title: Int. J. Rob. Autom. – volume: 24 start-page: 487 year: 2005 end-page: 500 ident: bib0011 article-title: Efficient factorization of the joint-space inertia matrix for branched kinematic trees publication-title: Int. J. Rob. Res. – volume: 37 start-page: 1263 year: 2016 end-page: 1281 ident: bib0030 article-title: A convex relaxation for the time-optimal trajectory planning of robotic manipulators along predetermined geometric paths publication-title: Optim. Control Appl. Methods – volume: 18 start-page: 865 year: 2007 end-page: 879 ident: bib0020 article-title: An improved dynamic neurocontroller based on Christoffel symbols publication-title: IEEE Trans. Neural Netw. – year: 2017 ident: bib0026 article-title: Modern Robotics: Mechanics, Planning, and Control – volume: 3 start-page: 115 year: 1987 end-page: 123 ident: bib0022 article-title: A concept for manipulator trajectory planning publication-title: IEEE J. Rob. Autom. – volume: 41 start-page: 73 year: 2000 end-page: 83 ident: bib0016 article-title: PID regulation of robot manipulators: stability and performance publication-title: Syst. Control Lett. – year: 2016 ident: bib0028 article-title: Springer Handbook of Robotics – volume: 24 start-page: 487 issue: 6 year: 2005 ident: 10.1016/j.mechmachtheory.2019.103589_bib0011 article-title: Efficient factorization of the joint-space inertia matrix for branched kinematic trees publication-title: Int. J. Rob. Res. doi: 10.1177/0278364905054928 – volume: 54 start-page: 2318 issue: 10 year: 2009 ident: 10.1016/j.mechmachtheory.2019.103589_bib0031 article-title: Time-Optimal Path Tracking for Robots: A Convex Optimization Approach publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.2009.2028959 – start-page: 826 year: 2000 ident: 10.1016/j.mechmachtheory.2019.103589_bib0007 article-title: Robot dynamics: equations and algorithms – volume: 36 start-page: 1081 issue: 9 year: 1991 ident: 10.1016/j.mechmachtheory.2019.103589_bib0018 article-title: Robust tracking control of robots by a linear feedback law publication-title: IEEE Trans. Autom. Control doi: 10.1109/9.83543 – volume: 4 start-page: 743 issue: 6 year: 1987 ident: 10.1016/j.mechmachtheory.2019.103589_bib0004 article-title: Symbolically efficient formulations for computational robot dynamics publication-title: J. Rob. Syst. doi: 10.1002/rob.4620040604 – volume: 7 start-page: 565 issue: 4 year: 1991 ident: 10.1016/j.mechmachtheory.2019.103589_bib0015 article-title: Adaptive PD controller for robot manipulators publication-title: IEEE Trans. Rob. Autom. doi: 10.1109/70.86088 – ident: 10.1016/j.mechmachtheory.2019.103589_bib0006 – year: 2010 ident: 10.1016/j.mechmachtheory.2019.103589_bib0005 article-title: Dynamic modeling of robots using recursive newton-euler techniques – volume: 18 start-page: 876 issue: 9 year: 1999 ident: 10.1016/j.mechmachtheory.2019.103589_bib0010 article-title: A divide-and-conquer articulated-body algorithm for parallel o (log (n)) calculation of rigid-body dynamics. Part 2: trees, loops, and accuracy publication-title: Int. J. Rob. Res. doi: 10.1177/02783649922066628 – volume: 9 start-page: 117 issue: 1 year: 1993 ident: 10.1016/j.mechmachtheory.2019.103589_bib0014 article-title: Comments on adaptive pd controller for robot manipulators publication-title: IEEE Trans. Rob. Autom. doi: 10.1109/70.210803 – start-page: 5614 year: 2018 ident: 10.1016/j.mechmachtheory.2019.103589_bib0012 article-title: Reducing the computational complexity of mass-matrix calculation for high DOF robots – volume: 41 start-page: 73 issue: 2 year: 2000 ident: 10.1016/j.mechmachtheory.2019.103589_bib0016 article-title: PID regulation of robot manipulators: stability and performance publication-title: Syst. Control Lett. doi: 10.1016/S0167-6911(00)00038-4 – start-page: 1812 year: 1989 ident: 10.1016/j.mechmachtheory.2019.103589_bib0025 article-title: An efficient algorithm for automatic generation of manipulator dynamic equations – year: 2006 ident: 10.1016/j.mechmachtheory.2019.103589_bib0027 – volume: 14 start-page: 45 issue: 2 year: 1999 ident: 10.1016/j.mechmachtheory.2019.103589_bib0013 article-title: On the uniform boundedness of the coriolis/centrifugal terms in the robot equations of motion publication-title: Int. J. Rob. Autom. – volume: vol. 3 year: 2005 ident: 10.1016/j.mechmachtheory.2019.103589_bib0029 – year: 1973 ident: 10.1016/j.mechmachtheory.2019.103589_bib0002 – volume: 18 start-page: 865 issue: 3 year: 2007 ident: 10.1016/j.mechmachtheory.2019.103589_bib0020 article-title: An improved dynamic neurocontroller based on Christoffel symbols publication-title: IEEE Trans. Neural Netw. doi: 10.1109/TNN.2007.894070 – volume: 3 start-page: 115 issue: 2 year: 1987 ident: 10.1016/j.mechmachtheory.2019.103589_bib0022 article-title: A concept for manipulator trajectory planning publication-title: IEEE J. Rob. Autom. doi: 10.1109/JRA.1987.1087090 – year: 2016 ident: 10.1016/j.mechmachtheory.2019.103589_bib0028 doi: 10.1007/978-3-319-32552-1 – volume: 87 start-page: 1297 issue: 6 year: 2014 ident: 10.1016/j.mechmachtheory.2019.103589_bib0023 article-title: Minimum-time speed optimisation over a fixed path publication-title: International Journal of Control doi: 10.1080/00207179.2013.875224 – volume: 37 start-page: 1263 issue: 6 year: 2016 ident: 10.1016/j.mechmachtheory.2019.103589_bib0030 article-title: A convex relaxation for the time-optimal trajectory planning of robotic manipulators along predetermined geometric paths publication-title: Optim. Control Appl. Methods doi: 10.1002/oca.2234 – volume: 7 start-page: 921 issue: 7 year: 2013 ident: 10.1016/j.mechmachtheory.2019.103589_bib0003 article-title: A survey of underactuated mechanical systems publication-title: IET Control Theory Appl. doi: 10.1049/iet-cta.2012.0505 – volume: 40 start-page: 1432 issue: 8 year: 1995 ident: 10.1016/j.mechmachtheory.2019.103589_bib0019 article-title: A semiglobally stable output feedback PI/sup 2/D regulator for robot manipulators publication-title: IEEE Trans. Autom. Control doi: 10.1109/9.402235 – year: 2010 ident: 10.1016/j.mechmachtheory.2019.103589_bib0021 – volume: 10 start-page: 317 issue: 3 year: 1995 ident: 10.1016/j.mechmachtheory.2019.103589_bib0001 article-title: Lagrange and newton-euler dynamic modeling of a gear-driven robot manipulator with inclusion of motor inertia effects publication-title: Adv. Rob. doi: 10.1163/156855395X00427 – year: 2017 ident: 10.1016/j.mechmachtheory.2019.103589_bib0026 – volume: 102 start-page: 69 issue: 2 year: 1980 ident: 10.1016/j.mechmachtheory.2019.103589_bib0008 article-title: On-line computational scheme for mechanical manipulators publication-title: J. Dyn. Syst. Meas.Control doi: 10.1115/1.3149599 – volume: 18 start-page: 867 issue: 9 year: 1999 ident: 10.1016/j.mechmachtheory.2019.103589_bib0009 article-title: A divide-and-conquer articulated-body algorithm for parallel o (log (n)) calculation of rigid-body dynamics. Part 1: basic algorithm publication-title: Int. J. Rob. Res. doi: 10.1177/02783649922066619 – volume: 42 start-page: 37 issue: 1 year: 2001 ident: 10.1016/j.mechmachtheory.2019.103589_bib0017 article-title: On the PID tracking control of robot manipulators publication-title: Syst. 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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