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Robot dynamics: A recursive algorithm for efficient calculation of Christoffel symbols

Article dans une revue avec comité de lecture
Author
SAFEEA, Mohammad
164378 Faculty of Sciences and Technology [Coimbra]
NETO, Pedro
164378 Faculty of Sciences and Technology [Coimbra]
ccBEAREE, Richard
13338 Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697 [L2EP]
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]

URI
http://hdl.handle.net/10985/17237
DOI
10.1016/j.mechmachtheory.2019.103589
Date
2019
Journal
Mechanism and Machine Theory

Abstract

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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