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

Archive ouverte : Article de revue

Safeea, Mohammad | Neto, Pedro | Bearee, Richard

Edité par HAL CCSD ; Elsevier

International audience. 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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