Robot dynamics: A recursive algorithm for efficient calculation of Christoffel symbols. (December 2019)

• Record Type: Journal Article
• Authors: Safeea, Mohammad; Neto, Pedro; Bearee, Richard
• Is Part Of: Mechanism and machine theory. Volume 142(2019)
• Publication Date: 2019-12
• Subjects: Dynamicss -- Christoffel symbols -- Recursive algorithms; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2019.103589
• Languages: English
• ISSNs: 0094-114X

Abstract

Highlights: 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. 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.