Recursive algorithm for calculating Christoffel symbols efficiently

Christoffel symbols are very important in robotics. 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 literature, Christoffel symbols are calculated from the Lagrangian formulation using an off-line generated symbolic formula. In this study we present an efficient recursive nonsymbolic method where Christoffel symbols are calculated based on the robot’s transformation matrices and inertial parameters. 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. Index Terms — Dynamics, Christoffel symbols, recursive algorithms