An efficient Lagrangian formulation of manipulator dynamics has been developed. The efficiency derives from recurrence relations for the velocities, accelerations, and generalized forces. The number of additions and multiplications varies linearly with the number of joints, as opposed to past Lagrangian dynamics formulations with an n4 dependence. With this formulation it should be possible in principle to compute the Lagrangian dynamics in real time. The computational complexities of this and other dynamics formulations including recent Newton-Euler formulations and tabular formulations are compared. It is concluded that recursive formulations based either on the Lagrangian or Newton-Euler dynamics offer the best method of dynamics calculation.
