A New Lagrangian Formulation of Dynamics for Robot Manipulators

Abstract

In this paper, a new Lagrangian formulation of dynamics for robot manipulators is developed. The formulation results in well structured form equations of motion for robot manipulators. The equations are an explicit set of closed form second order highly nonlinear and coupling differential equations, which can be used for both the design of the control system (or dynamic simulation) and the computation of the joint generalized forces/torques. The mathematical operations of the formulation are so few that it is possible to realize the computation of the Lagrangian dynamics for robot manipulators in real-time on a micro/mini-computer. For a robot manipulator with n degrees-of-freedom, the number of operations of the formulation is at most (6n2 + 107n − 81) multiplications and (4n2 + 102n − 86) additions; for n = 6, about 780 multiplications and 670 additions.